CA1239983A - Microprocessor controlled d.c. motor for controlling printing means - Google Patents

Abstract

MICROPROCESSOR CONTROLLED D.C. MOTOR
FOR CONTROLLING PRINTING MEANS

ABSTRACT
An improvement in combination with apparatus including rotary means, wherein the rotary means includes a periphery having indicia printing means and is adapted for feeding a sheet in a path of travel. The improvement comprises: a first device for sensing a time interval during which a sheet having a leading edge is linearly displaced a predetermined distance in the path of travel; a d.c. motor coupled to the rotary mean for rotation of the rotary means;
a second device for sensing angular displacement of the rotary means and a computer coupled to the first and second sensing devices and to the d.c. motor; wherein the computer responds to the first sensing device for providing respective amounts representative of desired angular displacements of the rotary means during successive sampling time periods, responds to the second sensing device for providing respective amounts representative of actual angular displacements of the rotary means during successive sampling time periods, compensates for the difference between desired and actual angular displacements and generates a d.c. motor control signal for controlling rotation of the motor to cause the linear displacement of the indicia printing means to initially engage the sheet in the path of travel a predetermined marginal distance from the leading edge of the sheet.

Description

~IIC:ROPROCE:SSOR CON~OLLE:D D . C . ~qOTOR
P~)R CONl'ROLLING PRIl~TING PIEANS

BACKGROUND OF THE INVENTION
The present invention is generally concerned with apparatus including sheet feeding and printing means, for example, a postage meter including a rotary sheet feeding and printing drum, and improvements therein.
In ~.S. Patent No. 2,934,009 issued April 26, 1960 to Bach, et al. and assigned to the assignee of the present invention there is described a postage meter which includes a drive mechanism connected by means of a drive train to a postage meter drum. The drive mechanism includes a single revolution clutch for rotating the drum from a home position and into engagement with a letter ~ed to the drum. The drum prints a postage value on the letter while feeding the same downstream beneath the drum as the drum returns to the home position. Each revolution of the single revolution clutch and thus the drum, is initiated by the letter engaging a trip lever to release the helical spring of the single revolution clutch. The velosity versus time profile of the peripherary of a drum driven by the clutch approximates a trapezoidal configuration, having acceleration, constant velocity and deceleration portions, fixed by the particular clutch and drive train used in the application. This being the case, the throughput rate of any mailing machine associated with the meter is dictated by the cycling speed of the postage meter rather than by the sp~ed with which the individual mailpieces are fed to the postage meter. Further, although ~3~ 3 the single revolution clutch structure has served as the workhorse of the industry for many years it has long been recognized that it is a complex mechanism which is relatively expensive to construct and maintain ? does not precisely follow the ideal trapezoidal velocity vs. time motion profile which is preferred for drum motion, tends to be unreliable in high volume applications, and is noisy and thus irritating to customers.
Accordingly, an object of an aspect of the invention is to replace the postage meter drum drive mechanism of the prior art with the combination of a D.C. motor and a computer, and program the computer for causing the D.C. motor to drive the drum in accordance with an ideal trapezoidal-shaped velocity versus time profile which is a function of the input velocity of a mailpiece; and An object of an aspect of the invention is to replace the trip lever as the drive initiating device and utilize in its place a pair of spaced apart sensing devices in the path of travel of a mailpiece fed to the postage meter, and program the computer to calculate the input velocity of a mailpiece, based upon the time taken for the mailpiece to traverse the distance between the sensing devices, and adjust the time delay and acceleration of the drum before arrival of the mailpiece at a position at which drum rotation is commenced to cause the drum to timely engage the leading edge of the mailpiece.
SUMMARY OF THE INVENTION
Various aspects of the invention are as follows:
In a system for controlling rotary means having a periphery, wherein the periphery includes indicia printing means, and wherein the periphery is adapted for feeding a sheet having a leading edge in a path of travel, an improvement in the system comprising:
a) first means for sensing a time interval duriny which the leading edge of the sheet is linearly displaced a prede-termined distance in the path of travel;

~,:!. ' 2 ~3~
b) a d.c. motor coupled to -the rotary means for rotation thereof;
c) second means for sensing angular displacement of the rotary means and, d) computer means coupled to the first and second sensing means and to the d.c. motor, the computer means comprlsing:
i) means for providinq successive sampling time periods;
ii) means responsive to the first sensing means for providing respective counts representative of desired angular displacements of the rotary means during successive sampling time periods, iii) means responsive to the second sensing means for providing respective counts representative of actual angular displacements of the rotary means during successive sampling time periods, and iv) means for compensating for the difference between desired and actual counts and generating a d.c.
motor control signal for controlling rotation of the motor to cause the indicia printing means to initially engage the sheet in the path of travel a predetermined marginal distance from the leading edge of the sheet.
In a system for controlling rotary means, wherein the rotary means includes a periphery having indicia printing means and is constructed and arranged for feeding a sheet having a leading edge in a path of travel, a process for controlling rotation of the rotary means, the process comprising:
a~ providing means for providing successive sampling time periods;
b) sensing a time interval during which the leading edge of the sheet is linearly displaced a predetermined distance in the path of travel and providing counts representative of respective desired angular displacements of the rotary means during successive sampling time periods;
c) providing a d.c. motor for rotating the rotary means;

~, ~ ., :~23~313 d) sensing angular displacement of the rotary means and providing counts representative of respective actual angular displacements of the rotary means during successive sampling time periods; and e) digitally compensating for the difference ~etween desired and actual counts and generating a motor control signal for controlling rotation of the rotary means to cause the indicia printing means to initially engage the sheet in the path of travel a predetermined distance from the leading edge of the sheet.

-3a->i B~IEF_ DESCRIPTION OF THE DR~WINGS_ As shown in the drawings wherein like reference numerals designate like or corresponding parts throughout the several views:
Figure 1 is a schematic view of a postage meter mounted on mailing machine in accordance with the invention;
Figure 2 is a schematic view of the mailing machine of Figure 1, showing the location of the mailpiece sensors relative to the postage meter drum;
Figure 3 shows the relationship between ~he position of a sheet and the postage meter drum as a function of time, and an ideal velocity versus time profile of the periphery of the drum;
Figure 4 is a perspective view of the quadrature encoder mounted on a D.C. motor drive shaft;
Figure 5 shows the output signals from the quadrature encoder of Fig. 4 for clockwise and counter-clockwise rotation of the D.C. motor drive shaft;
Figure 6 is a schematic diagram of a preferred counting circuit for providing an eight bit wide digital signal for the computer which numerically represents the direction of rotation, and angular displacement, of the motor drive shaft, and thus the drum, from its home position;
Figure 7 shows a power amplifier circuit for coupling the computer to the D.C. motor.

~z~

Figure 8 is a truth table showing the status of the transistors in the power amplifying circuit fox clockwise and counte~-clockwise rotation of the D.C. motor;
Figure 9 shows the relationship between the encoder output signals for various D.C. motor duty cycles;
Figure 10 shows a closed-loop servo system including the D.C. motor and computer;
Figure 11 is a block diagram portraying the laplace transform equations of the closed-loop servo system shown in Fig. 10;
Figure 12 shows the equations for calculating the overall gain of the closed loop servo system of Fig. 10 before (Fig. 2a) and after (Fig. 2b) including a gain factor corresponding to the system friction at motor start up;
Figure 13 is a bode diagram including plots for the closed loop servo system before and after compensation to provide for system stability and maximization of the system's bandwidth;
Figure 14 shows the equation for calculating, in the frequency domain, the value of the system compensator;
Figure 15 shows the equation for calculating the damping factor, overshoot and settling time of the servo controlled system;
Figure 16 shows the equation for the laplace operator expressed in terms of the Z-transform operator;
Figure 17 shows the equation for calculating the value of the system compensator in the position domain;

Figure 18 shows the equations for converting the system compensator of Fig. 17 to the position domain;
Figure 19 shows the equation of the output of the system compensator in the time domain;
Figure 20 is a block diagram of a preferred microprocessor for use in controlling the D.C. Motor;
Figure 21 (including Figs. 21a, 21b and 21c) shows the time intervals during which the motor control signal and its separable components are calculated to permit early application of the signal to the motor;
Figure 22 (including Figs. 22a and 22b) is a block diagram of the computer according to the inventionj and Figure 23 (including Figs. 23a-1, 23a-2, 23b and 23c) shows the flow charts portraying the processing steps of the computer.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
As shown in Fig. 1, the apparatus in which the invention may be incorporated generally includes an electronic postage meter 10 which is suitably removably mounted on a conventional mailing machine 12, so as to form therewith a slot 14 (Fig. 2) through which sheets, including mailpieces 16, ~uch as envelopes, cards or other sheet-like materials, may be fed in a downstream path of travel 18.
The postage meter 10 ~Fig. 1) insludes a keyboard 30 and display 32. The keyboard 30 includes a plurality of numeric keys, labeled 0-9 inclusive, a clear key, labeled "c"
and a decimal point key, labeled n . n ~ for selecting postage _ ~ _ :~2~

values to be entered; a set postage key, labeled '511, for entering selected postage values; and an arithmetic function key, labeled "-", for adding subsequently selected charges tsuch as special delivery costs) to a previously selected postage value before entry of the total value. In addition, there is provided a plurality of display keys, designated 34, each of which are provided with labels well known in the art for identifying information stored in the meter 10, and shown on the display 32 in response to depression of the particular key 34, such as the "postage used", "postage unused", "control sum", "piece count", "batch value" and "batch count"
values. A more detailed description of the keys of the keyboard 30 and the display 32, and their respective functions may be found in U.S. Patent NG. 4,283,721 issued ~ugust 11, 1981 to Eckert, et alO and assigned to the assignee of the present inventionO
In addition, the meter 10 (Fig. 1) includes a casing 36l on which the keyboard 30 and display 32 are conventionally mounted, and which is adapted by well kno~n means for carrying a cyclically operable, rotary, postage printing drum 38. The drum 38 (Fig. 2) is conventionally constructed and arranged for feeding the respective mailpieces 16 in the path of travel 18, which extends beneath the drum 38, and for printing entered postage on the upwardly disposed surface of each mailpiece 16. For postage value selecting purposes, the meter 10 (Fig. 1) also includes a conventional postage value selection mechanism 40, for example, of the type shown in U.S. Patent No. 4,2B7,825 issued September 8, 1981 to Eckert, et al. and assigned to the assignee of the present invention. The mechanism 40 which is operably electrically coupled via the postage meter's computer 41 to the keyboard 30 and display 32, includes a first stepper motor 42 for selecting any one of a plurality of racks 43, associated on a one for one basis with each of the print wheels 44, and a second stepper motor 45 for actuating each selected rack 43 for positioning the appropriate printing element of the associated print wheel 44. The rack selection stepper motor 42, which is referred to by skilled artisans as a bank selector motor, is appropriately energized via power lines 46 from the computer 41 for selecting the appropriate rack; and the rack actuating stepper motor 45, which is referred to by skilled artisans as a digit selector motor, is appropriately energized via power lines 47 from the computer 41 to move the selected rack for ~electing the appropriate digit element of the associated print wheel 44. ~ more detailed description of the value selection mechanism 40 may be found in the aforesaid U.S.
Patent No. 4,287,825.
The computer 41 for the postage meter 10 generally comprises a conventional, microcomputer system having a plurality of microcomputer modules including a control or keyboard and display module, 41a, an accounting module 41b and a printing module 41c. The control module 41a i5 both operably electrically connected to the accounting module 41b and adapted to be operably electrically connected to an external device via respective two-way serial communications ' ~3~ 3 channels, and the accounting module 41b is operably electrically connected to the printing module 41c via a corresponding tw~-way serial communication channel. In general~ each of the modules 41a, 41b and 41c includes a dedicated microprocessor 41d, 41e or 41f, respectively, having a separately controlled clock and programs. And two-way communications are conducted via the respective serial communication channels utilizing the echoplex communication discipline, wherein communications are in the form of serially transmitted single byte header-only messa~es, consisting of ten bits including a start bit followed by an B
bit byte which is in turn followed by a stop bit, or in the form of a multi-byte message consisting of a header and one or more additional bytes of information. Further, all transmitted messages are followed by a no error pulse if the message was received error free. In operation, each of the modules 41a, 41b and 41c is capable of processing data independently and asynchronously of the other. In addition, to allow for compatibility between the postage meter 10 and any external apparatus, all operational data transmitted to, from and between each of the three modules 41a, 41b and 41c, and all stored operator information, is accessible to the external device via the two~way communication channel, as a result of which the external apparatus ~if any) may be adapted to have complete control of the postage meter 10 as wPll as access to all current operational information in the postage meter 10. In additionl the flow of messages to, from and between the three internal modules 41a, 41b and 41c is in _ 9 _ ;~2~ 33 a predetermined, hierarchical direction. For example, any command message from the control module 41a is communicated to the acc~unting module 41b, where it is processed either for local action in the accounting module 41b and/or as a command message for the printing module 41c. On the other hand, any message fr~m the printing module 41c is communicated to the accounting module 41b where it is either used as internal information or merged with additional data and communicated to the control module 41c. ~nd, any message from the accounting module 41b is initially directed to the printing module 41c or to the control module 41a. A more detailed description of the various prior art modules 41a, 41b and 41c, and various modifications thereof, may be found in U.S. Patent Nos. 4,280,180; 4,280,179; 4 r 283,721 and 4,301,507; each of which patents is assigned to the assignee of the present invention.
The mailing machine 12 (Fig. 2), which has a casing 19, ineludes a A.C. power supply 20 which is adapted by means of a power line 22 to be connected to a local source of supply of A.C. power via a normally open main power switch ?4 which may be closed by the operator. Upon such closure, the mailing machine's D.C. power supply 26 is energized via the power line 28. In addition, the mailing machine 12 includes a conventional belt-type conveyor 49, driven by an A.C. motor 50, which is connected for energization from the A.C. power supply 20 via a conventional, normally open solid state, A.C.
motor, relay 52, which is timely energized by a computer 500 for closing the relay 52. Upon such closure the A.C.

motor 50 drives the conveyc~r 49 for feeding mailpieces 16 to the drum 38. To facilitate operatox control of the switch 24, the ~nailing rnachine preferably includes a keyboard ~3 having a "start`' key 53a and a "stop" key 53b, which are conventionally coupled to the main power switch 24 to permit the operator to selectively close and open the switch 24.
Assuming the computer 500 has tirnely energized the relay 52, the A.C. motor 50 is energized from the ~.C. power supply 20.
Whereupon the conveyor 49 transports the individual mailpieces 16, at a velocity corresponding to the angular velocity of the motor 50, in the path of travel 18 to the postage pr i nt i ng pl aten 5 ~ .
According to the invention, the machine 12 includes f irst and second sensing devices respectively designated 56 and 58, which are spaced apart from each other a predetermined distance dl, i.e., the distance between points and B in the path of travel lB. Pre~erably, each of khe sensing devices 56 and 58, is an electr~optical device which is suitably electrically coupled to the computer 500; sensing device 56 being connected via corr~nunication line 60 and sensing device 58 being connected via cornmunication line 62.
The sensing devices 56, 58 respectively respond to the arrival of a mailpiece 16 at points A and B by providing a signal to the computer 500 on cornrnunication line 60 from sens.ing device 56 and on cornmunication line 62 rom sensing device 58. Thus, the rate of movement or velocity Vl of any mailpiecè 16 may be calculated by counting the elapsed time tv (Fig. 3 ) between arrivals of the mailpiece 16 at points A
-- :Ll --3~3 and B, and dividing the distance ~1~ by the elapsed time tv.
To that end, the computer 500 is programmed for continuously polling the communications lines 60 and 62 each time instant Tn at the end of a predetermined sampling time period, T, preferably T=l millisecond, and to commence counting the number of time instants Tn when the leading edge of ~ given mailpiece 16 is detected at point A, as evidenced by a transition signal on communication line 60, and to end counting the time instants Tn when the given mailpiece 16 is detected at point B, as evidenced by a transition signal on communication line 62. Since the distance dl, is a mechanical constant of the mailing machine 12, the velocity of the mailpiece may be expressed in terms of the total number Nt Of time instants Tn which elapse as the given mailpiece traverses the distance dl. For example, assuming a maximum velocity of 61 inches per second, dl=2.75 inches and T=l millisecond; the total number Nt of elapsed time instants Tn may be found by dividing dl=2.75 inches by Vl-61 inches per second to obtain Nt=45, i.e., the total number of time instants Tn which elapse between arrivals of the mailpiece at points A and B. Thus, the number Nt=45 corresponds to and is representative of a mailpiece velocity of Vl=61 inches per second.
Assuming normal operation of the transport system and calculation of the value of Vl having been made, the time delay td (Fig. 3) before arrival of the mailpiece 16 at point C may be calculated by dividing the distance d2 between points ~ and C by the mailpiece's velocity Vl, provided the ~`

distance d2 is known. Since the integral of the initial,triangularly-shaped, portion of the velocity versus time profile is equal to one-half of the value of the pr~duct of Ta and Vl, and is equal to the arc d3 described ~y point E on the drum 38, as the drum 38 is rotated counter-clockwise to point D, the distance between points C and D is equal to twice the arcuate distance d3. Accordingly, d2 may be conventionally calculated, as may be the time delay ~d for the maximum throughput velocity. Assuming rotation of the drum 38 is commenced at the end of the time delay td and the drum 38 is linearly accelerated to the velocity Vl to match that of the mailpiece 16 in the time interval Ta during which point E on the drum 38 arcuately traverses the distance d3 to point D, Ta may be conventionally calculated. In addition, assuming commencement of rotation at the end of the time delay td and that the drum 38 ls linearly accelerated to the velocity Vl during the time interval Ta, the mailpiece 16 will arrive at point D coincident with the rotation of point E of the outer periphery 73 the drum 38 to point D, with the result that the leading edge 73a vf the drum's outer periphery 73, which edge 73a extends transverse to the path of travel 18 of the mailpiece 16, will engage substantially the leading edge of the mailpiece 16 for feeding purposes and the indicia printing portion 73b of the periphery 73 will be marginally spaced from the leading edge of the mailpiece 16 by a distance d4 which is equal to the circumferential distance between points E and F on the drum 38. Since the ciroumferential distance d5 on the drum 38 between points E
and G is fixed, the time interval Tc during which the drum 38 is rotated at the constant velocity Vl may also be calculated. When point G ~n the drum 38 is rotated out of engagement with the mailpiece 16, the drum 38 commences deceleration and continues to decelerate to rest during the time interval Td. The distance d6 which istraversed by point G, as the d~um 38 is r~tated to return point E to its original position of being spaced a distance d3 from point D, is fixed, and, Td may be chosen to provide a suitable deceleration rate for the drum, preferably less than Ta. In addition, a reasonable settling time interval Ts is preferably added to obtain the overall cycling time Tct of the drum 38 to allow for damping any overshoot of the drum 38 before commencing the next drum cycle. For a typical maximum drum cycle time period Tct of 234 milliseconds and a maximum mailpiece transport rate of 61 inches per second, typical values for the acceleration, constant velocity, deceleration and settling time intervals are Ta=37 milliseconds, TC=124 milliseconds, Td=24 milliseconds and Ts=234-185=49 milliseconds. Utili~ing these values, the required acceleration and deceleration values for the drum 38 during the time intervals Ta and Td may be conventionally calculated. In addition, since the integral of the velocity versus time profile i5 equal to the distance traversed by the circumference of the drum 38 during a single revolution of the drum 38, the desired position of the drum 38 at the end of any sampling time period of T=l millisecond may be calculated. For target ~elocities Vl which are less than the maximuJn throughput velocity, it is preferably assumed that integral of, and thus the area under, the velocity versus time profile remains constant, and equal to the area thereoE
at the maximum throughput velocity, to facilitate conventional calculation of the values of the time delay td, , ............................... .
~ ~ .

,~

the time intervals Ta, Tc and Td, and the acceleration anddeceleration values for each of such lesser velocities Vl.
For computer implementation purposes, the computer 500 is progra~med as hereinbefore discussed to continously poll the communication lines 60 and 62, from the sensing devices 56 and 58, respectively, each time interval Tn~ and count the time intervals Tn between arrivals of the mailpiece 16 at points A and B as evidenced by a transition signals on lines 60 or 62. Further, the computer 500 is programmed to calculate the current velocity of the mailpiece 16 in terms of the total number Nt of the counted time intervals Tn~
store the current velocity and, preferably, take an average of that velocity and at least the next previously calculated velocity (if any) to establish the target velocity Vl. In addition, it i5 preferable that precalculated values for the time delay td, acceleration and deceleration corresponding to each of a plurality of target velocities be stored in the memory of the computer 500 for fetching as needed after calculation of the particular target velocity. For marginally spacing the indicia a different predetermined distance from the leading edge of the sheet then would be provided due to the drum's periphery initially engaging the leading edge of the sheet, the value of td may be altered at the time of programming the computer to cause the indicia to initially engage the sheet a different predetermined marginal distance from the leading edge of the sheet. The velocity at any time "t" of the drum 38 may be expressed by adding to the original velocity VO each successive increment of the product of the acceleration and time during each time period of T=l mi llisecond, each successive increment of constant velocity and each successive increment of the product of the deceleration ~3~ 3 and ti~e during each time period T. Preferably, theacceleration and deceleration values are each stored in the form of an amount corresponding to a predetermined number of counts per millisecond square which are a function of the actual acceleration or deceleration value, as the case may be, and of the scale factor hereinafter discussed in connection with measuring the actual angular displacement of the motor drive shaft 122; whereby the computer 500 may timely calculate the desired angular displacement of the motor drive shaft 122 during any sampling time interval T.
In this connection it is noted that the summation of all such counts is representative of the de~ired linear displacement of the circumference of the drum 38, and thus of the desired velocity versus time profile of drum rotation for timely accelerating the drum 38 to the target velocity Vl, maintaining the drum velocity at Vl for feeding the partlcular mailpiece 16 and timely decelerating the drum 38 to rest.
The postage meter 10 (Fig. 1) additionally includes a conventional, rotatably mounted, shaft 74 on which the drum 38 is fixedly mounted, and a conventional drive gear 76, which is fixedly attached to the shaft for rotation of the shaft 74.
According to the invention, the mailing machine 12 (FigO 1) includes an idler shaft 80 which is conventionally journaled to the casing 19 for rotation, and, operably coupled to the shaft 80, a conventional home position encoder 82. The encoder 82 includes a conventional circularly-shaped disc 84, which is fixedly attached to the shaft B0 for rotation therewith, and an optical ~ensing device 86, which is operably coupled to the disc 84 for detecting an opening f , 88 formed therein and, upon such detection, signalling the computer 500. The machine 12, also includes an idler gear 90 which is fixedly attached to the shaft 80 for rotation therewith. Further, the machine 12 includes a D.C. motor 120, which is suitably attached to the casing 19 and has a drive shaft 122. The machine 12 also includes a pinion gear 124, which i5 fixedly attached to the drive shaft 122 for rotation by the shaft 122. The gear 124 is disposed in driving engagement with the idler gear 90. Accordi~gly, rotation of the motor drive shaft 122 in a given direction, results in the same direction of rotation of the drum drive shaft 76 and thus the drum 38. Preferably, the pinion gear 124 has one-fifth the nurnber of teeth as the drum drive gear 76, whereas the idler gear 90 and drum drive gear 76 each have the same number of teeth. With this arrangement, five complete revolutions of the motor drive shaft 122 effectuate one complete revolution of the drum 38, whereas each revolution of the gear 90 results in one revolution of the gear 76. Since there is a one-to-one relationship between revolutions; and thus incremental angular displacements, of the drum shaft 74 and idler shaft 90, the encoder disc 84 may be mounted on the idler shaft 90 such that the disc's opening 88 is aligned with the sensing device 86 when the drum 38 is disposed in its home position to provide for detection of the home position o the drum shaft 74~ and thus a position of the drum shaEt 74 from which incremental angular displacements may be counted.

For sensing actual incremental angular displace~ents of the mo~or drive shaft 122 (Fig. 1) from a home position, and thus incremental angular displacements of the drum 38 from its rest or home position as shown in Fig. 2, there is provided a quadrature encoder 126 (Fig. 1). The encoder 126 is preferably coupled to the motor drive shaft 122, rather than to the drum shaft 74, for providing higher mechanical stiffness between the armature of the d.c. motor 120 and th~
encoder 126 to avoid torsional resonance effects in the system. The encoder 126 includes a circularly-shaped disc 128, which is fixedly attached to the motor drive shaft 122 for operably connecting the encoder 126 to the motor 120.
The disc 128 (Fig. 4) which is otnerwise transparent to light, has a plurality of opayue lines 130 which are formed on the disc 1~8 at predetermined, equidistantly angularly-spaced, intervals along at least one of the dics's opposed major surfaces. Preferably the disc 128 includes one hundred and ninety-two lines 130 separated by a like number of transparent spaces 132. In addition, the encoder 126 includes an optical sensing device 134, which is conventionally attached to the casing 19 and disposed in operating relationship with respect to the disc 128, for serially detecting the presence of the respective opaque lines 130 as they successively pass two reference positions, for example, positions 136ra and 136rb, and for responding to such detection by providing two output signals, one on each of communications lines 136a and 136b, such as signal A tFig~
5) on line 136a and signal B on line 136b. Since the d.isc 3~2~

128 (Fig. 4) includes 192 lines 130 and the gear ratio of thedrum drive gear 76 (Fig. 1) to the motor pinion gear 124 is five-to-one, nine hundr2d and sixty signals A and B (Fig. 5) are provided on each of the communications lines 136a and 136b during five revolutions of ~he motor drive shaft 122, and thus, during each cycle of rotation of the drum 38.
Since the angular distance bet~een successive lines 130 (Fig.
4) is a constant, the time interval between successive leading edges (Fig. 5) of each signal A and B is inversely proportional to the actual velocity of rotation of the motor drive shaft (Fig. 1) and thus of the drum 38. The encoder 126 is conventionally constructed and arranged such that the respective reEerence positions 136a and 136b ~Fig. 4) are located with respect to the spacing between line 130 to provide signals ~ and B ~Fig. 5) which are 90 electrical degrees out of phase. Accordingly, if signal A lags signal B
by 90 (Fig. 5) the D.C. motor shaft 122 ~Fig. 1~, and thus the drum 38, is rotating clockwise, whereas if signal A leads signal B by 90 tFig. 5) the shaft 122 and drum 38 are both rotating counter-clockwise. Accordingly, the angular displacement in either direction of rotation of the drum 38 (Fig. 1) from its home position may be incrementally counted by counting the number of pulses A or B, (Fig. S) as the case may be, and accounting for the lagging or leading relationship o pulse A (Fig. 5) with re~pect to pulse B.
The quadrature encoder communication lines, 136a and 136b (Fig. 1), may be connected either directly to the computer 500 for pulse counting thereby or to the computer -- lg --~3~

500 via a conventional counting circuit 270 (Fig. 6), depending on whether or not the internal counting circuitry of the compute~ 500 is or is not available for such counting purposes in consideration of other design demands of the system in which the computer 500 is being used. Assuming connection to the computer 500 via a counting circuit 270, the aforesaid communications lines, 136a and 136b are preferably connected via terminals A and B, to the counting circuit 270.
In general, the counting circuit 270 (Fig. 6) utilizes the pulses A (Fig. 5) to generate a clock signal and apply the same to a conventional binary counter 274 (Fig. 6), and to generate an up or down count depending on the lagging or ~eading relationship of pulse ~ (Fig. 5) relative to pulse B
and apply the up or down count to the binary counter 274 (Fig. 6) for counting ~he~eby. More particularly, the pulses A and B (Fig. 5) which are applied to the counting circuit terminals A and B (Fig . 6) are respectively fed to Schmidt trigger inverters 276A and 276B. The output from the inverter 276A is fed directly to one input of an XOR gate 278 and additionally via an R-C delay circuit 280 and an inverter 282 to the other input of the XOR gate 278. The output pulses from the XOR gate 278, which acts as a pulse frequency doubler, is fed to a conventional one-shot multivibrator 284 which detects the trailing edge of each pulse from the XOR
gate 278 and outputs a clock pulse to the clock input CK of the binary counter 274 for each detected trailing edge. The output from the Schmidt trigger inverters 276A and 276B are ~;~3~

respecti~ly fed to a second XOR gate 286 which outputs a lowlogic level signal t~ero), or up-count, to the up-down pins U/D o~ the binary counter 274 or each output pulse A (Fig.
5) which lags an output pulses B by 90 electrical degrees.
On the other hand the XOR gate 286 (Fig. 6) outputs a high logic level (one) or down-count, to the up-down input pins of the binary counter 274 for each encoder output pulse A (Fig.
5) which leads an output pulse B by 90 electrical degrees.
Accordingly, the XOR gate 286 (Fig. 6) provides an output signal for each increment of angular displacement of the encoded shaft 122 (Fig. 1) and identifies the direction, i.e., clockwise or counter-clockwise, of rotation of the encoded shaft 122. The binary counter 274 (Fig. 6) counts the up and down count signals from the XOR gate 286 whenever any clock signal is received from the multivibrator 284, and updates the binary uutput signal 272 to reflect the count.
Accordingly, the counting circuit 270 converts the digital signals A and ~, which are representative of incremental angular displacements of the drive shaft 122 in either direction of rotation thereof, to an eight bit wide digital logic output signal 272 which corresponds to a summation count at any given time, of such displacements, multiplied by a factor of two, for use by the computer 500.
Since the angular displacement of the shaft 122 from its home position is proportional to the angular displacement of the drum 38 from its home position, the output signal 272 is a count which is proportional to the actual linear displacement of the outermost periphery of the drum 38 at the end of a given time period of rotation of the drum 38 from its home p~sition. For a typical postage meter drum 38, having a circumference, i.e., the arc described by the outermost periphery of the drum 38 in the course of revolution thereof, of 9.42 inches, which is connected to the motox drive shaft 122 via a mechanical transmission system having a 5:1 gear ratio between the motor 120 and drum 38, wherein the encoder disc 128 has 192 lines; the counting circuit 270 ~ill provide an output of 2 x 192 = 384 counts per revolution of the shaft 122, and 5 x 384 = 1920 counts per revolution of the drum 3S
which corresponds to 203.82 counts per inch of linear displacement of the periphery of the drum. Accordingly, the maximum mailpiece transport velocity of Vl = 61(10-3) inches per millisecond may be multiplied by a scale factor of 203.82 counts per inch to express the maximum transport velocity in terms of counts per millisecond, or, counts per sampling time period T where T=l millisecond; i.e., 61(10-3) inches per millisecond times 203.~2 counts per inch = 12.43 counts per sampling ~ime period T. Similarly, any other target velocity Vl, or any acceleration or decceleration value, may ~e e~pressed in terms of counts per sampling time interval T, or counts per square millisecond, as the case may be, by utilization of the aforesaid scale factor.
For energizing the D~C. motor 120 (Fig. 1) there i5 provided a power amplifying circuit 300. The power amplifying circuit 300 (Fig. 7) is conventionally operably connected to the motor terminals 302 and 304 via power lines 306 and 308 respectively. The power amplifying circuit 300 ~z~

preferably comprises a conventional, H-type, push-pull, control signal amplifier 301 having input leads ~, s, C and D, a plurality of optical-electrical isolator circuits 303 which are connecte~ on a one-for-one basis between the leads A-D and four output terminals of the computer 500 for coupling the control signals from the computer 500 to the input leads A, B, C, and D of the ~mplifier 301, and a plurality of conventional pull-up resistors 305 for coupling the respective leads A-D to the 5 volt source The amplifier 301 includes four conventional darlington~type, pre-amplifier drive circuits including NPN transistors Tl, T2, T3 and T4, and four, conventional, darlington-type power amplifier circuits including PNP transistors Ql, Q2, Q3 and ~4 which are respectively coupled on a one-for-one basis to the collectors of transistors Tl, T2; T3 and T4 for driving thereby. The optical-electrical isolator circuits 303 each include a light emitting diode Dl and a photo-responsive transistor T5. The cathodes of Dl are each connected to the 5 volt source, the emitters of T5 are each connected to ground and the collectors of T5 are each coupled, on a one-for-one basis, to the b~se of one of the transistors Tl, T2, T3 and T4. With respect to each of the opto-isolator circuits 303, when a low logic level signal is applied to the anode of D1, Dl conducts and illuminates the base of T5 thereby driving T5 into its conductive state; whereas when a high logic level signal is applied to the anode of Dl, Dl is non-conductive, as a result of which T5 is in its non-~onductive state. With respect to each of the combined 3~3 ~mplifier circuits, Tl and ?1, T2 and Q2, T3 and ~3, and T4and Q4, when the lead A, B, C or D, as the case may be, is not connected to ground via the collector-emitter circuit of the assoclated opto-isolator circuit's transistor T5, the base of Tl, T2, T3 or T4, as the case may be, draws current from the 5 volt source via the associated pull-up resistor 305 to drive the transistor Tl, T2, T3 or T4, as the case may be, into its conductive state. As a result, the base of transistor Ql, Q2, Q3 or Q4, as the case may be, is clamped to ground via the emitter-collector circuit of its associated driver transistor Tl, T2, T3 or T4, thereby driving the transistor ~1, Q2, Q3 or Q4, as the case may be, into its conductive state. Contrariwise, th~ transistor pai~s Tl and Ql, T2 and Q2, T3 and Q3, and T4 and Q4 are respectively biased to cut-off when lead A, B, C or D, as the case may be, is connected to ground via the collector-emitter circuit of the associated opto-isolator circuit's transistor T5. As shown in the truth table ~Fig. 8) for clockwise motor rotation, Ql and 74 are turned on and ~2 and ~3 are turned off; whereas for counter-clockwise motor rotation, Q2 and Q3 are turned on and Ql and ~4 are turned off. Accordingly, or clockwise motor rotation: terminal 302 ~Fig. 7) of the motor 120 is connected to the 30 volt source via the emitter-collector circuit of Ql, which occurs when Q2 is turned off and the base of Q1 is grounded through the emitter-collector circuit of Tl due to the base of Tl drawing current from the 5 volt source in the presence of a high logic level control signal at input terminal A; and terminal 304 o the motor 120 "

is connected tc ground via the emitter-collector circuit of Q4, which occurs when Q3 is turned off and the base of Q4 is grounded through the emitter-collector circuit of T4 due to the base of T4 drawing current from the 5 volt source in the presence of a high logic level signal at the input terminal D. On the other hand, for counter clockwise rotation of the motor 120: terminal 302 of the motor 120 is connected to ground via the emitter collector circuit of Q2, which occurs when Ql is turned off and the base of Q2 is grounded through the emitter-collector circuit of T2 due to the base of T2 drawing current from the 5 volt source in the presence of a high logic level control signal at the input terminal B; and terminal 304 of the motor 120 is connected to the 30 volt source via the emitter-collector circuit of Q3, which occurs when Q4 is turned off and the base of Q3 is grounded through the emitter-collector of T3 due to the base of T3 drawing current from the 5 volt source in the presence of a high logic level control signal at the input terminal C. For turning off the respective powers transistors Ql-Q4, on a two at a time basis, low level control signals are applied on a selective basis to the two terminals B and C, or A and D, as the case may be, to which high logic control level signals are not being applied; which occurs when the opto-isolator circuit's transistors T5 associated with the respective leads B and C or A and D are driven to their conductive states.
When this occurs the bases of the transistor~ T2 and T3, or Tl and T4 ~ as the case may be, are biased to open the emitter-collectors circuits of the transistors T2 and T3, or Tl and - ~5 -~2~ 3 T4, as the case may be, as a res~lt of which the bases of thetransistors Q2 and ~3, or Ql and Q4, as the case may be, are biased to open the emitter-collector circuits of ~ransistors Q2 and ~3, or Ql and Q4, as the case may be.
The velocity of the motor 120 tFig. 7) is con~rolled by modulating the pulse width and thus the duty cycle of the high logic level, constant frequency, control signals, i.e., pulse width modulated (PWM) signals, which are timely applied on a selective basis to two of the leads A-D, while applying the low level logic signals to those of leads A-D which are not selected. For example, assuming PWM signals (Fig. 9) having a 50~ duty cycle are applied to leads A and D (Fig.
7), and low level logic signals are applied to leads R and C, for clockwise rotation of the motor 120, the velocity of the motor 120 will be greater than it would be if high logic level PWM signals (Fig. 9) having a 25% duty cycle were similarly applied and will he less than it would be if high logic level PWM signals having a 75% duty cycle were similarly appliecl. Accordinyly, assuming rotation of the motor 120 (Fig. 7) is commenced by utilizing high logic level PWM signals having a given duty cycle percentage, the velocity of the motor 120 may be decreased or increased, as the case may be, by respectively decreasing or increasing the duty cycle percentage of the appliec1 high loc;ic level PWM
signals. Further, assuming the motor 120 is rotating clockwise due to PWM signals having a selected positive average value being applied to leads ~ and D, in combination with low level logic signals being applied to leads B and C, the motor 120 may be dynamically braked by temporarilyap~lying high level PwM signals having a selected duty cycle corresponding to a given positive average value to leads s and C, in combination with low logic signals being applied to leads A and D. To avoid damage to the power transistors ~1, Q2, Q3 and ~4 which might otherwise result, for example, due to current spikes accompanying back emf surges which occur in the course of switching the circuit 301 from one mode of operation to the other, the ernitter-collector circuits of the power transistors Ql, Q2, Q3 and 24 are respectively shunted to the 30 volt source by appropriately poled diodes, Dl, D2, D3 and D4 connected across the emitter-collector circuits of Ql, Q2, Q3 and ~4.
To control the motion of the drum 38 (Fig. 1) during each cycle of dr~ rotation, the D.C. motor 120 and its shaft encoder 126 are respectively connected to the computer 500 via the power amplifier circuit 300 and the counting circuit 270. ~nd the computer 500 is programmed to calculate the duration of and timely apply PWM control signals to the power amplifier circuit 300 after each sampling time instant Tn, utilizing an algorithm based upon a digital compensator D(s) derived from analysis of the motor 120, motor load 38, 74, 76, 90 and 124 amplifying circuit 300, encoder 126, counting circuit 270, and the digital compensator D(s) in the closed-loop, sampled-data, servo~control system shown in Fig. 10.
With reference to Fig. 10, in general, at the end of each predete~rmined sampling time period of T=l millisecond, the eight bit wide count representing the angular displacement of the motor drive shaft 1221 and thus the drum38, from its home position is sampled by the computer 500 at the time ins~ant Tn. Under the control of the program of the computer 500 (Fig. 10), a summation is taken of the aforesaid actual count and the previously calculated count repr2senting the desired position of the motor drive shaft 122, and thus the drum 38, at the end of the time period T, and, under control of the computer program implementation of the algorithm, a PWM control signal which .is a function of the summation of the respective counts, or error, is applied to the power amplifier circuit 301 for rotating the motor drive shaft 122 such that the error tends to become zero at the end of the next sampling time period T.
To derive the algorithm, the servo-controlled system of Fig. 10 is preferably analy~ed in consideration of its equivalen~ Laplace transformation equations shown in Fig. 11, which are expressed in terms of the following Table of Parameters and Table of Assumptions.

Table I - Parameters ,_ .

Parameter Symbol Value and/or Dimenslon Zero-Order-Hold ZOH None Laplace Operator S jw Sampling Interval T Milliseconds P~ D.C. Gain Kv Volts PWM Pulse Amplitude Vp 5 Volts PW~ Pulse Width tl 10-6 Micro-seconds P~wer Switching Circuit Gain Xa None Motor back e.m.f. Constant Ke 0.63 Vol~s/
radian/second Motor Armature Resistance ~a 1.65 Ohms Motor Armature Moment of Ja 2.12 (10-5) Inertia kilograms (~eters2) Motor Torque Constant Kt 0.063 Newton-Meter s/am2 Drum Moment of Inertia Jl 70.63 (10-5) kilograms (meters2) Gear Ratio, Motor to Load G 5:1, None Motor Armature Inductance La 2.76 Millihenrys Motor Shaft Encoder Gain Rp Counts/radian Motor Shaft Encoder Constant Kb 192 Lines/
revolution Counting Circuit ~ultiplier Xx 2, None Motor Gain Rm 16, None Poles in frequency domain fl;f2 48;733 Radians/
second Starting Torque Gain Kc None System Overall Gain Ko None Table II - ~ssumptions ZGH: Since the output and input are held constant during each sampling period a zero-order-hold is assumed to approximate the analog time function being sampled.

Veq.: Since the integral of the voltage in time is assumed equal to the area under the PWM pulse, the output from ~he PWM is linear.

~ 29 -:~3~

With reference to Fig. 10, D(S) is the unknown transfer function of an open loop compensator in the frequency domain. Due to a key factor for providing acceptably fast motor response being the systemls resonance between the motor and load, the derivation of the transfer function D(S) for stabilization of the system i5 preferably considered with a view to maxi~izing the range of frequencies within which the system will be responsive, i.e., maximizing the system's bandwidth, Bw. For calculation purposes a sampling period of T=l millisecond was chosen, due to having chosen a Model 8051 microprocessorr available from Intel Corporation, Palo Alto California, for control purposes, and inasmuch as the Model 8051 microprocessor equipped with a 12 MHz crystal for providing a clock rate of 12 MHz, is able to conveniently implement a 1 KHz sampling rate and also implement application software routines, after control algorithm 1terations7 during the sampliny period of T=l millisecond. ~lowever, other sampling periods and other conventional microprocessors may be utilized without departing from the spirit and scope of the invention.
The open loop system gain Hl(S) without compensation, of the servo-loop system of Fig. 10 is shown in Fig. 12(a).
To tolerate inaccuracies in the transmission system between the motor and drum load, such as backlash, it was considered acceptable to maintain a steady-state count accuracy of plus or minus one count. To reflect this standard, the gain equation oE Fig. 12ta) was adjusted to provide a corrective torque Ct with a motor shaft movement, in radians per count, ~ j equivalent to the inverse expressed in radians per count, of the gain Kp of the encoder counting circui~ transfor~. Since the corrective torque Ct is primarily the friction of the transmission system which has to be overcome by the motor at start-up, the value of Ct msy be assumed to be substantially equal to a maximum estimated numerical value based on actual measurements of the starting friction of the system, i.e., 35 ounce-inches, as a result of which a numerical value of the starting voltage VS may be calculated from the expression VS
= (Ct)Ra/Kt, i.e., Vs = 6.5 volts, which, in turn, permits calculation of a numerical value for the minimum overall system gain Ko~ at start-up, from the equation Ko = Ys/Kp, i.e., Ko = 397 volts per radian, or for simplication purposes, 400 volts/radian. ~ccordingly, the open~loop uncompensated gain Hl(S) may be rewritten as H2(S) as shown in Fig. 12(b), in which a gain factor of Rc has been included, to account for the torque Ct and the value of Ko is substituted for the overall D.C. gain, i.e., ~KV)(Km)(Kp)(Xa)(Kc) = Ko~ Although the numerical value of ~c may also be calculated, it is premature to do so, since it has not as yet been established that Ko~ which has been adjusted by the value of Rc to provide a minimum value of K
is acceptable for system stability and perormance purposes.
Otherwise stated, Ko may not be the overall system gain which is needed for system compensation for maximizing the system bandwidth BW, as a result of which it is premature to conclude that Xc will be equivalent to the D.C. gain of the system compensator ~S).

At this j~lncture, the B~de diagram shown in Fig. 13, ma~ be c~nstructed due to having calculated a minimum value f~r ~O. ~s sh~wn in Fig. 13, the abs~lute value of H2(S), in decibels, has been plotted against the frequency W in radians per second, based on the calculated minimum value of Ko~ the selected value of T and calculated values of the poles fl and f2. From the Bode diagram, a numerical value of the cross-over frequency Wcl of the Bode plot of H2(S) may be determined, i.e., Wcl was found to be substantially 135 radians per second. And, since the value of Wcl is substantially equal to the bandwidth BWU of the uncompensated open-loop system H2(S), a calculation may be made of the phase margin em of the uncompensated system from the expression 0m = 180~ - e [H(S)] at Wcl, or, otherwise stated:
a 1 f Wcl ) -tan~l(Wcl/fl)-tan~l(W l/f2) tan~l (WClT/2). From this calculation, there was obtained a phase margin value which was much, much, less (i.e., 5) than 45, which, for the purposes of the calculations was taken to be a minimum desirable value for the phase margin 0m in a position-type servo system. Accordingly, it was found that the uncompensated system H2(S) was unstable if not compensated.
Since an increase in phase lead results in an increase in bandwidth BW, and the design criteria calls for maximizing the bandwidth BW and increasing the phase margin to At least 95~; phase lead compensation was utili~ed.
By definition, a phase lead compensator D(S) has the Laplace transform shown in Fig. 14, wherein ~c is the phase lead D.C. gain, and fz and fp are respectively a zero ~2~ 3 frequency and a pole frequency. ~dding the transferfunction of the phase lead compensator D(S) to the Bode plot of the uncompensated system's transfer function H~(S), results in the Bode plot of the compensa-ted system -transfer function H3 (S), if the zero frequency fz of -the phase lead compensator D (S) is chosen to be equivalent to fl in order to cancel the lag due to the mechanical time constant of the uncompensated transfer function H2S. As shown in Fig. 13, the cross-over frequency Wc2 for the compensa-ted system H3(S) may be read from the Bode diagram, i.e., Wc2 was found to be substantially equal to 400 radians per second. Andl since by definition the cross-over frequency Wc2 lies at the yeometric means of fp and fz, the value of the fp may be established by doubling, from fz, the linear distance between Wc2 and f~, as measured along the logarithmic frequency axis, W, and reading the ~alue of fp from the Bode diagram, i.e., fp was found to be substantially equal to 3,400 radians per second. Since numerical values may thus be assigned to both Wc2 and fp from the Bode diagram, the compensated phase margin mc' i.e., the phase margin for the phase lead compensated system H3lS3 in which fz has been equated to fl, may be found from the expression Omc=180-90-tan l(WC2/f2) tan (WC2T/2). Upon calcula-ting the compensated phase margin mc it was found to be 50 and, therefore, greater than the minimum phase margin criteria of 45.
In addition, the value of Wc2 for the compensated system H3(S) was found to be substantially three times that of the uncompensated system H2(S), as a result of ,; .;

~ 23~
~L ~

w~ich the bandwidth BW of the system H(S) w~s increased by a factor of substantially three to BWC.
At this juncture, the compensated system H3(S) is preferably anal.yzed with reference to the system's overshoot s and settling time tS based on a calculation of the system damping factor df and the assumption that the system will settle in five times constants, i.e., tS=5tX. The relevant values may be calculated or estimated, as the case may be, from the expressions, for df, o5, tx and tS shown in Fig. 15.
In connection with this analysis~ reference is also made to the typical mailing machines hereinbefore described, wherein a maximum drum cycle time period TCt (Fig. 3) of 234 milliseconds and a maximum mailpiece transport speed (Fig. 2) of 61 inches per second are typical values. Assuming the velocity profile of Fig. 3, and, as previously discussed an acceleration time period of Ta=37 milliseconds, a constant velocity time period of TC=124 milliseconds and deceleration time period of Td=24 milliseconds, the longest permissible settling time for the system was calculated, i.e., TCt (Ta+TC+Td) = 234-185 = 49 millis~conds. For analysis purposes a series of calculations of the aforesaid system characteristics and phase margin were performed, assuming incremental increases in the overall system gain Kol while hol.ding fz=fl. The results of such calculations are shown in the following Table III.

- 3~ -~23~

Table III - H~(S) with f~--f~

KO=sys~em ~c=sw ~m=Phase 05=overshoot tS=settling gain (rad.~sec.~ ~argin (deg.) (percent) time (~S.) 400 400 50 28 28.67 ~47 45~ 46 31 27.78 501 500 42 34 27.50 56~ 550 38 38 27.41 As shown in Table III, the system bandwidth ~-~ may be maximized at 450 radians per second while maintaining a phase margin 0m of at least 45 the two design criteria discussed above. Although this results in an increase in system overshoot s accompanied by a negligible decrease in the settling ti~e tS~ the settling time tS is well within the maximum allowable settling time, Ts=49 milliseconds. On the other hand, if a bandwidth of 400 radians per second is acceptable, it is desirable to reduce the percentage of overshoot Os~ and increase the phase margin to emc~50 to provide for greater system stability than would be available with a phase maryin value (i.e., 46) which i5 subgtantially equal to the design criteria minimum of 45; in which instance it is preferable to choose the bandwidth of BW=400 radians per second, overshoot of Os=28% and compensated phase margin of emc=50- For the example given, a compensated Bandwidth of ~Wc=400 radians per second is acceptable inasmuch as ~orst case load conditions were assumed. In this connection it is noted that the foregoing analysis is based on controlling a postage meter drum, which has a high ~oment of inertia, contributes high system friction, and ~, calls for a cyclical start-stop rnode of operation during which the load follows a predetermined displacement versus time trajectory to accommodate the maximum mailpiece transport speed in a typical mailing machine. Accordingly, the compensated system bandwidth BWC=400 radians per second may be chosen, as a result of which the overall system gain Ko may be fixed at Ko=400~ and the value oE Kc may be calculated from the expression KC=Ko/(Kv)(Ka)(Kp). Since fz=fl, and fl and fp are also known, the Bode plot of the compensator D(S), Fig. 14, may be added to the Bode diagram (Fig. 13) wherein the system compensator D(S) is shown as a dashe~ line.
Since the analog compensator D(S) was derived in the frequency domain, D(S) ~as converted to its Z-transform equivalent D(Z) in the sampled data domain for realization in the form of a numerical algorithm for implementation by a computer. Of the numerous well-known techniques or transforming a function in the frequency domain to a function in the sampled-data domain, the bi~linear transformation may be chosen. For bi-linear transformation purposes the Laplace operator S is defined by the expression shown in Fig. 16.
Using the values K~=13.64, fz=fl=48, and fp=3,400 in the expression for D(S) shown in Fig. 14, and substituting the bi-linear transfor~ation expression for S shown in Fig. 16 and the sampling interval T=l millisecond, in the expression shown in Fig. 14 results in the expression for D(Z) shown in Fig, 17~ As shown in Fig. 11, D(T)=output/input=g(T)/e(T), which, in the sampled data domain is expressed by the ~2~ 3 equation D(Z)-G(Z)/E(Z). Accordingly, the expression for D(Z) shown in Fig. 17 may be rewritten as shown in Fig. 18a.
Cross-multiplying the equivalency of Fig. 18a results in the expression shown in Fig. 18b, which defines the output G(Z) in the sampled data domain of the system compens~tor D(S).
Taking the inverse Z transform of the expression shown in Fig. 18b, results in the expression shown in Fig. 19 which defines the output G(Tn) in the time domain of the system compensator D(S), and is a numerical expression of the algorithm to be implemented by the computPr for system compensation purposes. As shown by the expression in FigO 19 and in the following Table IV the output of the digital compensator for any current sampling instant Tn is a function of the position error at the then current sampling time instant Tn~ is a function cf the position error at the end of the next previous sampling time instant ~n-l and is a function of the algorithm output at the end of the next previous sampling time instant Tn_l.

TABLE IV
~ . ~

Function Definition G(Tn) Algorithm output for current sampling time instant Tn E(Tnl Position error for current sampling time instant ~n G(Tn 1) Algorithm output for next previous sampling time instant Tn-l E(Tn-t) Position error for next previous sampling time instant Tn_ ~2i~ 3 K1r K2 & K3 Constants of the compensated sy~m which aIe a function of the parameters of the motor load and system friction for a sampling time period of T~l millisecond.

Accordingly, the algorithm which is to be implemented by the computer 500 for system compensation purposes is a function of a plurality of historical increments of sampled data for computing an input value for controlling a load to follow a predetermined position trajectory in a closed loop sampled-data servo-control system.
As shown in Fig. 20 the computer 500 preferably includes a conventional, inexpensively commercially available, high speed microprocess~r 502, such as the Model 8051 single chip microprocessor commercially available from Intel Corporation, 3065 Bowers ~venue, Santa Clara, California 95051. The microprocessor 502~ generally comprises a plurality of discrete circuits, including those of a control processor unit or CPU 504, an oscillator and clock 506, a program memory 508, a data memory 510, timer and event counters $12, programmable serial ports 514, programmable I/O ports 516 and control circuits 518, which are respectively constructed and arranged by well known means for executing instructions from the program memory 508 that pertain to internal data, data from the clock 506, data memory 510, timer and event counter 512, serial ports 514, I/O ports 514 interrupts 520 and/or bus 522 and providing appropriate outputs from the clock 506, serial ports 514, I/O
ports 516 and timer 512. A more detailed discussion of the internal structural and functional characteristics and - 3~ -features of the Model 8051 microprocessor, including optionalmethods of pr~gramming p~rt 3 f~r use as a conventional bi-directional port, may be found in the Intel Corporation publicati~n entitled MCS-51 Family ~f Single Chip Microcomputers ~sers Manual, dated January 1981.
For implementing the sampling time period of T=l millisecond, one of the microprocessor~s timer and event counters 512 (Fig. 20) is conventionally programmed as a sampling time period clock source. To that end, a timer 512 is programmed for providing an interrupt signal each 250 microseconds, and each successive fourth interrupt signal is utilized as a clock signal for timing the commencement of successive sampling time periods of T=l millisecond.
In general, as shown in Fig. 21, at the commencement of each sampling time period of T=l millisecond, during the sampling instant Tnr a sample is taken of the count representative of the actual angular displacement of the motor drive shaft and, substantially immediately thereafter, the actual count is summed with the count representative of the desired angular displacement of the motor drive shaft which was calculated during the next preceeding time period T
in order to obtain the then current error value E(Tn) for calculating the then current compensation algorithm output value G(Tn). Due to the recursive mathematical expression for G(Tn) [Fig. 19] being a function of the then current error value E(Tn), the next previous error value E(Tn_l) and the next previous compensation algorithm output value G(Tn_l), the expression for G(Tn) is preferably separated ~ 6~ ~ ~

into tw~ comp~nents for calculation purposes, i.e., G(~rl~ =

gl + 92i wherein gl = Kl ~ ~(Tn)~ and wherein g2 = -[K2 x E(Tn-l) + K3 x G(Tn-l)]l to permit calculation of the value of g2 in advance of the time period T when it is to be added to the value of gl for calculating the value of G(Tn), thereby reducing to a negligible value (in view of the time period T) the time delay Tdy before completion of sampling the actual displacement of the motor drive shaft at the instant Tn and applying the PWM motor control signal to the output ports of the microprocessor. For example, when calculating the value of G(Tn) based upon the first error value resulting from the summation of the counts representing the desired and actual angular displacements of the motor drive shaft, the value of g2 is by definition equal to zero since the error signal E(Tn_l) is equal to zero, due to the desired and actual angular displacement values during the next previous sampling time period T having been equal to each other. Accordingly, upon obtaining the value of ~he first error signal El(Tn), the value of Gl(Tn) may be calculated as being equivalent to gl, i.e., Gl(Tn) = gl = K
x El(Tn). And, upon calculating Gl(Tn) the value of g2 for use in calculating the next successive compensation algorithm output value G(Tn+l) may be calculated for subsequent use, since g2(Tn+l) = -lK2 x El(Tn~ ~ K3 x Gl~Tn)], and K~, K3, El(Tn) and Gl(Tn) are all known values. In addition, during any given time period T, a calculation may be made of the desired angular displacement of the motor drive shaft or the next subsequent time period T. Preferablyr the ~L23~

microprocessor is programmed for implementation of theaforesaid calculation process to facili~ate early utilization of the compensation algorithm output value G(Tn) for driving the D.C. motor. Accordingly, the microprocessor is preferably programmed for: during the first sampling time period Tl, sampling the count representative of the actual angular displacement of the motor drive shaft at the time instant Tn, then taking the summation of that count and the previously calculated value of the desired angular displacement of the motor drive shaft to obtain the first error value El(Tn), then calculating the first compensation algorithm output value Gl(Tn) = Kl x El(Tn) ~92~ wherein 92=~ and generating a PWM motor control signal representative of Sl(Tn), then calculating the value of g2 for the next sampling time period, i.e., g2 = -~R2 ~ El(Tn) ~
K3 x Gl(Tn)3, and then calculating the count representing the desired anqular displacement of the motor drive shaft for use during the next sampling time period T2; during the second sampling time period T2, sampling the count representative of the actual angular displacement of the motor drive shaft and taking the summation of that count and the previously calculated desired count to obtain the error value E2(Tn+l), calculating the compensation algorithm output value G2(Tn+l) = Kl x E2(Tn+l) ~ ~2 = Kl x ~2(Tn+l) - K2 x El(Tn) - R3 x Gl(Tn), and generating a PWM motor control signal representative thereof, then calculating the value of g2 for the next sampling time period T3, i-e-, g2 -[K2 x E2(Tn+l) +
R3 x G2(Tn+l)], and then calculating the c~unt representative ~23~

of the desired angular displacement of the motor drive shaftfor use during the time period T3; and so on, during each successive sampling time period.
Accordingly, as shown in Fig. 21, the microprocessor is programmed for i~nediately after calculating the ~hen current com?ensation algorithm output value G(Tn), and thus while the calculation of the value of g2 for the next sampling time period is in progress, generating a motor control signal for energizing the power amplifier. For this purpose, the relative voltage levels oE motor contr~1 signal are determined by the sign, i.e., plus or minus, oE the compensation algorithm output value GtTn), and the duty cycle of the control signal is determined by the absolute value of the compensation algorithm output value G(Tn). Preferably, for timing the duration of the motor control signal, the other timer and event counter 512, i.e., the timer 512 which was not used as a sampling time period clock source, is utilized for timing the duration of the duty cycle of the motor control signal. For examplel by loading the absolute value of the G(Tn) into the other timer 512, commenciny the count, and tirnely invoking an interrupt for terminating the duty cycle of the control signal. As shown in Fig. 21tc), the time delay T~y from co~nencement of the time period T to updating the PWM motor control signal at the output ports of the microprocessor is substantially 55 microseconds, and the time interval allocated for calculating the value of g2 and he count representative of the desired angular displacement of the motor drive shaft for use during the next time period ~:3~3 is substantially 352 microseconds. As a result, substantially 593 microseconds of microprocessor calculation time is available during any given sampling time period T=l millisecond for implementing non-motor control applica~ions.
As shown in Fig. 22 the computer 500 is preferably modularly constructed for segregating the components of the logic circuit 501a and analog circuit 501b of the computer 500 from each other. To that end, the respective circuits 501a and 501b may be mounted on separate printPd circuit boards which are electrically isolated from each other and adapted to be interconnected by means of connectors located along the respective dot-dash lines 516, 527 and 528. In any event, the components of the logic circuit 521a and analog circuit 521b are preferably electrically isolated from each other. To that end, the logic circuit 501a preferably includes 5V and ground leads from the mailing machine's power supply for providing the logic circuit 501a with a local 5 volt source 530 having 5V and GND leads shunted by filter capacitors Cl and C2. And the analog circuit 501b includes 30 volt and ground return leads rom the mailing machine's power supply for providing the analog circuit 501h with a local 30 volt source 536 including 30V and GND leads shunted by filter capacitors C3 and C4. In addition, the analog circuit 501b includes a conventional 30 volt detection circuit 542 having its input conventionally connected to the analog circuit's 30 volt source 536, and its output coupled to a power up/down lead from the analog circuit via a conventional optical-electrical isolator circuit 544.
- ~3 -~L~3~

Further, to provide the anal~g circuit 501b with a local 5volt source 546, the analog circuit 501b is equipt with a conventional regulated power supply h~ving its input appropriately connected to the analog circuit's 30 volt source 536 via a series connected resistor Rl and a 5 volt, voltage regulator 548. A zener diode ~1, having its cathode shunted to ground and having its anode connected to the input of the 5V regulator 548 and also connected via the resistor Rl to the 30 volt terminal line, is provided for maintaining the input to the 5V regulator 548 at substantially a 5 volt level. In addition, a pair of capacitors C5 and C6 are provided across the output of the regulator 548 for fiitration purposesO
To accommodate interfacing the postage meter's computer 41 (Fig. 1) with the computer S00, any two available ports of the computer 41 may be programmed or two-way serial communications purposes and coupled to the computer 500. For example, the postage meter's printing module 41c may be conventionally modified to include an additional two-way serial communications channel for communication with the computer 500.
Assuming the latter arrangement, serial input communications to the computer S00 ~Fig. 22) are received from the postage meter computer's printing module 41c via the serial input lead to the logic circuit 501a (Fig. 22), which is operably coupled to port P30 of the microprocessor 502 by means of a conventional inverting buffer circuit 550.
Accordingly, port P30 i5 preferably programmed for serial - 44 ~

input comm~nications, and the input to the buffer circuit 550 is resistively coupled to the logic circuit's 5 volt source 530 via a conventional pull-up resistor R2. Serial output communications from the microprocessor 502 are transmitted from port P31. Accordingly, port P31 is preferably programmed for serial output com~unications, and is operably coupled to the input of a conventional inverting buffer 552, the output of which is resistively coupled to the logic circuit's 5V source 530 via a suit~ble pull-up resistor R2 and is additionally electrically connected to the serial output lead from the logic circuit 501a.
Since it is preferable that the microprocessor 502 be reset in response to energization of the lo~ic circuit 501a, the logic circuit's 5V source 530 is connected in series with an R-C delay circuit and a conventional inverting buffer circuit 554 to the reset pin, RST, of the microprocessor 502.
The R-C circuit includes a suitable resistor R3 which is connected in series with the logic circuit's local 5V source 530 and a suitable capacitor C7 which has one end connected between the resistor R3 and the input to the buffer circuit 554, and the other end connected to the logic circuit's ~round return.
In addition to the VCC and GND (i.e., VSS) ter~inals o~ ~e microprocessor 502 being respectively conventionally connec~ed to the logic circuit's 5 volt source and ground, since the microprocessor 502 does not utilize an external program memory, the F,A terminal is connected to the logic circuit's 5V source. And, since no other external m4mory is used, the pr~gram storage enable and address latch enable terminals, PSE~ and ALE are not used. In addition to the EA terminal being available for future expansion, ports Pls-P17, ports P20-P27, the read and write terminals, RD and WR, and one of the interupt terminals INTO/P32 are also available for future expansi~n.
In general, the microprocessor 502 is programmed for receiving input data from the postage meter drum's home position encoder 82 each of the envelope sensors 56, 58 and the D.C. motor shaft encoder 126, and, in response to a conventional communication from the postage meter's printing module 41c, timely energizing the D.C. motor under the control of the CP~ of the microprocessor 502. Port P0 is programmed for receiving a transition signal representative of the disposition of the postage meter's drum 38 at its home position; transition signals from the envelope sensors 56 and 58 which represent detection of the leading edge of a mailpiece or other sheet 16 being fed to the drum 38 to permit calculation by the computer 500 of the velocity of the mailpiece and thus the desired angular displacement of the D.C. motor shaft 122 and thus the drum 38; and a count representative of the actual angular displaçement of the D.C.
motor shaft 122. Preferably, port P0 is multiplexed to alternately receive inputs from groups of the various sensors, under the control of an output signal from Port P34 of the microprocessor 502. The shaft encoder 82 which is utilized for sensing the home position of the postage meter drum 38 is coupled to the computer 500 via the drum home position lead of the logic circuit, which, in turn, isconnected to one input of a differential amplifier 562, the output of which is connected to the other input of the differential amplifier 562 via a feedback resistor R4. The aforesaid other input to the amplifier 562 is also resistively coupled, by means of a resistor R5, to the mid-point of a voltage divider circuit including resistors R6 and R7. Resistors R6 and R7 are connected in series with each other and across the logic circuit's 5V source and ground return leads. The LED sensors 56 and 58, which are utilized for successively sensing the leading edges of each envelope being fed by the letter transport, are separately coupled to the computer S00 via the en~elope sensor-l and envelope sensor~2 input leads of the logic circuit 501a. In the logic circuit 501a, the envelope sensor-1 and sensor-2 leads are connected on a one-for-one basis to one of the inputs of a pair of conventional amplifiers 564, the other inputs of which are connected together and to the mid-point of a Yoltage divider including resistors R8 and R9. Resistors R8 and R9 are connected in series with each other and 2cross the logic circuit's 5V source and ground return leads. Further, the three output signals fxom the differential amplifier 562 and the two amplifiers 564 are connected on a one-for-one basis to the three input ports POo-2 of the microprocessor 502, each via a conventional tri-state buffer circuit 566, one of which is shown. The input signals A and B from the D.C. motor ~haft encoder 126 are coupled to the logic circui~
501a - ~7 -~3~ 3 by means of leads A and B, which are conventially electrically connected to the counting circuit 270 to provide the micropr~cessor 502 the the count representative of the actual angular displacement of the mot~r shaft 122 from its home position. The counting circuit's leads Q0-Q7 are electrically con~ected on a one-f~r-one basis to Ports POo-PO7 of the microcomputer 502 via one of eight conventional tri-state buEfer circuits 568, one of which is shown, having their respective control input leads connected to each other and to the output of a conventional inverting buffer circuit 570, which has its input conventionally connected port P34 of the microprocessor 502. Thus, either the three input signals, i.e., from the drum home position and the two envelope position sensors are operably electrically coupled to Ports POo-P02 of the microprocessor 502, or the eight input signals Q0-Q7 from the counter circuit 270 are operably electrically coupled to ports POo-PO7 of the microprocessor 502, for scanning purposes, in response to an appropriate control signal being applied to the respective buffer circuits 566 and 568 from port P3~ of the microprocessor 502.
In operation, assuming a low logic level signal is re~uired for activating either of the sets of buffers 566 or 568; when the microprocessor 502 applies such a signal to port P34, the buffer circuits 566 operate, whereas since the buffer circuit 570 inverts this signal to a high logic level signal before applying the same to the buffer circuit 568, the latter is inoperative. Conversely, a high logic level siqnal from port P34 will operate buffer circuits 568 and not operate the buffer circuits 566. Accoraingly, d~pendins upon the level,high or low, of the signal from port P34 of the microprocessor 502, the eight bit input to one or the other buffer circuits 566 or 568 will be made available to port Po for scanning purposes. Aside from the foregoing, to permit the microprocessor 502 to clear the counter 2~0 for any reason in the course of execution of the program, port P35 is connected to the clear pin CLR of the counter 270 via a conventional inverting buffer 572, and the microprocessor 502 is programmed for timely applying the appropriate signal to port P35 which, when inverted, causes the counting circuit 270 to be cleared~
In general, ports Plo-P13 are utilized by the microprocessor 502 for providing pulse width modulated (PWM) motor control signals for controlling energization of the D.C. motor 120 and port P14 is utilized by the microprocessor 502 for controlling energization of the solid state, A.C~
motor, relay 52 and thus operation of the mailpiece conveyor 49. To that end, ports Plo-P14 of the microprocessor 502 are each conventionally electrically connected on a one-for-one basis to the inp~t of a conventional inverting buffer circuit 580, one of which is shown. The outputs of each of the buffer circuits 580 are sonnected on a one-for-one basis, via a conventional resistor R10, to output leads from the logic circuit 501b, one of which is designated solid state, A.C.
motor, relay, and four of which are respectively designated ~1, T3, T2 and T4, since, as shown in Fig. 7, the four preamplifier stages of the power amplifier utilized for -- 0,9 --~:3~

driving the D.C. motor 120 include the t~ansist~rs Tl-T4.
Thus, the upper nibble of the signal from port Pl is utilized for controlling energization of the D.C. motor and one bit of the lower nibble is utilized for controlling energization of the solid state, h.C. motor, relay 52 and thus the A.C. motor 50. In the analo~ circuit 501b, each of the leads Tl, T2, T3, T4 and solid state relay, from the logic circuit 501a, is electrically connected on a one-for-one basis to the anode of the light emitting diode Dl of five, conventional, photo-transistor type, optical-electrical isolator circuits 303.
Since the cathodes of the light emitting diodes Dl of the opto-isolator circuits 303 are connected to each other and to the 5 volt lead from the analog circuit 501b which extends to the 5 volt source of the logic circuit 501a, the motor control signals are isolated from the power system of the analog circuit 501b to avoid having spurious noise signals in the analog circuit 501b and its components interfere with the control signals generated by the microprocessor 502. The analog circuit 501b also includes a lead, designated power up/down, which extends from the analog circuit 501b to the logic circuit 501a and is connected to the microprocessorls interrupt INTI, port P33, to provide the microprocessor 502 with an appropriate input signal when the power i5 turned on, off or fails. In the analog circuit 501b, the power up/down lead from the logic circuit 501a is coupled to the thirty volt detect circuit 542 by means of a conventional opto-isolator 544, the power up/down lead being electrically connected to ground through collector-emitter circuit of the -- ~0 --opto-isolator's photo-transistor when the light emitting diode Dl is lit in response to the D.C. supply voltage lev~l matching the internal reference voltage level~ e.g~, 30 volts, of the 30 volt detection circuit.
In the analog circuit 501b each of the output~ from the photo-transistors of each of the opto-isolators 303 are resistively coupled to the analog circuits 5V source by means of a conventional pull-up resistor 305, and the emitters of the photo-transistors T5 are connected to the analog circuit's ground system. In addition, the collectors of the photodiodes of the opto-isolators 303, which are utilized for transmitting the motor control signals from ports Plo-P13 of the microprocessor S02 are connected on a one-for-one basis to the appropriate input leads A, B, C and D of the power amplifiers shown in Fig. 7, the outputs of which are connected to the D.C. motor 120. Further, the collector of the photodiode of the opto-isolator 303 which is utilized for transmitting the A.C. relay control signals from port P14 of the microprocessor 502 is connected to the input lead of a conventional darlington-type power ampliEier 550, the output of which is conventionally connected to the mailing machine's 30 volt D.C. source via a solid state, A.C. motor, relay 52, which is turn conventionally connected for energizing the A.C. motor 50 from the local A.C. sollrce.
In general, the computer 500 includes three software programs, including a main line program Fig. 23, a transmit and receive program and a command execution program, respectively identified by the 600, 700 and B00 series of ~Z3~39~3 numbers. When the mailing machine l0 is energized byactuation of the main power switch 24, the resulting low level logic signal from D.C. supply is applied to the reset terminal RST of the computer's microprocessor 502, thereby enabling the microprocessor 502. Whereupon, as shown in Fig.
23, the microprocessor 502 commences execution of the main line program 600.
The main line program 600 ~Fig. 23) commences with the step of conventionally initializing the microprocessor 602, which generally includes establishing the initial voltage levels at the microprocessor's ports, and interrupts~, and setting the timers and counters. Thereafter, the D.C.
motor drive unit is initialized 604. Step 604 entails scanning the motor home position sensor input port PO0, to determine whether or not the D.C. motor 120 is located in Its home position and, if it is not, driving the motor 120 to its home position. ~ssuming the D.C. motor 120 is in its home pos1tion, either before or after the initiali~ation step 604, the program then enters an idle loop routine 606.
In the idle loo~ routine 606, a determination lS
initially made as to whether or not the sampling time period of T=l millisecond has elapsed, step 60B, it;being noted~that each successive sample is taken at the time instant Tn;
immediately after and in response to the fourth 250 millisecond interrupt generated by the timer uti~lized~for implementing the~sampling;t1me per1od~T. Assuming the time period T has not elapsed, the program loops to idle 606. On the other hand, ass~uming the time~period~T has elapsed, the 52 ~

~: :

~3~

microprocessor 502 updates the servo-control system, step 610. F~r the purpose of explaining step 61Q it will be assumed until otherwise stated that the desired location of the postage meter dr~n 38, and thus the motor drive shaft 122, is the home p~sition. Step 610 includes the successive steps 610a and 610b, respectively, of sampling the count of the actual position Pa of the motor drive shaft 122 at the sampling time instant Tn~ and fetching the previously computed count representing the desired position Pd of the shaft 122 at the same sampling time instant Tn. If for any reason the motor drive shaft 122 is not located in its home position when the value of the desired position count Pd(Tn) is representative of the home position location, then the values of Pa~Tn~ and Pd(Tn) will be different. On the other hand, if the motor drive shaft 1~2 is located in its home position when the desired position count Pd(Tn1 is representative of the home position location, then the values of Pa(Tn) and Pd(Tn) will be the same. Accordingly, computation of the error count, 610c, may or may not result in an error count value E(Tn) of zero. Further, independently oE the computed value of E(Tn), the computed value G(Tn) of the motor control signal~ step 601d, may or may not result in a value of G(Tn) of zero; it being noted that although step 610c results in a computed value of E(Tn)=O, the value of g2 may not be e~ual to zero due to the computed value of the error for the next previous sampling time instant E(Tn_l~ having resulted in a non-zero value, ~tep 610g. ~ssuming steps 610c and 610d both result in zero ~ ~3 -value computations, then, upon updating and generating thePWM motor control signal, step 610e, no motor control signal will be generated. Under any other circumstances, step 610e will result in generating a P~M motor control signal for driving the D.C. motor 120, and thus the drum 38, to its hom~
position. Thereafter, as shown in step 610f, the computed values of E(Tn) and G(Tn) are utilized as the values of E(Tn_l) and G(Tn_l) respectively for pre-calculating the value of g2 for the next subsequent time instant Tn~
Accordingly, the computation made in the next step, 610g, to obtain the value of g2 for the next sampling time instant Tn is made by utilizing the replacement values E(Tn-l) and G(Tn-l). Thereafter, as shown in step 610h, the desired position count Pd for the next sampling time instant Tn is made, which, as previously stated has been assumed to be representative of location of the motor drive shaft 122 in its home position. At this juncture it should be noted that the next step 612 in the program is to determine whether or not the enable flag is set, and, as hereinafter further discussed, this inquiry will be ans~ered in the negative, causing the program to return to idle 606, unless a command has been received from the postage meter's computer 41 which results in feeding a mailpiece 16 to the postage meter drum 38. Accordingly, until a mailpiece 16 is fed to the postage rneter drum 38, the main line program will continuously loop through steps 60B, 610 and 612. As a result the motor drive shaft 122, and thus the drum 38, will be driven to the home position, against any force tending to move the drum 38 or ~ ~4 -shaft 122 out of the home position, u~til a mailpiece 16 isfed to the drum 38.
At this juncture it will be assumed that the enable flag is set, as a result of which the inquiry of s~ep 612 is answered affirmatively, or, as above stated, a mailpiece 16 is being fed to the drum 38. Accordingly, the microprocessor 502 commences polling the ports connected to the envelope sensors 56 and 58, step 61Ç. Since polling occurs at one millisecond time intervals, the polling sequence is continuous. ~s shown by the follo~ing step 616, between successive time instants Tn~ the program continuously loops to idle 606 and through steps 608-616 inclusive until the envelope sensing sequence for a given envelope is complete.
Whereupon the microprocessor comr~nces executing step 618, which includes the steps of calculating the envelope's velocity, 618a; then fetching from memory the corresponding acceleration, deceleration and constant velocity constants 618b, for computation of the desired position counts Pd at each successive time instant Tn in advance of sampling the actual position counts Pa as hereinbefore discussed in connection with step 610; then fetching and implementing the time delay td for timely commencing acceleration of the drum 38 to the target veloclty V1; and then commencing drum rotation by generating the desired position Pd for the initial one millisecond sampling time instant of acceleration of the motor drive shaft 122 and storing the value for subsequent use in step 601b. Accordingly, the value of Pd - 5~ -~L23~
will no longer be assumed to be the value representative ofthe home position.
Thereafter, the inquiry is made as to whether or not the drum cycle is complete, step 620. ~ssuming as stated above that only the initial desired value of Pd has been computed and stored, the inquiry of step 620 will be answered in the negative. Whereupon the microprocessor 502 transmits a status message, step 622, to the postage meter's computer 41 and the program loops to idle 606. Thereafter the microprocessor 502 continuously executes steps 60B-620 until the entire Pd count sequence 618d for the trapazoidal-shaped velocity versus time profile for the target velocity Vl has been exhausted. In this connection it is noted that the drum cycle TCt is not complete until the settling time interval Ts which is allowed for damping any overshoot of the motor drive shaEt 122 is complete. During the settling time interval Ts the value of Pd is a constant and representative of the home position of the shaft 122 and thus the drum 38. Assuming that the drum cycle is complete, the inquiry of step 620 will be answered affirmatively~ Whereupon the microprocessor 502 transmits a status message, step 624, to the postage meter's computer 41 and the program loops to idle 606. Thereafter, the foregoing steps 606-622 of the main line, servo-control, idle loop are continuously executed by the microprocessor 502 in accordance wlth the above discussion until the main power switch 24 is opened by the operator.
The serial communications program 700 includes the transmit status routine 704. The latter routine 704 includes the steps of receiving and decoding any message, step 706,and invoking the execute command routine, step 708, both of which steps are self explanatory.
Assuming the execute command routine 800 has been invoked, step 708, the microprocessor 502 executes the routine 80~ commencing with the step B02 of inquiring whether or not the decoded message is an enable command. ~ssuming the answer is yes, an enable status flag is set, step 804, to indicate that an envelope is to be fed to the drum 38.
Whereupon the A.C. motor relay 52 is energized, step 806, for feeding the envelope to the drum 38, and the transmit status routine is invoked, step 808. On the other hand, assuming the decoded message is not an enable command, step 802, a ena~le status flag is cleared, step ~10. Whereupon the A.C.
relay is deenergized, step 812, and the status transmit routine is invoked 808.
Assuming the status kransmit routine 702 has been invoked, step B06, the microprocessor 502 executes the routine 702 commencing with the step 71D of inquiring whether or not the drum cycle is complete. Assuming completion of the drum cycle, a drum cycle complete message is transmitted to the postage meter's computer 41, step 712. On the other hand, assuming the drum cycle is not complete, an inquixy is made as to whether or not the A.C. relay is energized, step 716, and, if it is, an A.C. relay energized message is transmitted to the postage meter's computer 41, step 718. If however the drum cycle is not complete, step 710, and the A.C. relay is n~t energized, step 716, then, an A.C xelay ~23~

deenergized message is transmitted to the postage meter'sco~ ter 41, step 720. ~pon transmitting any of the messages, drum cycle ccm?lete, step 71~, A.C. relay energized, step 716, or A.C. relay deenergized, step 720, the microprocessor 502 returns to the idle 606 of the main line program 600.
The term postage meter as used herein includes any device for affixing a value or other in~icia on a shee~ or sheet like material for governmental or private carrier parcel, envelope or package delivery, or other purposes. For exam~le, private parcel or freight services purchase and em?loy postage meters for providing unit value pricing on tape for application on individual parcels.
A more detailed description of the prosrams herein-before discussed is disclosed in the appended program listing which describes in greater detail the various ro~tines incorporated in, and used in the operation of, the postage meter.
Although ~he invention disclosed herein has been described with reference to a simple embodiment thereof, variations and modifications may be made therein by persons skilled in the art without departing from the spirit and scope of the invention. Accordingly, it is intended that the following claims c~ver the disclosed invention and such variations and modifications thereof as fall within the true spirit and scope of the invention.

" APPENDEX " ~3~8~
For patent application entitled MICROPROCESSOR CONTROLLED
D.C. MOTOR FOR CONTROLLING PRINTING MEANS
Inventors: Edilberto I. Salazar and Wallace Kirschner -o m P~
er eD
0l _I

U ~
:1~ Z C
F
o C
~J U

O
a ~ r ~ V _ V
-- V cr V
~ D

3~ 23~3 n r n , ~ ~ c c ,c V ~ ~ ~ . U
C F ~1 ¢ ~ C ~
~' ~ ~ r L ~ n u n 1 ~ D ~ r o ,, ~ 5 V . _ _ ~ V
. V ~ ~ ~n ~ > U ~r ~ - V Ln ~ ~ ~ ~ O O
u ~ o . ~ c r ~ ~ c ~ u-- L r ~ ~ L n c F V
n c ~ m ~ e ~ F U _ ~U .J 1'1 _ O ~_ T _- ~ V :.- V ~ m ~
r u ~ ~ o O v ~J ~ ~ ~ ~ ~ cC C u c h C ~ r n -r e F r ~ ~C > ¢ ~ _ L ~ ~ 0 ~ L
. I ~ u _ _ ~ r. o _ ~ ~ '~ n ~ _ ~ L u r ~:
r ~ 1 K V V~ V J h. C _ C ~ Cv C ~ Cr ~ r LL ~U U ~ ~ Y _ U ~ r _ v ~ C
* ~ 4 ~ C. O ~J ~ C C~ 'U C ~ r ~: r~ o. F.. _ c . hl ~ O -.b ~ V ~ C~

V ~
C C C ~ CK C C/~ C ~ cn CV. CK cq c C~ c~ ~ VJ V, V K~ K U V, K~ V~ r ..o ~ v ~ .o K K V, Z C~ _ Z ~ ~ I .. hl .. _ ~ :.) X ... --. ~ ..... IJ :.1 V
* r ~ v, u ~ C ~ ~ U v ~ U
K ~ Y U * ~ F ~ C ~ c ~ ~ U ~ ~ U U z _ I ~ X U U 3 ~ h h ~ ~ ~ O y -V h z --t -h, O--t n hl C~ C u ~J7 r~ ~ ~ .I h 1, C h o r~ ~ v u ~ ~ c ~c c L~ h -- 1~ r u r ~ 1l; c C~ c7 o rJ o o o c o c Cl ~ o O o o o o o o c~ o ~ o e~ e~ o 7 rJ ~ ~ o o C>
~t ¢ h~ _ r. ~ .r u~ t 1 Y l? c ol Ir r Ut 1` Qt C' O _ ~ t 'O U' u7 1~ ICt ~ C _ ~t -- ~ U Lt ~ ~t O` O _ ~t ~ 'C
Ul ~ t ~ r~ N ~ t~ r~ r t ~ I't l t ~ ~t ~ t ~
-~t Y

r r n 0 ~, ~, U . ;_ .
U C' ~ U _ C ~
S: 'C _ L ~ L ~ -<~. * ~ . C ~ _ ~
~ ~ o o ~D o ~ ~, ~ " ~ E -C 1~ ~ -- -- E _ ~ ~ C ~ a C 5. _ ~_ C ~ O C ~ * C
C f` ~G G V' ~, ~ G U I U ~ U
* ~' ' C _ _ _ ., _ a u T~
* ~ 2 ~ ~ Ic ~ h Q, ~ C CJ c~ ~` ~ Ul V ~
C U U ~D C U U U
C E: 10 111 1,' 1.; ~ 11 V * _ V U
O _I N ~
1~ ~ C ~ ~ a a ~ L ~C ~ V, V
.. * ~ O _ N ~ ~ '11 C:l ~ G

-.r w -O ~i' C~

C C C c U C a~
a ~ oo o C o o o o c V lu ~o r~ a~ C _ ~ ~ .J U~ 1~ a ~ _ ~ ^ ~r Ir ~C r~ ~ o~ C. _ ~ r~l ~r V~ ~ r--C

~2~ 3 L ~. . L' _ . _ ,, ~"c _ O r c u v ~C C C ~ e L ,, ~ ~, V C o _ _ ~` O O ~1 C LJ V _ U
~r-- L _ _ u F IJ F. O
O -- ' ` ~ 0 ~> *
~ 0 0 .:C ~ 11. ~ _ F F C
/~ ~ C~ L7 ~
V * ~ _ C C ~ U _ 4 '' ,5 7 17 C7 ~7 -- ~
~ v ~ , C ~ F ~? ~
Y 1- L7 C) C C ~_ L~ C ~ -- ~ ' 7 U " ~ ~~ V~ ~ U

4 ~ 2 ~ ~ ~ ~ ~ a r O I * 1~ h ' C
' Y ~ U ~~ ~ C
-.r h - z7 -h O
h~ O o _ c~: r~ `r U, ca 7 o o C o ~ C. C~
~.~
v. W~ c _ ~ ~ v IC ~c r C.7 O C _ ~ ~ ~ ~ ~O r. O~ l r V
U~ 21_ C7 77 t.7 ~7 ~ o7 ~ 107 O ~ O\ V. O. a a o a a a C~
57 Cl:

~23 n ;
L ~ r . ~_ L; C o L ~ r cl c V ~ IJ O ~ r K ~ O~ 1.> ~--~ I r c G~ O ~O Tl ,t O al U 1~ ~ n W ~ ~ ~ rr ~ a O v c a v ~o r 1~ c _I E C O ~ D O ~ _ O
u~ ~ C ~E ~ L ~ ~ _ V C V r o c i ~ ~ c F
~ C ~~ L C V~ ct '~ _ 1., In ~ ~ U~ C.~ 1., C.~ ~_ ~ ~. O

.I>C ~CIr___________________ O

*~:O~ C~CCCCCCCC~C~C~CCCCCC
;D C
* V u * h ~ ~ L I ~. h _ ' ~ . ~ h ~ J _ * ~ ": 1~, ~ v ~ h * ~ C ~ ~ ~ ! h ~ , S I X :~
C '~ O ~ ~ i.l ~ ~ ~ O F-. ~ ~ O
.. * ~ ~ O _ O 1.~ ~ 1~ .~ Z C~ ; Q :~ Q Y ~ r S t_~
C ~ ~ ~ ~ C C V~ ~_' V~ V~ 0 o r ~
z h C
W o ~ o o o o o c~ c> o o o o _ _ _ _ _ _ _ _ C Co rO C~ ~C, C~ o Co Co Ca Cc~ ~ Co c~ o o o C o V~ h. cr o _ r~ r~ ~ v~ C~ ~ ~ IG ~0 ~ Ir Ir C _ r r~
a v C, W

~ 3 ~ r F -- -- ;
r -- r ~ F _ ~, ~, ~ n ~ c c 4 r ~ 1.~ D .~ _ T. ~ r I n r L r ~ L F _ G ~ ~ V C O F C C G
L v L ~ c r ~

*
~ c ~ c o ~ u ~

* V ~ V V ~ V) ~ V

* h V ~
V ,,h, -- -- _ _ _ -- _ _ _ -- _ _ * -- R. * U h ~ ' h h h h, 1. IL
il V U~ `.
~C ~ It h _ h ~
C' W I h! ~.: Z :~ h' h ~- C C' r~ ~ o U V C' C ~-- :J O S ~ ~ IJ 5.
'J C~ ~ ~ Z
~ ~ r vJ c ~ c ~ r v ~
o v --h' o K C .5 V` ~ C l.J C _ 1~1, ~D 1`
~ c) O rO ca cl cc~ c~ o c~ o o o o VJ W ~ O _ N r ~ r v~ ~D
v~ z r- ~ r .t ~ Vl U~ ~ v~
r c~

G5~

~~ r L ~ , m 1 C ~ -- . ~ V~ C V; ~
v _ . ~, t _ r ~ ~ ~ v ~, v~ O - ~ f 1l, 0 v t~ L ~ ~; L c, F V
C 11 ~ c 0 ~ _ _ C ,C ~ O ~ ; ~ L. ~ m m K ~ O 8 -- U _~ U Ci 0 0 _ 7 _ ~ IL n 7 -- L. ' C -- ./ ~ L _ .~ IU t~ tJ U O _ 1 tJ _ .- L~ --~ C V~ C C ~ ~, '' t F ~ _ _ - -- t~ L x C O . X
r ~_ C O C E L L. C O v 0 r C C c Ir F ~ E e a c, c F ~ L F L ~ n L D n c o F F ~ C r o .0 . K _ ~ _ C V. . ,, L .LI IU F 1,1 V~
:1 ~ L C -- L E~ C L V~ 'G 'G r. ~ _ Ib L :V C. C` C L.
O F _ F C O L. L. L. L. '_ r~ U 10 1.1 8 8 8 .Q ;1 L 0 _ L C C Q~ _ S -C Ul O ~ ~ I -- -- --t' ,. ,~ -- -- '. _ _ _ ,, e~ ~ ~ C; c ~n _ C ,C U ~ c Q ~ O ~ O ~L O c r c u ~ ~ S c ~ ;. ~ c~ _ c 1f 0 r cl c _ ~ ~ ~ ~ ~ ~ ~ ~ ~ n ~ ~ ~ ~ ~ C~ ~ ~~ C~ ~~ ~
h h h~ h h h L~ .. h h L h 1. h h L 1. ~ 1. h h ~ h, ~ h h h h .. h . t, cl. C .
t~ ~ h r v c~ 7 J- -- ;J F- I-- h~ h t-- a r ~ ~ t~ ~ i . X .1 1 F- ~ F- U Ul U, ' ' t. h~ 1. h h ~ I C ~ 2 r t ". 1, ~ h 7 ~ ~ c ~ s~ Q ~ tr h ~ _ V ~ h r l 1., la, .s LJ t t, ~ C x 0. ~ I-- t~: t~ T I tr _ _ u ~ tJ t_i t, a: Q Q ~ D r -- t o ~r I.
:o -Q
D
Q C~ C tC .s ~ c ~.r m ~ .~ ~ r C h .r _ Cr ~7 .~ Q~ h C c _ t tr h~ CD c C C
C C ~^ t` C C~ C O O O O O CO O CO O C~ V~ O _ ~ Q o~ o o Q. .~ o o o .~ -- :~ o o o o o o o o o o O C.~ o o o ~ o C~ O O o o _ te 1~1 Q t~ O _ t`l I-- ~ r D 1~ ~ v C _ ~ I-- r Ir ~D 1~ Q~ ~ C _ ~ ._ .r V~ 7 1' Y C C

o K

G~

~23~ 33 ~ ~ E
c . ~r r C O . O ~I y _ C~
u u ~ ,~
C ~ Q ~ ., O G ~
A. C~l 1 5 ~ Y ~ ~ .S U
C G ~. C C
c 1- _ o C o o & & ~ ~ Y U ~ o ~ ~ ~ I ~ h -D, c ~ ~ ~ _ c ~ c a~ u L ~ Ir. a c _ ~ c S ~ c c ~ c e C c o c c c C
v ~ 3 ~ ~
v ~ ~ ~ n o S ~ ~Cl r ~ ~ { ;' ~ h 1~ o U
_ ~ C ~
~ 5 1 ~ ~L 1.; X ~ V! ¢
r~ C ~ 3 ~ 3 3 ~
z ~ ~ ) o :~ o x ~Ul ~ & & Vl ;~: _ vl _ _ ._ ~ CL tL a a. 1.~ U C C C o = ~ O Y ~
-O ~
--U

tl:' O
5 t:: C ~ C O 1~ i U tt ~ C
~') O C. 0 ~0 C C Cl C C' C~ O ~ ~ ~ C
D ~: Ja ¢I 111 D 0~ _ ~I W 1~ 1 W W W ~J U
C~ o~ o o o o. o o o 1~ _ _ _ _ _ _ _ Ol t~ N N t~l ~ ~ N N N 1`: 1~1 N ~1 1` ~ N ~ N N
o 5~ 3 b~

G

~3~

., C V ,t ~o V, F " ~ C O ~ C c O Y ~ ~ ~Y j c 7 _ _ 0 r ~ ~ _L ~ tJ C L tO
.r ~ . a tu j ~ ~.
U n 4 0 ~ O O h ~ c ~ r ~ r C t, ~ * U/ L ~r r ~ ~, h ~I L
- * ~ C ~' ~ Q ¦ ~ h t, ~. C
o~ ~ t ~o :~L, _ c ~ _ ~ -- C C t~ ~
* ~ ~ ~ * C ~ t C _ C L
* h ~ ~ * * t~J 7 ` ~ C O ~J X ~ ~ a ~ r ~ ~ r ~ h ~ r ~5 a C ~ o h t * ~ ~ h~* :~J * tJ * r-- ~ tL J ~ C _ _ o ~ o tr tr ~ W ~ t~
~ U * o v, t ~ n ~ A t, t~ * t~ ~ L ~ O ~ _ ~ r ~ C~ V, t C ~ ~ ~ r Ç~' * * h~ r h ~ ~ C -- ~ i ~ tY * * V ~ tL ~ ~ ~ C S C ~ ~ _ ~ c ~ S tl~
* ~ ~ _ 7~ r ~ t^ ~ u ~ * o * t~ tl, ~ o o ~ r ~ tt~ c~ h~ tJ ~
. * C h ~r~ _ C _ C c~ tl * ~ ~ C ~ ~ i i t~ i 1 ~ * C '' L tu tE ~ r j ~ ,h t * ~ h ~ ~ ~r ,~ r L~ i V: 3 * * ~ t. * o . .
r~ * * ~ t * ~t ;_ * ~ r ~ r 2 t ~ i? h~ t ~ ; c ~ r ~ Z
r _ _ _ ¢ . _ _ I_ I-- _ _ _ _ _ _ .~ _ .. _ _ 1-- ._ .~ _ _ h o .tt~) ~ . . .. .. ..
CtJ . C C. tt . C` C tr -~.~ r^ _ h CJ t~ O O ~ O ~O cr _ N Cl ~ c o tri o c ~ c~ tt hl :.C; 1 Cl O tJ ~ C r~ C. h C, Ci h~~ C, O O O ~ O ' t~ h; _ I~' V~ ~` t7~
al~ t o o c~ c ci C o t~ ti c~ o r~ 1 V.h~ n ~ ~ ~n ~o r~ t~ C _. ol rr ~ C t~ tr C _ N ~ ~r Ir ~ tr tr e _ t~ ~ V. ~C r~ t& tP C
V Z ~I N r'i r'i N r~l r` t"l N t~l N ~ r~ N N ol ~ N N N N t~J t~l N ~ N N N N N N t`' rl; UN tU~' t~ t~

C.
h~

r C, ~ . ~ L
Cr _ ~ w ~ .. r Cl L .' .r o~ ~ ~ ~ c ~ n O ~ tJ
e Ll ~ ~ v ~ ~ ~ r ,, ~, ~ L
* n LC~ Lt 111 -- ~ '~I --' ~ V ~U " ~ r v _r o, ~L ~ ~ ~ r~ C~ *
* F r c ,~ 00 r ~ ,, _ _ o r: L *
o n ~ o~ c ~ ~ L ~
~ ~ ` ` L t, ~ ., ~' ~ c V~ L/l 4 t, C . ~ T f r~ I vl C ~ -- F -- L C a *
C .,_ ~ U E~ ~ V ~ r rr v~ ~ ~ r . CL~ ~ x w~ ~ v~ L T~
t ~--I w L C ~ ~L ~ ~ ~ U C ~ 4 tL, _ 3: Vl C ~
.S ~ U ~ L. V L D ID ~ V C ~, r O ~, r; 4 tJ
C, O _ O C ~ L ~ ~ o v _ r * ~ tC r c r~ ; c F r P ~ '~ ~ C ~
r c C ~ I t- ~ _ U ~ t: r ~
o C ~l ~ vJ r ,. L c E T: ~ E O c r r ~.1 * L~C C ~ VJ t I C tJ h _ r- e v r, _ ~ 5 _ t~
* Lr-- ~.1 D _ V; V t~ ~: b r ~ h r ~ r, ~ ~ rt - ~ z ~t ~ O~ rt f ~
r _ _ _ _ _ _ _ _ _ _ _ _ ., _ _ ~ _ _ r D J. C G

-~S
t r~ ~J
O '~ _ tt ~ V; ~ L
tt C C o C.

~r .c C~ O O
~ ~ ~ r~ N N D 'D D D ~ ~ ,~ ,~ J~ C O' O -- ~ ~-- V U' D ~ IJ' o o v~
a~ r~

1~23 r L _ C ~
r o c L . ~ -V F I I C --, Ir C -- C ~ ~ ~
C w C L t~ ~ Y 11 ~' ~
O O ~ tv 31 _ 3~ _ C ' ~ ~J C r-~ ~,., _ IL T r _ n L C IC r w n v~ h t- ~ r;

C C C, o C; ' _ C C ~7 C , v t, 11 :~ L C
v ~ o~ v w 1~ ~ ~ _ C~ nl t` ~ n ~ n L
t~ L C L ~ V r ~ 1- c 0 r 5 c ~ c c ~ r ~ c 0 c c c `- o r ~ w _ C
rl 11 L L. 1~ 111 r -- 01 : ~t r h ~~ ~ G tJ
V ~ L L _ 0' V! ~ t` t/ C h _ X 7r O O
~ rr, w -- _ h ~ ~ r t v - t ~ c ~ r . --7 ~ i c a ~ ~ v ~ ~ t c r r ~ t~
h C', ~ L~
r c Lr ~ t~ r~ i hl I ~ _ a>
Cr ~ r h; ~_ 7- v~ _ hl ~ r 7 ~ ~ v~ u r r ~ ~ G r ~ I rA t~ r- ~~ _ tJ ~ C t. CL ~ r~r r r r C~ ct O .n r O ct a t7 r t ~ n o r 7, h. ~ , r~ ~r, t~ n & ~1 tr C` ~r r~ r j c~ 7 tJ i~
c r~ ~ c L .4 rt Cl t, c 1~7 C ~t h V r~ C c a C l,. C c~ C -- t, c .1 r 7 7 r ~r ~ V
t~ h 7 7 1- 7 :< X hl rL ~r D r t l r" t~ r tt) r77 ct 7 tL.
cr ~ ~ S ~ ~ ~ tr C ~ :~ ~ t, ~7 r ~ ~ ~ _ 5 ~ 5 C a c ~ tr ~s 5 ¢ ~ C ~
h :L } _ t, V~ S S = L U ~ --I Vl t& - r ~ -- t t x t x c x I v t v x v. = i ~ ~ v ~ h 7 7 CL 7 7j ~ ,7 7 o r r r 3 r t i C~ hl h~ ~ r 1 r W ~L ~ 7j, ~ rr r ~ tr r v r } ~ &

t~ _ .. _ r U t~ tJ :~ _ .. =
C
~r h ro CL. 1: Y ~ CC 3 ~ . Y r~ r tr ~ c; r~ C r r~ r~ c c tt r~ r & tt r~
~r o o c ~ ~a o rO
t7 Ln c~ ~ rh~ C~ _ C, t~ 2 Lo c r~ L; ~ _ ~ C7 h~ h, ~ ~ D D tr.~ ~ LF7 t~ rC~ t7~ ~C~7 CFi ~ `O Cl ~ r Lr tJ ~7 7~ ~n ~ c 7~ r~ c t t; CC et ~D r7 r7 rr r~ tr r~ ~ r r t~ t r~ ~J C 7~! o r~ Ln ~ r C hl C _ 0I C^ Lr ~0 C~ r h^ t,~ h~ ~ C _ r~ ~r r a h7 C~ C~ C~ C, C r O O C C~ C, C~ C C. a c c ~ c c c~ c c c c o c c c c c c c c 7 c o c~
D ~r O D O O O ~ o O O O ~ O O O O O O ~ O ~ O O O o o O O a o o o o o a o o h v Z r~ r~ o a o t~ ~a Lo o rO rO ra Ct _ t~ r L~7 ~t7 r; rD r~' r~ 7 r~ r~ r.7 1`7 r~i Crr C) "7 N _~ ~ Lt' v~ r` rr c _ r ~r r r~ r~ ~ r~ ~ r n ~ r ~ r~ ~n r r~ ~ r ~ ~ r o rl rn ~ r~ ~ ~ ~ ~ n~ l m ~ rn vt ro r b~
-G~l j - c c - vl ~
r .~ c ~ _ r O . O1~;,, C ~ v~ r ~, ~ L ,,C C L. C . L. L
C v, c c - . c: ~ r ~
.v~~ L,,_ ~ ~ v~ L r o C 1~ 1 ~ -- C D C ~ L: C
r rv ~ O _ L' _ Ir C _ ~ c c L . r _ . ~ L ~. o ~ ~ . - r ~v C~
~ o c~ ~O v F C " ~ C' T ~ I~ r V Z ~ ~ J X O ~ x C ~ Vl ~ _ ' ~ ~ ~ --C t' _ g C ~. O F _ L~ vl g C , r C ~C 1, C v) C )- r C r ~
C C C g '~ c " ~J It C ~J L' C --~ T ~. :. ~rl ~4 L, ~. 1~ ~ ~ V ~ r ~ "I ~1 -- C -- C -- C g g -- ~ C~ ~-- ~ C.
V
L. -- _ _ C L, L~
L' _ r _ _ h ~.
~ v h? c _ ~ c~ ~~! ~! ,,, .~ ~ Z ~ D ~ _ S ~ l ~ r ~ ~
o. 1~ I C C~ ~I n _ - c~ C 8 ~ _ n ~ C F- ~ r 5 c C ~ C ~ C C t~ L ~ r v ~- c c ~~ c, c. Y n Y c c ~ :. L ~-- f- F ~ ~ ' L' C. I.~, ~L 18L ~ D C r _ n c Y ~c _ _ --~ _ r _ L, r c ~ - s ~ V C ~ C ~ :;. 7 ~ C U~ C ~ C :e L X L, I ~ ~~ V~ . C. O :L C C~

.. h W L~ V~ U, .. y r =~ C v .~ ~ c z w ~ a ~,;
L :It IL L ~ C I :r ~ v, u, c u. u, c c c r ~, c, n c Y c c c c. c. c ~c _ c c~ c, cc c -- - c . L
f. ... .... ... .. ... ~ ..... .

r h ~ h r c 1-L r- r- o ¢ ~.~ m L' '" o? _ O c h r. oc o n, ;c 0 ~ u c~ r c~ L!Uv.~¢C~o~r.U~UU~r¢~rv~n~r ~ct~co~_r~
o _ cr ~ I-- o c~. c~D ~ VO OD ~r r o s v_ L s s v~ CD O W Q O O ~ O 1"1 K Ko ~ i h -- ~1 ~ C ~C LD n ~ rN r~ r r ~ ~ 0 ~ 0~ OD Y~ 0 0 0 O~ ~ O. C7 c o c o c o c o ~ ~ c ~ c ~ ~ c c ~ ~ o ~ o c c ~ c c c o c r cD cc o o C~ o o o ~ C :D O O o ~ o o :1 o o o o o O o o o o o o O O
u, r. ~e r cP o ~ r v,~ ~ r 0 o _ r ~ ~.r v~ ~ r c c _ r ~ ~t v;~
U~ Y .r ~ ~ ~:r V U~l Il) 1~> In V~ V~ ~ V~ V~ D ~D ~? ~9 .D ~D ~ "".~ r ""~
v~

h' 7~

~2~

C ~ ~ ~n C
n ~; T~

C ~> ~ C L
c n .n r v _ * ~ -- ~ ~ t ~
" r c * * ~ ~ L. ~ ~ L

* ~ C
1~ _ D
* ~ u ~ W ~ U~
W~- L~ r. i C i ^
L~ _ ~ r ! ' " '` ' ~ C ,! n . . ~ L ~ n 1. ~ n ~ n ~ s ~ C j ~ n _ ~ ~ ~ C ~ ~ ~ ~ Ul ~ E ~ ~ --~ ~ ~ --Y
* ~ ~ ~ C c n ~ ~ ~r n. c ~ G O .I t~ t-, O C !' n * h ~
C L~ ~ X 1.: X
1- = * :5 ~ a ~ ~ n ~ L ~ n ~
Il` ~ D ~ L. ~ -- ~ ~ L~ S C ~0 ~ ~G` -~ o ~ ~ Z j _ o ~ o ~ ^. O n _ :~ ~ *
* C *
* ~ . ... c ~ 5 *** ~ ~ 3 i r* ~ * : ~ ~ u u : : L.
, , . ~ Y , . ~
lL SJ L' ~ ~ Z
o h~ .. .. . . ..
Ll C n ~ ¢ _ G

S O ~ L` O O O O
h /t O O n~ _ c 1.: a hl C' a L. o ~ o a~ O O ~ ~ h, h. 1-- rj b. C' N ~r C C <i' r, c, G C' O L' h. ~ r, ~ a L h. _ ~ ~0 ~r aJ L h' O ~ ~ I`
10 G C O C C O O O O C O C) O C C C, C, O ~GD cl Cal L~ LC~ L` L`
r2 a G O :~ O ~ O ~ O O G' ::~ O O O O ::~ O O O O O a o o ~ D D D D ~ D o~ ~ N 0~ r ~ cr O O O O O O O O O ~ _ _ _ o o n~
hl 7,~

ffl~3 .,<
F 'C C ~ c D
~a r C ~ r r c .. r r D

-- '' D ~
c crL o c 1~ ~ r C _ ~1,C ~ , _ -- Z
, " Cr r F L. V ~ U ~ r~
r 1l o, L _ F ~:
V L,~ U ~ V C
i ~ F U
~ U ~ _ r i ~1- i V ~ _ C C
C, r ~ rr c v,, c r- 5 r, r- a- ~ c ~ ~ h h r. . ~, r r~ j C j 5 ~ ~ c . _ v _ ~ L j L~
~ h) 1_1 ~ C~ 11 ~ L !.1 O 'L _ S ~L :.~ i C i i r~ ^ . Y ~ ' cl c ~ r! c r- _ C r _ ~ r- v ~ r c rr r~ ~ c rr C 5 j ~L V ~ ~ ~ j V
j h h j K ~ _ :~ c ~ O _ ~ ~ _ y j j c Z r o c, o c o ~L ~ j r~ i r-r~ w - ~ -o ~
~ ~ w o ~ h h-~ rL r; r; y c; r~ c ~ c~ c -f~ - v~ r~ ~ N r VJ
C r~- o ~ a~ ~ er r~ r r r r_ rr. "~ ~ rD r~ r~ a C ~r ~ _ r ~
cl ~r cr ~D~ ~ v~ V~ U u~ ~ ~ U ~ N r v~ r_ r In rr K r~ rr rL rJ h' C N rA V rl: ~t W ~ rr r~ c~ h ~ ~r h~ C~ O O O O r~ O O ~ O o O O r.~ C C c~ cw; C C C
V~ hr~ U r~ r~ ~ N r~ N '~ N rV~ `D r- r~ ~ ~ ~ r~ ~ ~1 ~ ~

vl ra r~

7~

n L
V " tv Vl ~. V t~ ~ ~
c _ ~ ~ ; r e C
? ~C tU ~ C
L ~ ~. W C
F ~ Vl -- F ~ -- t _ n O ? -- ~ C :1 _ . o - a to t vl -- .u Vl w ~.? I
t~ ~ _ tù C _ ,, C ~
L L 1~ J:D T ~ t~ _. t J
c .~ r r tJ C ~ C r t~ ~ L
'.1 .? t~ '.. ) VJ W 'Y Z _ '.~ ,.
_ _ _ _ _ _ _ _ .. _ _ .~

*
.-* ,", C I C ~ ~
* h * Q ~J t~ _ r ~ ~ ~7 ~ ~ _ ~r ~ i tr C V, I-- h 1- _ t ~ ~ = . h h _ h~ * ~ 11 " V. Ct~ _ _ C V Z -- ~ = t~ 2 2 1-- ~ ~
C ~ tr . t~ C~ h. h h ~ _ t t ~ h~ .1 J
V, C j ~ ~ I t? ~ ~ tr ~ ~ o ~ O ~ ~ ~ ~ ~ _ ~ 2~ h.
t_ _ V V ~ 2 ~ ~ c c .I h ~t. h tr C ~ V, ~ :~ ul T V C 5' h ~ c V. ~ h h ~ _ ~ _ j t _ j _ _ j C j V
* ~ * hl c~ _ ~ O O " Z~ ~r I-- 3' g g t~ tt t~? ~ ' ~' c * c * v. C ,~ E C t~ V V! C ~ 1!. ~ C t~ ~ V~
* ~ ~ ~ Y ~
1~ h. _ Z
* 3 ~ ~ ~ n ~ z ~ ~ c :~
~ O O ~ t~--~ h ~
r ~ c o ~ ~ c ~ ~ 2 ~ C
r ~ * ** t I ~ ~ h!
h-- ~ t ?
t _ ~ _ ~ _ t ? ~ t~ h o ~? t~ ~ t; t; ~r r~ tr~ tJ t~ t~ tr; C C tL C
-t o O UO~ ~ ~a tJ t ~ h' :r ~ ~ tJ h 1~ r ~ O _ ~ I~ rl C ~ ~ tr tr, tr h C tr _ hi tr C O C ~r t~ tr t~ q' C
D à t~ t~ r L a? a t~l r tl~ t~l C t~' O _ t ~
:.
h~ 3 h~ 1~. ~ h; h a O C~ O o O O -- _ ~ -- r~ r~-C O c c c c -- -- _ -- _ _ _ _ _ _ _ _ _ _ _ _ ? ~t OC~ ooac C: oooo ac~ooooo 000 V, I,~ G tr~ c t~ ~r r Yl ~? Vr~ t? ~ ? r tc t~ c, _ t~ .r ? r ~? 01 C _ ct ~ ~ V .r ~ r vr ~ r ~ .r ~ r .r .. r ~
-C? r :~L23~

U , C
~ ~n ,7 ~- L, F
C r 3 F r u ~
. O F ~ I~ n c _ o w t~ J "~ r . ~ r L~ u u~ ~ v v --f C
c o ~ _ n~ o 11 ~ X ù-- ~' ~l ~ ~ c v _ u o t t- ~ O r ~ ~ r r ~ ~ _ r 7 ~'I U--m ~ 7 ~ , _ _ o U o t O v _ v " ~ F F F
U _ C ~ .~ F " ,~ V ~ O U ~') ~ t, n ~ n ~ L o ~ ~ ~ N ~, ~ ~ LV `' ~ r C . ~ . L. 0 V) _ -- .. g c r r c r. n U; ~ ~ c `~ sJ _ _ _~ ~ C ' U ~ ~ i .. i a LJ V~ r ~ E C V. O ~ t l ~ C ~ . C ~ A C . ~ v ~ ~ t ~. ~ ~ u ~ ~ V ~7 t L^* * C _ n E v c ~ cc ~ U _ v~ _ L~ 1-- V L- ~ V ~ V ~ s h ~ :Z
* :~ ~ c Y ~ ~ v ~7 0 ~ :1 ~ e ~ 7 1 ~ I o ~ ;_ . i ~ i c, i ~
* -- ~ ~ L~ L ~ ~ I 9' ~ ~ t L, I L ~ U ~ , ~ L L L~ L~ _ ~ I s~ s_ ~ _ C; . L. c ~ c 0 ~ ~C7 r C~ V~ t C I
v Z ~ ~ t~ ~ L t~ ~ C v~ u ~ ~ C ~ s, ~ 2 ~
* ~_ * o _ _ ss ~ ~c . F t _ _ j S L ~ ~ r -- c--. v:~ . c--. c ~ c ,? ~, u.
~ ~ ~ E o _ o ~ r ~ v. o n ~ fi E L ~q '' ~ _ _ E ~ 7 ~ 7 ~ U ! -r- o ~ ~ U E~ r ~i ~ c r ~ u ~ 3 c 3 rn * ~ F C C C~ n7 L C C C~ ~ C ~ ~ _ Z ~ ~ Y Y c ~ ~ ~ 3 5 _ ~ _ U. ._ .
o o h: .. .......... .. ....
D .. Y .... Y ..... S U Y . ~ 2 ~ .. ... ~ ...... .. ....
-r. ~ V 1~. v~ ~
o 7 o U~ o N o hl O ~ C m N t. l N ~n O N r1 C, ~7 C~
L~ N U~ e C ~ C CD N o. U~ N ~ _ N r- D ~ ~ D
tl r~ V, r- ~ C ~ r ~ I c CJ h _. o r_ t ¢ C. o ~t o o o o o o o o o o o o o o C7 0 o o o o U~ 97 97 D 9D 9~ 117 ~ ~ LJ. Cll S1. S7. 01 :~ ~ L7~ O O O O O O O O C~ N s~ l N N N N N N N r ~ ~r o ~r o ~ r o .~ r er .~ s v~ ~ u. U~ u u~ Lr n vl Ln ul u~ un ~n u. ~ u u~ Lo ul u~ v~l vn Ln m u~ u so S

7~

~23~ 3 ~ C O C _ .J
c. o r7 U -~ U o ~ ~ C~
~' ~ ,u . o ~ v v r, ~ ~ ~ ~ F
,: L . o ~ f ~ o _ v ~ 11 v ~
C t r U n ù ~C ~ O -- ~
~ o ~ . ~ o C ~
o v-- ~o ~ r C o o o o C o .. ~ ~' D _ o ~" o O ~ C ~ U O C ~r V r, 5~ V U _ '~ V _ O ~O
o _ .. r ~ c ~o o rl L ~ ~ L
C o u ~J r r .n n . t F -- ~ ~ ,~ C . C C --' n ~
r~ ~11 C _ vl-- ./ L O ~ 1 L V ~, C C _ v o r ~ o r ~ ~ r U.
O O _ C ~ O 0~ U _ r o _ o O F ~. o U ~ c _ c ~ ~ D
r _ c ~ ~ o F ~ ~ _ _ Q _ y i- C C.
C CL ~L a 2 ~t C ~' C~ LJ '~ O D. ~ ' Dj J
Cl ~ 1 C VJ 1~ 2 ~ C t_ ~ C' 1- 5 -~ ~J C' D 5 L ~ t f-- ~_ E~' 1.1 ~ ~ .J D. ~ Ct_ ~ ~ U C~ S ¢
- -~ U U -I :.; - C ~ ~ I U I ¢ 2 ~

.. ~ ~ t ~ _ C, _ C` ~ Z
I~ U~ W C ~ ~ ~ C~
O

O
v 1: ' y U ~ ~ C~ ¢ ¢ ~ C ~
f. ... ........ .. ~ . , .
-1, r W ~ h c~ _, t C Cl C~ C" C ~ ~ ~ CD U~ O U --~ C~ C~
n:c c~ a ~ _ ~ c, _ o c c:-- c--O ~ CD .~ ~ C~. C7. ~ O ~ _ .. 0 N ~ ~'I ~t ~-1 o v~ .tl ~ ~ .. n ~ ~ ~D ,~ ,~"~, I~ C ,_ ~ ~ ~ C~
S~ "ISO Q ~ O O O ~ O O O O O O Q O C~ o o Wr I~ CO Ir C. ~ D r_ 5~ O C` _ o _ C
bl 7~ `

r. .
v ~ c, r~
t~ " V ._ 4 V Ir V r V U U V _ C t v. 1 v ~ v ~ r v v 0 4 C 11~ ~7 4 _ Vl ~-- r m ~
_~ 4 r~ c 7 C ~c; v C ~ x m r ~ r. o u q _ ~ o u m v q r~ I r v v o F C _ L r V V C ~ V t j ~ ~, ~ U ,,, ~,.' . C V ~
~ O ~7 i i r ~ w 4 C 4 C C m C U
D7 ~ _ .5 ~ ~ I ~ E, c _ '.1 -r J U _ .i h I ~ r -- C~
C ~ t~ W
~5 Vj S C` h h. ~ ~ t ~ _ V.
W ~ Z V, j ~ h j h h -- c c t 7 ~5 ~ ~ C~ r~ ~ r~ ~ ~ ~t r~ r~ j r ~ t 7 ~ t 7 ~ ~
h ~ t~ h. h i i ~ tr I h ~ tlC I t~ i I h V ~t ~ ~ hi ,~7 j I E ~ -- i ~ Y V L ~ e _ _ r~ r~ U~ - v~ t~ >~ v r~ ~ 2 ~ U~ t~ Q ~ ~ V. ~t r-j U j f ~ t_ 7 G r~ e ~ ~ h i c ~ G :r ~ h, ~ 7 7 .5 C 5rl j v _ -, c 7 t, t e j~ j G _--. " I X ~ n tJ q5 7 t~ _ ~7 7 t C~ Z -~ ~ ~ rA~ E, -7 h. U r~ h errJ ~ c r ~u~ w ~ ~ i t t~
i h z Ua ~ r~ ~ r t _ _ _ r7 1_ C' h~ 7 _ _ _ tJ h~ h.
o ro r~ t; r~ h. r K~ rJ rt - ~ rL tr; t tr; t~ ~ t i . . IL rJ a c ~L h~
-.er N _ L~ U C ~ h 1~ C
_ O r~ ~~ ~ O ~ O t~
tJ r rt ~7 ~ Q O ~ r ~ 3 rn c ~ G~ r7 h~ ~C rn r7 _ ~
¢ Q _ _ ru ~ rJ 0. ru tn _ U N N rJ~ N c~ _ ~J r~ N
t r~t r rtt~a : c~.r ~crr ¢w C~rt~a r h Q ~ ct ~t ~t ~t D n rq n rq ~q ~Q o r~ o cl o o o t~

r~7 hl v~ q r- r~ ~ C7 rl7 r7 tu 37 ~7 D~ r~7 r~7 rJ~ o~ rN tn tn rrn rVn rr` tr~l ttn co C ~ r`
_7 r ~o v~ ~ v~ u~ r r ui v~ U r, u~ r r r V7 ul u~ r U7 ~o U r V7 U V7 u~ .

a~ r o7~

~.2~ 33 e c v c O , V.
~,, _ . L ~I o . o~ r r ~: -- F ~ ~ t~
v v r 0 . o ~ ~ ~ F ._ L C r ~ ~ ~ -- r~ . n --l ~ F
n D O c C L _ O r~ ~r v~ C _ r h V. T ~. r r ~ cL. ~. v Vl v ~ v ~ _ S- V
:r _ v O --. C' CC ~ L C C C C -- V
u o ~ v~ r c v o v F _ c-- O
V V ~ O r V rCCLL ~ . r _ ,. _ _ _ _ .. _ _ .. .. .. h' . U_ C
L ~ :r. - C
Vl V V~
V ~ ,, _ _ _ _ h ,~ ' Z .-~ -- r ~
~r c ~ c h, ~ V, j j t _ i-- ~ 7 i u~ u --~ ~I rL ~ r~ r~ c rl tL t~ c G ~ ~ _ V V V
S h ~ _ O ~ ~ O O C O _ O -- C ~ 11 r i rs o ~ T CS C ,, ~,, J C C C ~C C C r rs Z T n c~ s :~
h ~ h C V` i- ! L ~ h h Vj V r -- v v~ Ir C C :~:
h ~ ~ r~ t4 r C~ C ~ C h ts ~7 ~ C. h _ ~ _ V, ~ ~ _ C _ _ ~ 47 ~ r ~ --v~ c r r ~ ~ r~ c. s r c t~
i r~ ~ i h~
C L) ^ r rL A t.,. t rL rL -L r r. r. r.. c~ s r~
r ~ ~ rs ~_ rL s = ~ 2 - ~; S 5 = ~ r- ~ r~
V~ 5 5 C i_ ~ ~ C h. ~ c ~ ~ C C .. ~ ~ C ~ ~ ~5 C h~ i h ~ ~ U V. s~ ~ c _ r ~ --5_ ~ C

Q - r ~ u ~
O ~r~ r _ v`
r ~ C r-~ U
~ h hi ~C l V~ C ¦ ~ r C
r ~ o r~ h O rs ~ _ _ h o h .... - . .............. ... .. .. .. ...
r~7 r. c~ ¢ r . r- U L ~, L l.J L'; L L L, I_ r 1, Ll c, C C` C', ~.1 L L c~ C` C ¢ ~v l_,..... . .............. ... .. .. .. ...
--v' h h I_ h~ o _ _ o o ~ rA o ~ rJ _ h. L. ~ r7 C r~ rA ~ r~ r~ r~l r~ r~ ra ~ r~7 h r~ rC~ ch O rr h r~ h r~
_~ r~ r ~ rC~ ~w Crr~ ~ ru r7 r~ N o N ~ N r~ N ~r N N n4 ~ r~ r~ r~ r. r.~ r~ a v --N c r rv ~t r r~l r~; o _ r~ r~ VA r- ~ c c c N ~ n ~ r~ r. c c~ rA v~ r- rJ~ c) c h _ ra ~ ~n r o~ r c~ h N ~ ~0 r~ r~ c c r^l V
hl c~ Q c~ c~ O O W W W hl W cl hl ;~1 hl h~ W ;.. h. 1~. h. 1~ h h. O r.7 0 0 0 0 0 Cl ~ _ _ _ _ _ _ N r.~ N
r~ C O O o o ;7 o o o c7 cl o o o r~ c7 e7 o o -7 o o~ r~ o c7 o o r.~ r.-~ r r~ rO rC c~7 rc~ o~ rO rO r~ O O r.7 C
hl vv~ rO ~ O _ _--_ ~----_ _ _ r~i r~ ~N rr 'r rV~ N rN- ri rr~' rA ~ rA r~ 'n ~ 3 ~j O--~ ~ ~ r U7 r~ 3 ri O _ r~ r ~
17 ~7 V~ 7 ~7 ~O ~D 'J7 ~7 7 J7 ~7 VJ I ~7 .D ~7 ~7 V7 .~: V~ V7 ~ 7 ~7 v7 VJ ............... U u7 ~7 ~7 v~ 7 ~ 7 .~7 ~7 ~ a v7 ~ID
~A
~17 K
r.~

ù ~ C a, ~ U
c ~r ~ .s --. ~ G ~ 1 h 1 z c ~ ~ ~ J a:

~` .
r-- O
~ ~n .,_ ~: ........
_, ~_ ........
O

C C h. O b. 1. 1. ~
O t`~ C' N ~J ~J .S O ~'1 1.1 Q N N N N ~ ~ 1 .t O C:~ O O O ~ C> O O
e o o _ N ~
-c ~ G' ~23~3 , C
V C
U o C r ,J
. F ~ O .r U
o _ ~ ~ ", ~ ~ ~ C . ~ ~ o ~ ~ O ~
~1 V ~ C ~ i o ~ C j F eo O ~ ~ ~ O v n _ _ F 1.1 _ ~ O ~ O ~ _ O O O i i~ r ~ ~ C C ~

~' O V . C 1~ C ~ C ~
~ C J ~ e C n o ~ I" o o ~ ~ ~J o o v C O ~J ~ ~ c ~ ; O c, a. o o c o c o C ~ i c JO~ -o ~ r ~ o C C ~ ~ " ~ ~= ~ O
., ~ V ~ U j 4, ~ ~ ~ - i C _ o cr ~ D * -- -- -- :~ ~
U ~ ~ ~ ~ * ~,, o ~ Z a u u -~ ~ G ~ _ j O O C ~ ~t~ li v C ~ ~ ~ G . ~ * O
G J ~n IC~ C E J ~ o 1 b ~ _I C _ ~'~ :.1 '` X ' Y~
li ~ v o m o ~ ~ o ~ 2 ~ O ~ O --1 ~ _ -~7 h ~ ~ ~ . .
c~
. .
-X
cD m r O'~
o ~ J7 r--o~ o, a: . G' C2 C r'l r. r~ Cr.
O o o Cl C~ O
~n U ~ ~O--~rm~or o~c--~u~7r~ ~rv~or.c~

GG' L.~

7~ `

v a -~ .

L L u~ O, L~ _ O v ~ _I F
IL ~ L D C
V O ~ O r al O a L 1. F . v L, a _ r V r ~ o C F
L -- a F C L 1: C L
c r c c _ c Y o ~ l n, t~ Q

r.
N C~ h ~ t~ h ~- C ~ '~
a ~ ~ C ~ , c ~ c ~ 1 ~ C ~ f V~ 5 ~ C C _ C C :~ t~

S t~ Ir ~ t- ~ f tJ C ~ tJ ~ O U U ~ e`
r, ~ r ,_ c~ ~ c .. o Z ~ _ , _ _ N Z .J C hl o -- L~ Q r' ¢ Cl: C
--U N C U ~ N ~ _ C~ r C t~ t~ C ~ ~ N ~ N

c r ~ c, .s ~_ w c:"~ r Cl~ ~ ~J W
] ~ O O O O O O O` C O O C; O O O O O
~n Z ~ ~ .~ ~ N ~ ~ N N ~

Ir h:

~.%3~3 .. C U
~ F F '-C
.. L. C L. O
O ~. r V ~ C~ t~ u ~
~ 0 C~ J
4 r ~ ~ _ F
_ O _ ' C ~ C C
C F 1^
* t ~ 7 C~i _ .. _ 1. c 4 .~ L L c C
* X * ~ O
v v _ r. ~ t ~ ~, ^ U ,~! r z _ v ~ ~ I _ c ~_ r ~ >- . ~ tr _ ~ C ' C ~ I_ ~ ~ tr C. r ~ c~ a 4 ~ Y :-~ ~ . x Y ~ ~ * c, ~r t, c o tr ~ ~ a r t~ r c c c ~ 1- c ,~r r r t~

* O ~ V ~f _ ~ t, ~
4 * * * o ~ U g z ~ _ v h~ V T ~t O G :~ a _ rl ~ Z ~ O ~ r, ~ ~ U ~ G ~ r~ O
~ ~ ~, V t ~ r~ C ~ _ 1 -- _ tc V C o 1 J r_ ~ V,J ~ J ~- V, S C I V ~ rc o ~ ~ ~ 1 1., a i, ~ ., * ~
r ~ ....... V a ~- ti ..
* * :~ * ~c il ~ h`
~~ 4 * W ~ O ", T C
4 * ~ ~, G X

o hi ....... . . . . ... .. ....
tr C C t ~ C C~ t~ C~ C C C. C C~ tt T L C, C` C. C
z Cr C
U r~ ~D a~ In V, ~ ~ ~ r~ O C~ U ta r~ r- N t~
1~. C C r~ .6r ~r C a C r^ tt ~ . O ~' ~D r^ r C O

rD C~ _ C U7 U C~ r ~ O ~ rl r~ ~C tJ r CC ~D ~ '.0 ~ C LJ U` r U Vl r ~--O U r~ ~ C~ O r~ r~ r V t~ a~ L~ ~ o t~ tr~ _ rn Cl ~ U r t ;J~
tc ~ o c~ tr~ a c ~ c, ~ D CD t~ ar U C ti o _ ~ r tC tr t~ C t~ C C~
~; O iD ~SI rAI CD tt~ trl CD ~ t a~ t c~ t t~ t ~ ct o ~ ~ t t a a r ~a ~D D
ca ~ o o o o o o o o c~ o o o o o o o o o o o o o o o o o o o o o rn w ~ , r~ Cr ~ ~ ~ ~t r r r ~ v~ n ,~ v~ r' ~ r, ~ a a ~ D a CD tr C~

V, ~

~/

C ' 5 o n rr C C ~ r ~.
c C v ~ rr O ~ F 4 ~r C r o T _ . . 4 a E a ' ~0 4. 0 _~ ~ Vl O V ~
L- ~ 'J r., r v. L 'J -- 4' 0 n ' C I a ~ C CtC _ _ ~ 5~ .~ O V ~1 ~ 'A _ ", r ~ _ ~ 4v C, C c O r_ _ T D m r a ~ C' _ C~ ru C u~ O u _ ~ t~ a ~ ~C U
c~ ~ ~ ~ r l r -- 4 F O r --V ~ ~ a t~ .L 4 ._ r .... _ _ ~ O
-- ~ ~ t- ~ C ~ ~ t. I . C _ ~ 5 C h * ~CO ~ < ~ ,v ~ O c j _ vrtL --,1 ~ rC _ _-- 5r -- * ~ ~1 ~ O r, FO Cr~ C t4 CC h ~J V~ V~ I r-- . X r~ ,.! Vl _ , "~ ~ ~ c, 4 r~ I C -- C~ t~ CC- tr~ '~ ~ 5 ~4 5 ~ J C _ * r * _ i t, _ C -- C ~ C. _t~ Cl 5 ~ r`' _ " tL r~c V. t. _ h V. ~ C ~ :-. r--,,~ ", -- ~4 O I 0 ' L. _ I j -- . _ U C' tC . T _ C _ Vl Vl ~ C~ ~ O ~ r~ ~ ~ _ t, r ~ 5 o ~ r ~ c~ ~ o ~ 5 j r z r ~ Y ~ z z t rr Y a Z ~--J ~ 5 t ~ r Y _ ~ 7 z 2 r, * ~ 7 C ~ tC, OC _ 0 r = t c cr ~ tu ~ rJ ~ w t-- ~ ~ c t ! cr ~ j~ ~ ~ _ ~r ~r 5~! T .~ r~ t ~t t~
~ * G ~ L -- C U D j r O tJ hl ~ I J r.~ U r~ ~ ~ r_ O 1- t, f-- C. rr rL rr r~ I-- r- rL r2 v T r_ r_ r_ c * C ~ _ ~ ro _ 4 ru 0` ~ G .D t~ r~, * ~ u r c d C~ t~ r rl V. V I r~ V. S S r~ rr 5 a v 7 r~ 7 u 5 1~ E
C ~ 11 ~ ~ t~ ~1 W
t4 t., rr .. - c :~ rt>
~ W t~ .r ~_ r~ ; ~ C C r ', i rL ~ vJ ~ v~
r ~o~ ~ rr~ ~ v; ~ r- t r~L rr rc- ~_ 2 v CL
t~ _ _ _ _ _ _ _ _ .. _ _ _ _ c c ~, ~ r2 o t4 ....... ~ .... ........ .. ........
rr,7 ~L C C C C r 'C~ Cr-- C tC C' C U C C C ¢ ¢ C~ t; tr. C C C t; C, C. t~ L C C

--t_ C~ c; r~ vt ~ C' r~ C V -- Cl t~ v~ 1~. ~ C7 1~. r~ ~n O O ~D
t~ G U ~ _ Irl Cr. ~ I ~ r,~ r U .cr ttl _ '~ N ~ U ~ N r~ ;rl CJ N tO U :1 O ~~ ~ ~ C ~r ~ r~ O ~r r C ~ ~ o r r~rrul~rrult~ ~r_ .rrru~r ~rro UlU rru~eu~lrul O r. r~ ~ r~ ;:n r~ ~ r ~ r~ r~ D 1.1 r.. r.. r~ O Q r-- r~ Y7 r~ r-- ~ ~ r r~ ~ r~ 1-- 1_ ~'Orrr a~ m ~n ¢ r~J rJ r~ ~ t~- t~l rG ~ t~ ~ N N ~ t~ r~ ,r~ ~ r. t~ ~ ~ h- r ~ Ir. 0 0 0 rn .~: o O O O r~ o O O O O O O O o o O r, r l o O O a C O C O O O ~ O
u, ~c 1- tr tr c _ rJ ~ .r U~ ~ r~ C c ~ r U~ r. r~ m t? O 1~ U~ ~n r ~r Cr C o: r~ rr cr O _ ,r~
V~ 2r~ r-- r~ r~ r~ D rD r77 'D rD r~ C2 rr, or~ tr. C . tr. Cr. c~ tr~ cr. cr, rr 01 o O O O O O O O O _ ~ r N r r _~ r~ 1~ r. r~ r~ r~ r~ 1~ r~ r~ r~ 1- r~ r~ 1~ r~ r 1~ r~ r r,~ 5 rC rr rJr I t~ rJr. Vr ¢ rr v: r.~ rr rr rr a: rr tC rr rr 'r~ rr ~23~

. U C~ ,.
o _ ~ r r -- L v, . ' v r C _ ~T _ -- ; C V/ C -- C T
~J o v~ C r L.
r r-,o ~ c c ~ ~ ~ Lo C ~
U _ ~ ~, _ C C L cc; r c, L T ~ 21 1/7 ~ O ~ ~ U
c . _ u r v~ c r C ~ C~ o o u c c X ~ _ ~ ~, c ~
C ~ C. ~) J C~ ,~ T
~ ~ V 1~1 1~ U ? VJ
1~! ToJ C _ _ .... ~ I C ~ _ C
~ c _ C L
h~ U
Y Ul ~ C~ c n ~ c, ~ , _ S . ~ : ~ h -- I L~ 5 C ~ .
r 3 o ~ C ~ _ h ~ h ~ ~ h L ~ I ~~ O ~ ~ ~ ~ c z ~ ~ ~ h J S ~ C h _ V C ~ ~ Z c. ~ c Dt L~ ~1 e Lr è ~ r~ c ë ~r v L. ~r c ~ v c I r~
S V~ ~ ~ h~ h1 ~ h h. IC:
1 1~ c L Y ~ ~ _ ~ 3 ~ L~ ~_ ~ V, ~ :~ V U (_ V.
.s ~
~ ~ ~ z ~ z ~ .. ~

N ~ Y S
Z ~ ~ ~ 1-- Y` h r ~ ~ x v ~ D.
o -~ h ... . .. . . .. .......
O :~' C C, C, ~ C, C' C IY C C. h~ a C h C' h. h

2 ' .......
c~ r ~C ~
~ ~ o ~ o o h` 1.1 0 ~ ~ W h. C ~ l 1.1 0 h ~ ~D h~ O 1`
C r ~ u~ ~ h~ L. W L O L ~ e ~ J ~ L VD U,~ r r~ r v c N
c~ o ~ c~ _ ~r U' ¢' h ~t e u L N C ~ Ir IC Ct~ U L c. J-- v r c~

.t ooo c~ooo::,ooooooos~ooo--:~oooo V h~ r U1 1-- CD G C _ N ~ r vl 1C ~ cD V~ O _ r~ L" .~ v ~o r cr r,~ c _ N
V _ CC CD h Cl CC 1 CD tD Ce CD a~ cr cr ~c L~ cr ec cc ele r h--C~
hD es ~73 ~2~ 3 _ C r r . -- C Ir o . V V F~; . _ _ C F
v ~ -- r T .11 r G r r . r ~ ~ C ,. C
ll r o n C ~ ~ 1 o-- r r r~
C L F o r r 3, ", F L' L ~ C r r' ~ - L r F C ~r r ~
c ~ ~ ~ r T C C _ -- _ V. T
L C ~ L ~ C v L -- r C ~ V r ~ y-- i i r r r ~ V T 0 _ r c c ~G . L T ~ ~ ~ r ~ Vl ro -- '~
~ ~ T,'J r~
* ~ l~ r; i - ~ L' D ~ r r rl ~ L rc C ~ h h. C 5 _ or. ~ o ~ .. c n. ~ r ~ _ r c r ~ Z
r~ u r,:~ .- r ~ ~ L, . L r ~ T 1, ~ _ ~ ~r V;_ a L~
~ r C _ r, V I r ~ r- r r hl ~ i r ~ _ ? ~ ,~ ~ r L~ r- ., ~ C ~ V ~ V "
r r~ ~r~ . ~ L! ' ~ J r-.-- rc 1~ o r~ h _~ V~ L C. .
U ~ F _l ~ r_ Y . ~ ~I r~ ~ r.. ~ z ~ l o r~ C ~ rA- - Z U ~ n ~ ~ U ~ X :.~ U
~o . ~ r v= ~ ~ ' c Vi ~, v ~ r~ c~ r~ c v r _ r ~ r C
~, ~ * r- c, C c 7 ~ L _ _ C -- C ~ C
~ r~ c t ~ ~ CD ~ U ~ _ 2, ~" L J _~ ~ Z ~ ~ r, ~, r~ c Cr c - ~ r tl ~ ~ ~ C ~: r -- _ :F --O V --<r O C -- ~ --V. V t. C C 3 C ~ O -`--C V .:1 ~ r~
r ~ " L= o ~
* C o t _ IJ C' i ~ ~ _ 1, r~ L E 0 0 rr ~ r E- ~
q Y ~ r ~ v ~ ~ O
r~ r L I L rl ~ ~ c t~ h _ 1_* 7 0 ~!: v V ~ ~ ~
rr ~ , ~ a Y ro O _ ~ ~ Z Z ~ T = n Y
o r~ r. ^ r. c~ rL U C r~ r~ c~ rL rL c, c C r~ r; a Ic r. C ri C r~
_. ~, .... ... . ................
-q~
O o O ~ ~ C ~, r ~r U ~r ~ C r~ r~ r,~ ~ r~ .: D _ rC ~ o r~ D o ~i r- rD L~, ~ ~ r-c r~ ~ ~rc r~ ~r r~ c r~ r~ rl r~ o rl^ C C r~ o C ~L C l~ _ r~ ;" ~tl vD ~ U ~ C rrl o ~ u ù r~ r O
LY. C rC h~ O r~ ~o r-- O~ r h h _ . ~ rr .5 c C ~~ V~ r~ ~ C C N ~ ~ rr ~AI C ~ r.~ r~ rl rr~ r~ r~ r~ ~ r^ rr r.l rr~ 1. r~ r_ r~ r~ r~ r~ ~,. "? ~ "~ ", ~
rD ~ o O o ~ O O O O O O a o C O O O O o ~ O O o O O O C O
r ~ ro r~r C _ ~ rr~ ~ U ~ O C _ r~ ~ U .~1 r~ o C _ N r~l ~ V ~O r r,~ C _ r~
~ r- r rr rUr ~ rr~ rD r~C r~ rD rD ~o ~ `D ~ r- r- r- r~ r l rr rO rs rr. rr r~ r~ r rS rs~ r~ r.~ r~ r~ r~ r~r rS r~D r;~
-C
rr rc ~23~3 r u c ~ u V -- T~
~ v ~ , _ U
F ~ V ~ ~ U U r v o c v ~ ~ r V F ::. V V L r r o ~ I ~ Vl C_ r V .~ r^ o C h C
rr v ~c c ~ ~ c e r o v~ r u T Ir vl u ~J r n ~ ol ~
~I r r ~ ~ ~ o ~~ r r ~r ~ r ~ a _ c v. ~1 c c _ _ v ~. v c ~ I
.~m _ C U _ ~ r o _ ~ r_ u ~ ~ _ u *~ c v c _ L ~_ v _ a __ _ o ~ j h r- ~~ o~ ~ a o o F C _ C - ~ _ ~. O 0 ~ O i U
~ ~~f r ~ ~ r _ r ~ ~ o u _ G V F ~ ~: ~' h ~ V~ ~ ~ C.. ' U J U _ h U. _ L ~ L~ ' c. r c rc ~ c ~ ~ . c r L' .. G ~. r~ Ol ~: :1. h ~ ~ C ~ C ~ U U ~r ~,?
r * K L~ r_ _~ V~ _ r K _ ~- O ~0 F ~ r r v L. v r ~ c -- h. C
o :L * C~ oJ ~ rl v. ~ o . 0 L~ O o n _ U 1~ v ~ v~ hi U ~ z ~ h G U ::~ U ~ = ~ I
*t r. r 0 ~ _ r ~ ~ w ~. W _ L C ~ r t c t o r v c . _ 01 C. O C O :. ~ L _ ~ _ V C~ ~D _ .C ~ ~ V ~ 5 L cl r ~ ~ ~ t I c ~ - h c c ~ c~
r L. ~ e o o _ v o ~ m rJ r~ C n l_ K. U U _ h . y o Cl 0 K v. r ri _ U al r~ r~ ~0 r~ v ~ o ~ ~I v~ ~ C s 5 ~ L ~ ~ ~ 55 ~_ hi 1 -- o c C O ~ ~ ~ ~ Q ~ ~ J-- ~ cc uU U 0 _ 0 . o j sl ~ Z '5 j é j _ L, ~ Kl i~ u. ~ _ L u ~r C = ~ U C _ ~. C ~ U C C ~ o ~ C L C L j ~ ~

* ~ o ~u r . C! 2 V z h u. ~ ~ ~ L- j ~ ...... C
r * * v~ c. c _ c U L L~ r _ I h. I I ~C rc w ~ ~ hl h r- * o ~ c '' c v oK~ " v~ U = ~! u hl U U Z L ~ ~ ~ ~ C i 5 a ~ j hl V
r ~ o c, u v u, 4 ~ ~. r ~ r~ ~ .s ~ c. u r~ a ~ u u r ~ S _ 1 5 ~ ~ U LC

-h ~ r L
U L L r V IL C. C; C; C 5 C. C

r o C ;~

h; I:D C~ ? r- IL. ID h~ N ~ ? r;
c~ a N ~D r~ C r~ u l~l J h~ V~ hl 51 3J 0 V 1. _ r~ Ir r t~ ~ c h _ r v.~ ~
hi C o t> o c, ~ r~. r~ r~ r r ~ ~ ~ r~.
v. h: v~ r Ir t~ C _ r~ r ~ v~ ~ r- ~ r. C _ N ~ .~ V~ ~C r. ~ o. c _ ~r~ s r cc ~ c _ ~ ~ v m .c r ~ cr c _ N r^
V z OD ~ ~ rl v cr rJ r~ o t~ ~ c~ u o t~ ~ ~ v v O O -- -- -- r.~J N r~ N N V t^ rr O t~ O v O rr v. v v o o v v v v v~
~ t~

., , c c v r L S I 11 V . -- ~ ~ ~ . Q T C
v~ r s ~ _ Ct ~ ~r R ~ I_ v ~ -- _ -- r h C L R t; , V
v, L C _ ~ _ v. ~ . c L o ~ r ~ c ~
r, --~ c ~ c _ ~ 'cC, t~ ' 5 r. ~ ~ c r ~ h _ v ~ _ h. r ~ . v R ~ C v v, ~ t' ~ ~ R c _ Q Q h _ t C c ~ V tJ ~ Qt, Q, t, _ ,~ V V. I.J --r t~ r t~ ~ '' r' ~ ~ ~J ~_~ tv v t, C ~ r r ~ 5, o t~ v.
L C _ L . Q' C ~ I Ir . t~ r C 11 ~ ~ ~ t~
r ~1 ~ i., tC v v C ~ ~ V C ; C~ c :- _ h C ~Cl V C ~L C- _ h~ T J ~ . V~ _ _ C V ~ L. C~
F T~ J-- 7 1 r, J ~, r r~ L _ _ Vl V~
Y V~ V _ C F O_ ~_ o~ 5 _ C ~ ~J ~> t. L.
c ~ v r Ic v~ r _ T L
t~ ~ ~ v _ vl v~ c v~ ~ - v, c s _ v, o ~ ~ v~ r ~ :~
C~ ~ s ~ L h~ r r~ _ Tl ' r~ ~L R _ _ r 1.~ o 1~
I V,~ L ~ c V, t.C Ir ~ t. V, r~ ~ ~ rt- t ~ t~ f_i C t~ ~- r~ i_ s ~ ~ ~ I . IZ ~ ~ z '~ . = ~ ~ C _ ~ Z ~C ~ V~
hi V, ~ c ~ z ~ j~ t, t t~ t~ V~ ~ h 4 V~
t t. L/ _ ~ _ ~ ; I h 2 _ _ ~ 4 r. ~ _ C V 2 C r~I h; ~J~ _ h I ~ C ~ r~ ~ L U z7 ~ i t ~ t~ c L, ~ ~ n h; I_ C~ h; ~., h~
;~ ;. ~W :~ I J ~n .~ J I ~ C Cl _ U~ t~ ~ t h; ~ Cr a ~ r~ r~, ,_ ~ ~ r ~ r' L ~ J Z x L ~ t; CE C ~ e ~ r; r. ~ Li U~ _ C _ r. C r r.~ ~ C 1- _ ~ 4 Z--_ rJ' rA h L r~ e C t~ h ~ L e ~ V h. :~ C ~ ~ C L 1- t~ t. h ~ ~ C c ir t, .C .I c c h U. 4 r.~ _ U V, z ~
:~ r. t. tL Ul ¢ r ~: J C~ C: 5 C S~ r ~D
~, L' r~ ~ 5 r 5 _ r~ ; r ~ ~ ~ C7 t-~ t7 ~ " ~ r~ ~ a ~ ~ ~ _ L _ L~ V~ Z ~
L _ e ~ ~ U ~ t~ ~ t~ t. I U ~ ~ C ~ _ U~ ~ ~ L _ ~ ~ U. L; V ~ L ~ V ~ U ~ ~ ~ t -- ~ U, i _ ~
t _ i O i r~ ; ~t h' i ; ~
~1 i_ 2 ~ I L.
r~ C, UJ U ~ C, L ~ jJ _ _ _ h ..
-r ~ ~ . L~ C L` ~C r~ t' L` C- L L' rC ~ L C L C. L` L. L` C, C, t~ h~ C~ ~ r h- ~

~ r- ~0 _ 4 h ¢ 4 r" r7 0 r- N trl _, Ll o 01 C t.~ .1 W D Cl~ ¢1 41 O a C~ ~ Ll 4. 7 .t r~ hl O ~ I_ ^1 a D ~ ~1 O t- N r l O _ N r~t t; O r~ C r~ O t~ r~ C t~ rr~ t~ ; h r~ r~ h O C ~ h r.. r~ h r~ r~ rJ~ C O _ ~r O
¢ h C _ O h C U~ Ir r~ _ rA r r C O _ r U r r C N r r ~ U r L r~l U U L ~I C r~ C L~ C C
C~ ~ O D D .r D rC~ tl; tJ D L~ W Cl~ D ~ UJ h. :~1 U~ Ll J~ . 5~ r~ Cb h. L U. ~ U ' I C~ r tJ ~ :rl r- N C~
CC CC C~ U C hL ~ C U~ U W ~ _ rlt r c~ C L h~ C N ~ ~C cr ¢ h C r~ D rC r~ .V L~ L h -- r~ U~ r C C
L.l C. S~ U. 0~ rl~ C C. .S .t .S ~ 5i D tt ¢. 5, ~ D J O CJ t~ L~ U t~ ~ O C~ O O Q Q ::t O C C~ h 41 1.1 1.1 ;1 h\
5~ ~ ooo~oooooo ooooooooooooooooooooaoo~ooooo ooo u~ h2~ ~r r~ ~ r I r~ c, ~ r ~ tc c~ o _ N S.l ~ [1 r cr o~ c, _ 1~1 1~ ~ r .o ~-- r~ r ~ ~r r Ic 1~ D C~ C _ ~t ~ o. c~ o~ o o. o~ o~ ~ o r~ o c~ o~ o o~ o r~ r.~ o~ o~ o~ o o o o o o r~ O O O ~ O O O O 0~ O O C~ 0~ O O Cl~ 0~
-o s o ~o, ~ o C
= vo _~ r _ v c . t:. z ~ r.
r r r; ~ I~O, V V ~ -- C
C F ~ c ,,O -- ,~ . W C
T - C ,,, ~' ~, V V ~, T -- -- ~ r~
V' F~ ~ - T ~ o .,, 1.~ ~r V
~ L h. ~~ r C ~ . .v r r ~ -- r LJ C~ _ ~J .J = ~ CJ IJ ~J v~ ~J 0 ~ vl r r vl _ r ~ _ _ F ~J-- C
r~ r~ r ~ ~ r~ I C~ V~ L
v F V
r ~~ -- _ C T T
s ~ ~ Z ~ r c I_ r~ Y ~ h ~ ~ ~
r~ -- 2 1~ r b~ L~ ~ h C ~ h h _ r~ _ ~ L/ L~ r _ ~ J _ 3 ~ J ^ .5 ~ LJ :J ~
r~ _ r ~ .~ er r.. h ~ C Uj _ _ h ~ r~. ~ o ~ I_ n T v~ ~ Z Z ~ ~ ~ Lh, L~ r ~ o ~ C L~
L r L L V v. r~ L.. h h: L V. V rr ~ .- h ~ ~ ~ V ~ c V h c rr Lr ~ C ~ r. Ll h L
h ~
c 2 :. 5 a hC :~ ~ ~ h-- :C ~ ~ CL ~ L~ h~ L Z L ~ C ~ i ~ ~ C~ F 5 r i ~ r~ SC~ V? Zi L~ VA~ V~ v~ C cJ ~ c~ ~ Z 5C L, h '5. C ~ C~ ~ h~ ~ C C C?-- ~r -VJ
O j ¦ J ~ ~ Z
_7 ~ C
51 ~ h7 ., E ~ L7 ..V ~ 1-1 ~ ~ h~ h~ ~ i X
Nrc Ll rr. .._ ~. C ~ _ _ .. h 1 o C ~ L. h~. C C. 3 a ' ' 3' ' ' Ir L C~ a: h~ L~

~r c. o N _ r ~ r~ O C~ O o U C~ r7 ~C .~ IC o hJ h L r- 3 N :D C _ r _ r~ r~ _ C. 1~ C C ~C rr L~ _ C V.~ V~ rC7 ~,7 ;1~ IV~ ~" r~7 U ~ L~ ~7 rr ~7 C u7 V~ r C h. h. C~ û. C _ r _ h~ tl ~ 7 ~hJ h 0 c~ ~r ~ D O O O _ _ _ _. _ r~ N N r~ ~ N N rJ r~l r~7 2 C C~ o C C~ 3 o O :: o o O o O o o O r~ O O O ~ O ~ ~ O O ~ C~ r5 3 v~ z r~ ~ r~ rJ~ ~ ~ C~ r~. r~ 3 o o O o o, r.~ r~ ~ _ ~ r.~ ~r V~ V7 1~ h- 0~ C, _ r. rr ~ v ~ CC
~ ~ 0~ CJ. o ~r C~ cr. c~ c c~ c c' c~ c~ C~ C~ c~ o C, C r_ C C O C O C' O C C~ C~ Cl CJ C~ o C, c, r_ -V~

~7 . r v ~ v ~r L ~ L r C~ O ~
_ ~., v ~, C v ~ F ~
L _ _ O L~ F C, r' Q ,~ r 1: Q ~t r 11 _ a _ ~ ~ _ ~ F r 3 a 1~ ~ v C C ~ r ~
L .~ C~ _ o vl _ * ~ ~ U J~ L
,, .. .. .~ .. .. ~~ ~ .. c ~ Ir c * ~ r C
* ~ Q ~ * ~ C _ ~ _ c ; ~ a * ~ *c ~ _ a ~ ~ , c ~ _ * _ * ~ ~ ~ *~. * 1.
C ~ * ~ ' 4 v ~ * ~ x * ~ c s * L; ~ ~
5.1 4 ~r o * _ ~ a rJ S 4 . * * ~ L ~ * *
a ~ . v~ C _ ~ ~ C: h. C, hj~ ~ ~ ~. v, _ _ ~ v.
~ ~ * C * ~ i- * j ~. h 5 Ir ~ ~ * ~ ~ * ~. I C ~ V ~ 4 * * ~ C ' 1- 1-- .I C~ 1 - ~ _ ~-- ~ C ~ ~V 1~ ~ a C~ ~-- ~ ~ v ~ h c~ v. C~ v 7 r * ~ ~ ~ i ~~, h " ~ * ~, _ n O
* a * ~ r o a ~ ~ w * E j ~ U ~ ~~ ~ ~ C~ Cj ~ . h * C ~ ~ c~ ~ * ~ *
: c * ~ ~ cl~ *~ h 1~ ~t h D
* y * ,, * ~ r r. * CJ *
* C ** ~ * -- * h. * .. ~ ~> S *
* * " * * C ~ j CL * ~ CJ * * h~ h i~ 1.
r * * ~ * r y ~ rl ~ * c~ o o z u * ~
r _ ~ _ U ~ V, _ _ _ CJ _ _ -- : ~ h _ _ .
o ~r hl .. . .. ... . .. ~
o : C r a C,, C ¢ C. C~ a L, C a -~r r. ~ ~r r.
O O D _ _ O
U al ~--h~ ~ ~ O v~ o m h hl o D ~t r~ h~
h~ a _C~ C u: _ c ~C C C h IC C c ~ C
~C v r ~ c CL~ r~ r~ ~r _ Y r ~ _ C h~ C~ _ C~ r~ ~ N r~
Q r-r-hl~h O~ r ~r ~ ~ rr o cl~----r ~ r ~ 5 U C h o r~ r Cr 5 C h _ ~ Ul r ~r C h ~" O ~ ~ ~ .r r r a~ r r 17 ~n ~n V ~n ~ ~n 'D .C O C~ O O O O O O O O O O O O O a O ~ o o a C
U hl C--r~ o~ c _ r~ .c r~ ~ r,~ c, _ r~ ~ ~ o r cr o o N ~ V~ ~c r r; r,~ c--r~ o r U 2 ~ ~ ~O c c c o c c C o oo c o c o C o o c c o~ c o c o o c o c C C c c c o C~ C O o C

K
.1 T
C ~o _ F
~v ~ v ~ r L, ,.1~ Jl ~, _ 11) Ul ~~ O ~ 1~ '~ O
F _ * V~ ~ .D; -- ~1 CC ~ 1~ *
J ~ Z
~ L~ *
>. ~ _ ~ U

a T V~ _ r u ~ _ ~ n ~ ~ h h o~ U ~ 1- _ _ ..~ .. ~ o C Q C CC C ~ C 1. C ~ = 3' Ir r ~ 1-* 'r * ~ 5, n- ~L C ~ ~
C -- U ~ C v 7 U 7 U 71: U =' U. :r C ~

.. ..U, In G
r~ V ~ * ~ O O
S ~ * r ~NC ~
~ ~ U b. _ _ c w cW c. c c, a v h . . .. . . . . ..
~r P 0: r. 1, ~ y U -~_ . . ... . . . . ..

-O O

u o r~ a N /'1~tl W ~ t W n rD N ~
b~ ¢ _ IC c _ c c _ c ~ c 1~ ~ h r~ h a: ~ ~ ~ r~l r~ _ c N N b~ ~ h~ c h~ c h~ c h~ N h~
~ a u r~ C U N tl. ~'101~ ~` U~ ` U~ r ~ r ~ o 1~ Cr C .~ I~r r r~ ~ h hl h ~ r It c b.
h~ c ~ n ~ ~ n n ~o ~n ~r ~r v ~ u :~
:1~ .Z 000000~00 oooooooor~ Oc c u h :c O~ c ~ o. o ~ e r a~
.t ~ C ~ C o o C C o C C C o o C o o o C C Cl r h' ~ . ~ h h 1~ * ~ ~ ~
~ ~ h O * ~ _ _ X .~ ~ * ~
~* .~r ~ U J ' X * *
* c v ~ ~ x c ~ ~ n ~
O ~ ,, o Q * h ~ C h Q
_ ~ h ~ ~ O ~ i . O C ;,.
Y. X * C ~ .S . O O ~ :.: h . . O tL
1~ . ~ O *
., ~ *,, 1.~
. C ~ ~ . ,' _ X f C * ~, ' ~X ~ X X
Tl ~ Z ~ ^ ~ o o o, ~ -- ~ .el 1/~ C = i ~ h ~S = O ~ ; C
~ O ~ ~ ~
O * C o O
~ ~ O X ~ *
* 1 r ~ * v C O
~ o v r~ 1 3 ~ ~ ~
~ ~ O ~ 2 ~ ~ ~ ~ z 1._ ~ _ C C U~ O C
o ~r h . ~ ~ .
Cl~ ~ C~ h~ C C' l_ , . . .

.~
C O O
U ~ r ~ r O
.: ~ O ~ ~ ~ ¢ C
¢ U ~ ~r~n C C r.~ C O UC ~ ~ C~C r.
o u~ . ~ h. r~ n 4. ~ o. ~1~ IA. .
C~ IL C 1.. ~ r~ ~r 1~ G O` .5 ¢ IA.` Il. ~
OOOOOOO OOOOOOOOOO
U, ~ I~~ C _ r ~ ~ O ~ er O
U~ r O O O O O _ _ _ _ _ _ ~ _ _ ,r~ r~ r~ ,r~ r~ N r~ r~ ~ r~
~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ _ _ _ _ _ _ 1~ Y

~2~ 3 u c G

F ~ n t~ c, ~ _ a ~ r r C _ ~ L I L
C~
O ~ C ~ c v, * ~- C ~ 1- Il~ h.
* ~ C L ~- C .-K ~ _ ~ *
_ . C Y r~ ~ _ ~ O
* h ~ C
~ * ~ n I ~ ~ ~ ~ ~ r~
o 7~ * v t~ ~ h, l C " " ~ t l U ~ a ~ . * f_ tc .1 * ~ n _ ~~ . t . L ~r ~ 3: ~ . .
* ~-- * L t'~ ~ C- ~
_ ~ L " 1~1 * h * ~t K ~ t ~ 0 ~O C'l ~ ~ t L~
* ~ t~. *
* ~ L n i ~
I` * O r~ c~ ~C hl * J.
n i ~ t U * j~ tc _ t_ c~ h, _ _ --L~
o t~

C -- C t~C C, C'C ~ C ~ CC
--- rr r o LJC~ ~s ~ CJ D :~ 0 1-- r- ~ O
r C C ~ C~ ~ ~ h t~ h~
a~ N Ll tn It~ v~ r ~ 4- Ll N C C N~ N
C~ ~ L~ r--0 D :.1 L - t.. ~ 1., 0 ~ a~ hl ~ ~1 Ir Ir N v r cr L h _ r~. ~ U r C~ ~r ~ C C _ ~_ ~ C~ t t S~ D r~ ~ ~D D ,D ~ tC~ t~ t J L~
CC .R OOOOOOOOOOOOOO OOOO
h~ N ~ ~ ~n ~O T-- 0 cr o _ N ~ ~r In 10 1~ 0 t~ C ~ ~ 0 tr v z r~ r ~ ~ r a. ~r ~r ~ ~r .r ~ v~ n ~n v~ n 0 tc h:

:

C "~ r J Y
L .- ~r ~ v~ C
~ r 1- ~ I c ~ _ _ L~ _ ~ O O
; L~ ~ ~ r o ~, ~ . L~ O_ V ~ ~

C ~ O ~ _ C ~ ~ -- c ~r V ~- --L~
-- ~ r L~ > ~ ~ ' G
~ Vl ~ r ,0 "~ C c~ U~
W ~ ~ 2 "~ L C ~ ~ _--U~ J ~ ~ ~ :,.
r u, V ~ ~ ~ ~ L. ~
c r ~ . v~ ~. v. ~ ~ L. V. ~ C
C _ ~ O V ~ V 1~ _ v~ = .S 1 V.
r~ ~-- ~ v~

r ~ ~ _ ~ L~ > ~ 7 ~: D. -- ~ T _ _ ~ r ~ - Z ~ ~--

3 ~ I O h 1~, Ir 7 I ~ v v 1, ~ z ~ ~ u~ ~ L -- -- L LÇ C v~ Ir S ~ ,, J e~
L-- ~ ~ 1 1- ~ V O U ~ ~_ v ,. O a ~ v ~ l> y ~ L.- c~ S _ _ _ 5 uJ ~, c~
cr ~ C r Ir ~: G c, r C L r~ ~ C r 2~
," r; r r N C.:
L~ 3 1~ ~ ~ c~ ~r ~ ~ r. C ~ C -- rl LÇ O~ O L i U O ~ ~ _ C C ~ P~ V r~
G ~/L.r r- 2 C O L. _ ~ C ~ 1~ .r C ~ IL r. .r U U L U L- L ~ C~ ' ~ ~ ~ "
U~ v~ ""o r ~C r r L r _ r- ~ .n ~O r~ cc --I.i .
-D

-e ~ _ r~ c ~ ~
C
* ~ c ~ . _ s ~. s * ~ c~
.i C C .~1 ~1 * -- 4f C h .- I.i U ~ _ ~, ~ ~ :.) * V~
5 ~ c ~ -7 e ~ ~ e .~ C
c * 4 h ~ s ~ ~ * ~ U ~ .. _ I~ li * s * ~ h. C
` * O I ~ ~ C ~_ ~ 4 ~ , h. C ~o o f" ~ C h. G
~ . . .

O
r~ 5 C N o N
¢ _ C C ~ r C ~r e Ir O O O O O O _ _ _ .t o o o :~ o o ~ o o o N ~ N ~ N ~I f`l N N N ~ ~ t`- ~ ~ N
-n~ e c= c ,; v r _ L a c; . L
~ C V~ L' Vl r, 1~ _ C ~ .
/r ~ n ~ .o n c c) 1l _ L ul v .: _ -- V. _ ~ ~. . V
---- T r, ~ C ~ rcv, -- c ~ c r~ ~ _ o o _ o :- ~. v c~ r . v~ c -- --~5v~ . . o O r C 4 C C _ . _ v _ ~ I
vi~ V L 4C v r 4-- - r~ ~, C--o " v. ~ 8~v L ID ~r r v ~ r n 71 L L. -- a 4 <r ~ C O r ~ v L ~r C C -- L 11.
r ~C r~ r c~ v ' ,! c _ _ 3, c rv 4 V o _ _ _ T, IL .r ~ r L S v V, L t, T, C. T 1~ ~ C 1' E IL
" v, ~ n r c7 ~ c T Y C 11 C rl -- ~ 1 t,l ~ 81 C ~ 14 '^ ~ C _ rl r~ r~ _ ~ F r C. ~ o v v :.. C ~ L~. 4 ~ O Jl :. ' / ~i .. 1 ~ 10 ~ _ ~r, ~ C V `~ _ .~ .. .... .. ~ C; ~r C V
-- v _ C' _ V, t,' _ L
* ~ O ~ L C, o~
V ~ _. _~ ~ h C ~ * 1-- ~c ~ ~. --* V;~ ~ t ~ ~

4 i- ~ ~ 4 _ ~- V. ~ ~ 2, * 1- tr 1~ X h1 tZ 4 V~ h 1~
1. ~. ~1 ~ ~ o r_ ~ c Y ~ . v. ~: rs 1.: r v. I . ~ _ z 11 h: I_ V
* ~ _ ~ L~ L' ~ V c ' hj ,1 L~ . r, ~ ~ * ~ ~ * t. t, L~ ~
~5 ~c 4 1 ~ 4 _ ~ t L. W n Y c~ _ * CL5 _ h 1. ~ L ~ _ 5- Il ~ ~ _ t-L O _ ~, ~ tJ * .. hj ~ V`j r~ r, IL L- _ _ ~ c, ~ ~ ~r; h x L t, o L~ . ~. ~ ~ r i~ I z v.
* 2' ~ r t, ~ t~ ~ C L t ` t~ c L t~ _ ~ r . C ~ _ c c .o rr f. C~ _ a s . ., r C~ c~ v. x o t. ~ 11 * * h, 4 ~ ~- _ ~
L~ r- * ~ ~: r. ~ . ~ ~ r ~ C ~- t~ ~ _ tJ ~ ~ L c :. c * L V ~ Lt ` t ~ :r ~ C
. v ~ C t~ L~ a * ~ ~ 5 : Jl Jr * L ~ L, L -- ' 5 Z C a ~r ~ c I-- * V. s ~ L _ CL` V--~ tJ tJ
t a* ~ ~ * ) * * h ~L~ *
* a~ 1~ ..* ~ * c. c. * c. ~ ~ c~ ~

* ~t. ~ Ct hl X * t ~ ~
r * ~ * t I * a v; v~ * z a a ~L L~ rc r ~ ~ ~ ~t V * ~ V~ ~ * ~' " " ~ hj h~
rr Y V ~ C, 2 * * ,z * C~ hl Vo ~ C_ _ _ = t~ Z tL
,_ r ~ c L t~ C Cc~ C C L ,'eL c L~. c c~ t, C~ L t-- C, L C, a L' t.
l_ ........ ... .. ... . .. ....
-- r~ O o ~r 1. 1. ~r ~J r ~D ~ r ~ ~_ r. _ r~ ~ r- ~ o r o ~ c~ tC~ c ~ v,' c~. u- r~
c~t j r~ v~ r~, rc~ _ to r_ r~ r~ r_ v r- ~r v, r r; _ rL _ n L~ V~ r~ ~ a hl n C, O r~ v~ r~ c tJ t. r~ ~ ~ L rc c h~ h ~ .~ V,, r r t~ c c r v ~D r 0~ 2 C~
C~ o O rrj ~q Lq rL L Lq rr tc o a o o a L~ o o o o o O O O O O tc rO O rc 0 v~ ~ ~r~ , ~`D r <s~ r~ C~ _ ~r ~ ~ " ~ v~ v~ n ~ v~ V-~ v~ v~ v; ~ rj vj v~ D ~ r~ t~ t~ O _ r~ ~ ~ Ul 'D
_ r~l N r~ N ~ ~ ~ r N rc- r~ r t a r r~ r~ r r~l r r~ N r r,~, N N ,r~ r~, r~ ,r~ r~ r,~ r~ r r ~ r r~ rc~ ~ N rv r~ r~ r r_ r~ Y
7~

~ r . --v ~ u C -- ~ 0 - ~ c ~ cl ~ -v _ r L, _ a <~-DLl _ ~ C

L ~ _ V
V C f C
~ J r .~ _ v r, ~ F
.. ., ~ J

rl L~
,~!
rl r ~ ~ c c S S _ J C a ~ 5 ~
n - c C ~ ~_ ~ c ~t ~ C C ~ n c s~ n o _ ~ ~ .~ L~
.. a ,_~ C c _ c - c c s ~ ; ~ a c v~ c . ~

r~ _ ....
J~_ ~ L c U: L n .~S O 1 o ~C1.~ ~ ............
tr~ c 5, c~ C L L n C- C~ L C`
-d.
o :a n~
LCJ 1. D ~- O hl L 5~ _ ~ C~ o o ~r a 5, e: v~ r _ .- C Ul r ~ c ~s r 5~ ¢

a:n~ o r r o~ ¢ C v. _ ~ ~D n: a o ~ O ~
WC~ ~ ~ r a ~ 0 r~ U n~ t~ r 5~ K m .to o o o o ~ ~ o o o o o o o o o o r~ o v~ r. m ro ~ ~ ~ m r~ n~ ~ 0~ ~; ~ .r v- ~C
N ~ N N N ~1 N N ~`i N N N ~ N _ N N N N
K

n c D C 0. O D ~ C
_ O c 1~: 'JC _ .~ L ~ _ _ .
r c L !~ r r r ~ rr C C C
c ~ n r. v o o l A y .~ r ~/ J c r c ~ ~ ; r~ r o c ~; r - r 7 rl ~ h~ C o F C n ro 4 _ _ _ D o r u r r ~ J c c rr r 3 c ~ rr r r c v ~ o ~ _ C . r- l c cJ m 11 ~ o L. o r ~ - c F r, c - c F
o 'r ~ ~ ~ .J c ~ ~ ~ U
r, a. rA Ll A -- c~ r~ tJ -- -- c r~
L ~ c~ r ~ rv F C _ F c, ,, _ ~ . r u v L~ ~ c CF n _. _ .~ v~ rt ~ rc rr L
4* C ~ r_ A C ~ o ~. c~ cJ C _ C - ~ C C C C
* ~
~ ~ * _ _ I L~ Y
* h C~ ~ F- ~ r_ V
* r- * -- \ ~ --~ .~ rr ~
* -- ~ r~ U ~ ~ ' U ~ ~ ~ h' --j h r~ --rr _ rr. r ~ ~ ~ L
* r~ ~ ~ r ~r rr c c~ c l ~ ~ G r r~ L ., y ~ h c :.~ C~ h-- ~ ~ C C ~ -- r c . ~ ~ . u r~
h * ~ a L, Cj _ ~. L L _ a ~ _ _ a ~ i L, _ ~ ~ ~ C ~ r~ ~ c ~ ~ h. ~r L a, C v .1 o rL C r~ :s ~r = h ~ .~r ~ h~ 5 r~ r~ S O C ~ G h r~ rA f-- r~

~ ~r 7 ~ - r; !r r~ C ~ r '~ ~ rL
~ E ~ L. ~ O C ~ h; _ L~ C~ 2 hl ~ rl U ::1 a z C; r. a ~ _ L~ v h 1~ rr 1., 7 * cr ~ ..
* * U~ .. ~
r ~ * v - ~ c ~
* ~ c c c r~. ~ * ~ ~_ Cj r ~ -- c .r c~

rr ~ r~ C C C C C c~ ¢ C rr ¢ ~L C ~ rc r~ . r~
=

v -- r r rr .. c ~ &~ rn C
U rn U7 u r~ o rr~ D ~ b. r~ C~ h .a ~r r, r ~r a r- rr~ o o &
D ~ h ¢ r~ h rn rr c ~ rs .-r C h~ _ C 1~ h~ - a c c r a ~ C ~n ~c c c r~l c (~ u u r~ o o ~ r o r^ N ~r C _ 1~ 01 r C r^ C r~l C ~ ~ r~ _ C r r~ o r~
& CJ~ hl rJ! :~ r,v _ r~ & 1~ U _ hl ~s Cl r r. r~l h. U r. crl ~ U D h. D r~ l,J ~ 1~1 O O 01 r~
rr rv rC ~ s ~ ~ r rc c h OD rn r u~ r C~ r ~/ h r~ r~ crr~ s ~ ce r~ c~ c~ rs r~ ~t o~oooooooooooooooo~oo CoooooooooooO
cu u ~ r r~ o r~ ~ ~ r ~ r D r~ o ~ ~ ~ r r r n ~ c N T r ~ r r ~ o N ~ ~ r o h`

~2~ 3 ~ V
v G
: r _ C ~ _ ~ . o c ~ v ~ - v. r c O ~ C
v. ~ q~ c ~ ~ v r.
. t C ~ s V 1. ~ r C
v ~_ r. ~ o _ _ ~ _ C I c c ~ c r c ~ ~ c.
.. c v ~ ~ rO S U . c. r ~
C ~ ~ ~ r O ~_ C ~' o t o ~ . r r _ ~
~_ > ~ ~ ~ C C C C
~; ~ _ _ 1, ~ ' *
_ e ~ v ~
- ~ ~ C L r. ~. C C ' b ~>
Z ~. o L ~ tY _ b 1.: D ~
2 .~ C o o v v v ~ .r t~ ~ C
b .~ 1- a ql ~. ~ v, v, _ ~ t~ t_ v.~. tL tc ~ Y ~ _ o O ,~ _ U :- Vl ~ r~ ; ~ tt. :1~ ~ t' ~ ~ V.
V , _ Vl l~ tt~Y ~
b ~ C _ xjc ~ . Cb ~ rj i r; kj ~ _ O _ a 1~ t t' ~_ C r i~ 0 F- rl~ ~ _ L C, :~ C ~ 7 I C VJ ~ ~ ._C ~C S ~- ~ = V = V ~- CL O ~ ~ r oC C _ ~ t I e ~ _ O ~ O ~ L & ~ a ~ r 4 ~ ~ _ C C t~ ai S 1~ G 2 ~ _ C
t ~ = ~t ~ V~ ~ U ~ ~ ~ C ~-C _ r r ~ _ 4 _ b b 4 L O t~ t 7 b V ~ 1 4 4 V4 i~t C~ _ & ¦ O L~ V~
U L 4~ Y E I b t-U ~ hj ~s C. ! o ~ u t~ ~ ~ ~ ~ ~_ ~ ~ ~ ~ ~ ~ ~ ~ -- ~ ~ L' L~ _ a X
O
~r h ~ .
tO & & Y ~ X ~ . Y X
tr;~ e~ t~ tr~ 3! tl C~ rl C
z ~ t _ C~ C 7 Cl o ~ 1lr h. _ r. ~4 c, "~ 7 ;cC O C' tJ C' C` Ct t~ Cl L C' te & r ~er C b~ b ~ ~- j~ r~ h~
h c~ Ctt O O ~ U7~ 0 0 t~` O O ~ t V7 L; r tl o -- c~i. ~ .r v ~Lt r- ct t O --~ ~ ~r i~ .D r~ t tl` O--~ ~t I t l t ~ ~ ~ ~ _ _ _ _ _ O
C~ Y
hi ~2~

.,, C C ~.
~c ., ~ C C ~ ~
r ~ C
O ~ D
V rl~ D ~ c ~ C
- ~C 11 r C 1: C
L 11 r >~ ~ ~ ~ c ~ x X ~ f _ 7 ~ 1/ 1l ~ L V, L _ U~ V t- h n U 1~ ~ L ~ C ~
,, _ _ _ h o_ cr hl ~ c: ~ x La ~ L
11. L ~ C r-- O _ C I C : C 5 C 1~ _ C C C
Z ~ ~ U a , , I ~ C, O C O C. C' .r C` ~ L C~ ~ C~ ~
~-- C ~ C~ C C C C r~ 6I rL L C C 1~: C ~ C ~ C C ~ ri C ~ C r; ~9 J ~ r c ~
~C ~ ~ a L -r ~ 5 C L ~ L Cr ~ ¢ ~ ~ L ¢ a 'r ~ O ~ C L ~ C-U D O Z D U C ~1 '~ Z i hl ~ ~ ~ O C~ Z ; C~ ~ C~ h VJ
C' V~
r- cl _ a.
I V~
C~ C4 h -h~
L h C. C` C. C r -C r~ L' O O O
h _ C h~ c~ ~ r o~ r' ~
_- C~ 4 ~ -- U r~ cJ rl o h _ U ~,J J~ h h~ ~ c,; h ~r ~ ~ r hi o ~ hl hl h ~ hl hi ~ h. ~ h ~ h h h ah~ U ~: ~. ~ ~0 ~ Vj r~ a ~ C h h .~ O r,~ U ~ ~7 ~ CC ~ U : U U r~ r,~ r,~ U U r~ r~ r,~ r,~ Cl rJ Cr a a o o o o o O C o :: o O O o ~ ~ O o O O O o O o o o ~ o o o o o v~ ~ I r U r C _ r r~ ruJ~ O~ C~ V~ o o l`o ~o o~ o o o o o ~
~1 ~ C~ C ~ --C r l C j C r l ~ C- C ~ r v ~ r r r ~r ~r ~ r r i c h.

/

~23~

., C .....
~ - ,. ~
L O ., _ V, _ -- U .
U ~ F U ~L
r ~L /1~ ~ ~ ~ _.
r ~
~ C U '': ~ -- .c r r ~ " u h L: ~ C
I C * I~ I V " ~
X ~ 1 U ~ ~-r' c v v ~ h -- ~ _ ~,z .~ h ~ tl: C ~ ~ h. q X
7 ~ n ~ a ~ ~ r~ ~I n ~' h ~
C ~ C ~ ~ C C~ 'f .s C ¢ ~ C~ ~ ~- o x _ V V ~ ~ ,. ~.
o ~ ~ ~ ~f V b CJ 7 .S X X 'J X _ 1.1 <. h~
~ h * :L ~ ~ 7 ~ n, :~ ~r 4 :.` 11' i-- U ~
7 C ~ * # * b X '.. 1 *
~i ~ * * ~ C ~ ~ *
' ~ * ;~ ~J .. X
r ~ * c 7 * U ~ C C.
~_ * ~ ~ * * e .J I I f ~ .IS X
r -.~ 1,; . . . .
C C

=

O O O
h1 ` ~OL ~ O
¢ C 1-` ID ~ U` ~0 ~C N C' C It- O Ir 1~' c N ~ ~r 5 ~
O 1.1 N 1~ o l~J /VI h. 1~1 0~ 1~1 1~. 1.1 D N bl ~ O D O N
n ~ ~ ~ e ~ N N 01 N

m ~ C ~ c _ ~ ~ C ~ c r c~

c r.

7~

V, ~
-- -- h C la r. n ~ I~ r ~
r, v . ~ _ .~. J' . ~, r t ~ c C ~ ~ a r ~ ~ ~ _ v ~ ~ ~ r, ; ,, F C -- .~ C v v ~ C -- .
. 5 _ . r, _ t ~
.7 ~ 1 U ~1 ~ -- ~ ~1 .5 ~ _ L ~ ~ ~ r, ;
r ~ r :~ r v_ r V ~ C;r ~ o o o " _ _ _ ~_ Vl ...... v N :. D
F J r v r,c _ ,~ _ o o n --F ~ :~. ~ r _r~ v ~ _~
.... _ .~ c ~ r 1~ T2J Vl _I r _ _ " t ~ ~ ~ C _ _ r~ r c ~
~ ~r t ~ C~ r~ ~ ~ r~ ~ C ~C ~
* L)1~ V ~ 7 _ ~a n ~ * u ~
.~~ t. h r ~ v ~ ~ ~ c ~ * ~ c ~
" 5 ~ ~ r -- -~ 7 '~ h ~ _ ~ 17 ~ h7 *
.S 'C ~ F ~ t7 ~ C` h t_. ~ U r~ ~ h~ ~. .C r .
r~ G t ~ . r tt _ h * F t~ 1~ tJ ~ Z' ~ ~
o r~ t_ ~ ~ ~ c _ G r~ 2 _ _ _ ~ ~ .r 'J ~ ~; -- ~1 * ~ O ~ ~ t` ~ t~ ~ h ~ ' '-~-t ~ ~ Y h~ r~ ~ _ Cl 'J C * r~ tL ~ ~_--~ t~
* t = ~ _ * C ` ~ ~ = P D _ * C ~> V j~ 4 ~tt ~ " 1l ~ _ 1- ~ t-- * llt ~ ~ t~7 tL * ~ L ~ ~ 'L ~ U r~
~; t~ v * t ~ a ~ t~ u ~ ~ v, c s~ ~ D ~- _ r C ~ t' _ C ~
* U _ * V ~ ~t V I V -- I S ~ VJ r~ h~ * IU 5 I I * t-- _ C 5 S~ ~ ~I t~ C 3 I r * t~ N ~ . ~ t-- U r 7~ t ~ L

0 ~t ~L t ~ ~ W ~ r ~ a ~ --~ a v,t ~~ ~ ~ 't * t' '~ t V ~- r~1,; ~ 1, c ~
r ~ r. * * ~ r ~ ~ 1l ~ r~
r; ~ tt I * * ~ ~ t~ v~
r ~ ~ G ~ c~ ~ Lt ~ tL ,,~ ~ t~, ~ z, r _ _ _ _ o~ _ rJ ttt ~ . Lt _ _ ~ _ r~ C
o 1- ~ C, C~ tc c C t~ C Ct C~ L~ ~ C~ C~

rr~ a E- C h~
L~ Y N /-J r~l ~17 ~I N O ~tt N i~t O r-- r ::1 o O
1.: h' c~ C CC C r~ V. ~ ~t r~ Vl 1. t.. C C h ~It ~~ ~r tr ~r vt C Vr V C` t~ C ~ N Vt ~r rJ .r V~ r~ r~
Ct t_t r ~ r. r ~ r r~ r. Y r,ttt a~ t t ~ .t ~t ~t u .~ h~ W rt ht O r~ rt ~t ~t r~ t l~t r~t ~ ~ vt . t rt tt- ~t t~t ~ o O O o c, o o O O O O o o tr r r,~ t~ tr r r tr tr 7r vj z u~t vl v~ u~ v, 'vS rv; c~t tvt CD ~t ~N7 ~t ~t Itt r~ tCt rr ci _ ~t rt r ~ r trt t~ c 7 ~ rt ~ V7 ~tt trr; ~htt ~t 0~ tr~
~ ________________ ______~__ _______________ Ot ~D Y
W

/~

,, c ~ r, a ~ c r c. c .Y o 1. ~ n ~ L ~ ~ D . ~ _ r r r ~ C c o C V. V L
G C~ a ~
a r ~! o ~ T ~ ~' v T ", F ~ ~ ~ n _ -- -- G l~ I r ~ ~. D
_ T ~ ~ C 1~ r~ c^ _ c O r~
L r ~ ~ C r ~ F o rO O ~ J
111 G -- ~ a ~ ~ ~ 1_ ~ ~ r v ~ ~. ~ L a ~r 0 ~ o o CL ... '' er v ~ C CJ I

V ~ ~n o ~ j C "' ~ ~ ~c C ci _ ` L ~ ~ ~
C~ ~ C _ 0 r. ¢ rr ~r ¢ c 5 C C r~ ~ .r n ~ ;- .r ~ C r~ r c ~ n ~ C ~ ~ v U I * O, ~ ~ V h r ~ I V V, ~ ~ ~ L C 2 C :~ C~ r 4` 0 h~ V O C -': C 2 ~-* ,J CL ~i u 0 c I ~ 1~ ~ _ ~ c~ ~ ~ C~ G U _ n C I ~ .~ ~ ~ CL O :J ^ C CJ ~ '' e ~L r_ ~' 0 o _ S ~ L r ~ ~ r L ~ Y ~ S D c~ ~ r r_ ~ C c x r_ ~ ~, c~;
* h~ ~ D _ ~ o :~1 U v n _ o r r ~D V~
v r~ v _ _ * r r; * L O r v C
~4 ~1 u r r~ r_ ' ~ V~ C
~>~ 5 ~C ~ c ~ * 3 1_ ~r - o r ~ O O
c~ ~_ . C C C C C C O C C C
r_ . .. . ... . .

C
h 1 O_~ rr h Ir.. r~ r~l ~ o C C _ o C h V~ r > r ~ c C rJ r r o r r ~r ~J C ~ ~r ~ r ~ ~ u~C~ h. crJ rC U t~ .~ co cc Q c~ c~ r~ h Q c h. r~ rJ S~
rs ~Y r~ oc O tJ 1~: C ~ r r- tr cr C h~ O ~ C r J cr h~ r~ L O` r ~ c C ~r cr cr r r r r c r O O O O O ~ O
Vh~ cr C~ C~ C~ ~ r c~ cC~ O No mO or o o ~', o r C--~ r ~ rC~ r~ rr.~ r~ rV r, r~ cr r~ - r .r ~ ~r .r r ~t r r, r r, r r r r Y r, ~ ~ r r, r, V,l r r, r r r, r 10 r, u r, r r ~~~~ ~~~~--__~____ ro h-/~/

~3.~

C L
I' ~ F r _ ~ ~ r 01 F r h ~ L L , ,~ n X n F V ~L r ~I , E ~ ~ .J ~ ^ L ~.;
v _ ~, c _, '~ ~ ~ O r~ U ~ rr G T 1.) c r _ ~ ~ c L F O _ F F q C ~ _ _ C L L
L _ V _ V O ~ _ r _ f. V _ ~ L
, ~ ~ ~ ~ ~ _ G C C V~ o c L ~ r C Ç ~i ~' ' O, L ~, _ V ~ G ~ _ _ _ O O G C ' ~ C ~ ,, ~ _ ~n ~J i~ :C 5 5 ~ _ vl r~ U V Vl ~ U, ' C~ rl ~ r i T. -~ ~ ~ r_ i c i ~ _ i~ _ r~ _ ~ ~ * L ~ _ _ _ D ~ r~ ~ r u c h, _ i.^ ~ r, r 2 C
'~ X X ~ _ ¦ E ¦ a _ Y X h a ~ q h~ ~S r r, c ~ ~r r c c^ ~ ~ ~ ~ ~ o ~ Ci ~ rC~ ~Cr '~ ~'i " U n ~.~ o C L ~ ~ u, o ~~
G ~r ~ C -- rt a. o rl ~ rl C~ ~ Ll Vl ~ r~ 2. ~ ~ h~ h * c ~ * C L~ ~ ~ h. h h, h ~ h h j ~ ¦ h. h h h, h. ~ h~ h h ~ h h h h * h V * i i n v 5 i-- C C
~ -- C; ~ ~ C ~ *
1~ a ~ v v~ I ~ ~ a r~ ~ i x ~ ~ rrl ~r I _ i x # x .^. _ r~ aJ ~ _ _ ~ X ~ ~ ~ ~ t ~ L~ r X ii x c ~ jc ~ h~
_ _ _ _ _ _ _ V u. z r_ c. c c c _ _ _ ~ u, a~ h. rt 7 rc C C C~ C' C C~ C ~ _ _ I--C;
-r ~

--U
o h~ Q ri ~' r 1ll. U r U a LA r~ r~ h'l ^ ~ _ L^. ~ _ U. m u ~c 2 ~ C' Q Q Q CC; Cj CC~ Q Cc; Q C; Cj C ~r j C cj cj c c c U.' IIL' C _ rJ r~ ~r L^ ~ I` rt O O _ r~l r^ ~r r ~A r~ ~ ~ C _ o~ n r~ cr cr o ~ A. ~A r c~i o C _ ~ .r r ~o u. ir m LA In Ul Lq LA r U~ L U,~ m LA u' u~ u' ~n In r u' r r u' ul U LA r v~ m u~ lA u' r u.~ ~n U- r n u~ v~ r ~r7 u~ r m u~ Ln ~A h /~

~. f o _ ~, 111 ~ F ~
V _ U
Vl I o r~ V
V ~ ,.1 _ -- _ . V
. ~ V, F _ _ ~1 ~ ~ C` V U, ~ ~
r ~ f _ v v, ; ~ a L V. C
v C~ ~- C c C ~ ~ _ _ _ _ n C ~ Q _ h * i. _ _ F . ~ F 1~ ~ F C

i- C ~ c .. ~ h v . C G r c G
h ~ 1 V ~ ~ h i- h ~ h * 3 ~ ~
t~ ~ V~ ~ ~ h ~ I I 1~ ~ h V Cr .- C ~ C ~ h~ C C'~ C
o r_ v. L ~ L ~s n C~ h2 n n' V ~ a ~ n~ L~ c h h r ~ * _ r ~ ~ f ~ ~ v o r F ro ~ I G G U, C n ,~ O ,*4 1_ ,,J ~ L C U F ,~ ~. _ G :' -'~ V ~ ~ ~ ~ ~ iO ~ ro r~l G
h _ ~ n~ C z U r _ L~ -, 0 r, Cl ~~ O U _ L~ C~ U ~ o ~ n * Z ~ ~ ~~ E ~ C n o v C i ~ ~ Z
J a ~ c ~ ~ ~ c z a ~~ ~. s ~ a 1 ~ = v _ ~ u _ ~ c r v o c ~ v. - ~ L
* v~ * 1~ ~ * V * r U r C. ~ Ll ~ G

r-- h 1 U ~ ~r r G ' C I
~ cr I r 0 7~ V U _ _ _ r _ _ _ _ _ _ X 0 r~
V b.' .. .. .. .. .. . .. . ..
r 7~. ~L c c~ c r- ~- c~ ~ - h h. e~
--~. h e~ C c hj r r'j` h 1.. : C _ h; r~ ro h~c r~ a r~ c `D h ~ . r`~ Q ~ C~ r rL re c eC ~ ..C ~ a ~r N _ er c v ~ r ~ ~ r~l _ rr o v~ r~ c- c h O hl U~ r~ ~ r-- i--r~ I`J 1-- n r~ _ c _ ~r r~ ~ r~ c~ r~l O
r~ ~ U C! h ~I V' i--rr L' 1.1 C r~ v~ h~ _ rr ~ rD ~ ~ r rr r hl Q r~ r,~ r~ rn rn r~D ~n D rD u ~ ~ cr~ e~ u. ~ a C ~ e c~ c a :1~ 51 a r~r rr r~r er rJ r.7~ rr rJ rr rr c rJ~ ~r rJ C r~ e~ rJ er c r,r c 2 o o o c.
V' h' r rJr C ~ n~ rr~ .r V' ~n r~ rs ~ c _ ~ ~ .r n v~ ~ rn ~ o _ r,~ r-~ ~ ~c r r~ G ~ _ O~ rr~ ~r 11` vn r~ rn er C--ro~ r ~ _ 2 v~ v v. ~ ~ v~ v~ v~ ~ ~ w~ ~ ~ e~ ~ ~ ~ vu ~ e~ ~ e~ O r G~ O O O` O O O _ _--_ _ ~ _ _ _ _ r ~ r ~ r r~ rY~
h~

/~3 ~,~a~.~

; ~ O
T' . ~ _ T' >
,, . r r w ., -- . _ r, .~ ~ X ~ . -- ~' hW
c _ v, _ c r v ~c -- ~ c G
L rG~ r . .. ~ r r O ~, 0 h . ", O ,~
tr .~ . c _ _, _ _ ~ GJ ~ T r E; r c v _ . ~ o v r .~ r, ~ L L C~ O L
n X C L _ ~ ~ ~ L F X ~ _ G~ r -- r r _ L G
Y c c C r c o c, r _ O L C~ r c v -- -- c c F
_ O c , o L' -- r o _ n r r r -- r r _ c, h' ~ ,. v. a _ G/ c ~ ~ o, G, r~ _ ~ Y CT c r G F G -- c c .. c _ ~ Gl c L c ~ ~ " ~ ~ L ~` L L r _ L 4 ~ ~ _ ~ L L
_ ,~ . _ ,, C 1~ L> ~ v~ ~ C ~ L.l X ~ h _ .~ _ cr ~ ~ v~ _ c :.1 h. L
L, x ~~ ~ ~ x ar~
L~ L~ h~
_, c~ h. _ T h.:: h, ~ ~ ::1 h. _ ~ h. h~
L~ ~ _ ~ I c r ~ h, ~ : ~ x c h~ c c _ cr~ h a -- ~ h~ n ~ ~ >- r~ _ J C C~ c r ~ v~
L v A; a ~ c, c .. h- h. L, L, T~, r c~ c~ c L, L, r a a. i h C L, -_ r L ~ v L c h~ h L~
hl .~ h~ ~ N ~ h~ ca :.1 CL D _l ~ I W~ h, ~ .~- ~
; =1 0 o ~ _ c~ Y ~~ r~ L~ -- r~ _ ~ r~ ~ ~ L a ~ ^ h~ ~ ~ ~ L c~ s a s cr ~ Z :c 5 ~ ~ ~ 5 ._ ~: h s 5 c ~ = L C = c L c ~ i- ~ u, I u u. c -- i_ ~ i_ c L L, C C c ~.
~r ca .. c .. C C ~C ~, C
~.~ t-- S~ ~ ~
a ¢ x o ~r h . .... . .. ~ . .. .... . ......
cD h~ r ¢ L~ c~ LC h-- h-- r L, 5 r ~t L~ Cr L, c~ r L, C h~ h-- cr L.
i_ . .... . .... .. .... . ......

"
o: .1: h h IL
t-- C'~ ~ O O
Ll vl _ L~ ~D o h~ ~ _ L~ ~ o -- O ~ Ll D o cr ~ h~ :.1 L~
O ~ iti h C _ h _ h-- h C t~ ri _ r~ h O ¢ ri c I h h cr tD ~ i~: r Cl tr ¢ ~ I ~ _ C ~ h o C ~ _. C o N C t~/ _ C O _ tY ~ c ~t _ O L~ ~ h~ t. o h~ _I h, cr~ o ~ cr ~ o a L~ v~ rl N O O U- 1~1 ~ N LJ r~ t~ O ~?
tt r, C W o _ N r~ a, tr V ~r O h i~ r c~ ~r rc C h _ ~ tr ~ h ~ ir~ r ir L~ _ r CC r O ~ o i~
s ~ O ~ o O O O O ~ t7~ 0 tcr r CO h` cr tr cr cr t~r ~r O thr' thr O '~ s s s o o o o o o u L~ t~ r u~ v ~D ~ n tr C _ t~ m cr C .~ C _ ~ 0~ C _ N r~ o _ r~ rr r~ o _ u, Z ~ ~ ~ ~ ~ r ~ a ~ ~ lo ~ r ~ D D D D ~0 ù ~ ~ Do ~5 D ~0 lO ~o u~ ~r ~D r~ r r v~
La C~
h /~

~ ç
, m r c~ . r V~ r _ ~ v ~ L ~, ~
L Ir ~ _ ~ v. G
~ v v. ~ ~ -- ~
c ~ r _ c_ r 2~ L C
~ ~ n ~n n ~ n .~ n F ~ F L~ . '5 T ~ Ll C -I ~' L. o . " _: .. r v ~ ~L ~ _ v n . C tJ .~ r ~J r L. r _ O ~ o ~' ~ L ~ 15 C. ~ C C ~ L
L~ C ~ ~ V. V ~
C' v, C ~ C ~ e C a, ~ c ~ .~
~ 5 ;~ L~ 5 ~ r~ 0 1~ ~5 S .^
~ S
o C ~:c Cr L5 r. ~ U ~ ~ s IAI Su ~ ~' L~ o ~ C L
1.: * ~ Z '~5 C .. Z ~ CL ~
~r o ~ 1~ n~ o r 1., o _~ v :.) D V.~ 5 .D O r~ ~ ~ D
G * ~ a ~L V~ ~ C L C, ~ ~ O ~ C~~
o C ~ C I L` ~ ~ I L; c ~ ~ c * C ~ ~ o, ~ L I _ . . L . .: C _ . L ~ _ h, ~ c c U v ~ r L .` c x LJ ~ ~1 ~ r. ~ h~ L * D -- L~ ~ i C G C_ v C IL C L~ C L ~ ~ L C
O Vl ~ ~ ~.:1 .0 ~ DL O O r.~ hl S ~ hl 1.1 hl v, c c h O U ~ ~~ U 2 ~ ~ ~ r ~ ~ ~ Ll rO O r _ :~ t ~ ~ ~ _ ~ n _ o S o s _c . 1l ~L ~ C5 a. ~ ~ -- 1, 1~ 5 5 1.: ~ h v _ L C 1- v, ~ 1-- L 5i ~- 1_ 5 / o.
* ~ O * ~ ~ v _ r _ -~ * Z hl ~ L ~ ~ ~ S
* K Cj '- * L ~ z al ~ ~ U
~ 5 ~ ~ C * _ v~ v o L v~ S
U. O I 1~` ~ I Li O O ~ n 1l 1~
I~ O L~ ~ Li LJ ~ ~ ~ r~ n _,-- L~ r. IL
r~~ -- L 1.~ c L' _ _ ~ V. 3- O, ..
o ~r L ..... ., ~ ,. . . .. . .
r ~ c, C l_ L- C C. C_: C t, LC L'_ L~ LL L L, L' CL
--- C ~5 r ~ V, ~ L~ V~ C
_ ~ C~ ~ rl O ~ ~ ~
L _ C r~ ~ L'l O qC' C ~ t. LL C` 1~: L~ O G C r L.
o V.` V,`--C V~ ~ Vr~ U--~ L~ N r. V7 r~l _ Li . r~ _ ~r o r~ U r~ L ~' G
V F~ It L~ L~ N ~ ~D K 1 ID C h ~ U r ID 5 C 1, r 5 r h C~ r liD C~ L C _ r ~D a c. o r o o o ,o o, o C, C o ,o o o C, o o o o O O O o o ~o o o c~ o C. o U LL' ~ V,~ .. D 1` L- O' O _ r~ ~ Vt vs r- cr C _ r~--~r V,~ ~o r~ o C --r~ V~ ~5 ~- o v ~D ~ ~ V ~0 r~ ~ C _ r~
V O O C~ O O O _ _ _~ _ _~ _ _ _ N N N N ~ ~ C~ r~ r V~ U- V~ 0 r~ 1~1~1~1~

VO
cc~ e / 6~5 ~2~ 33 L L L
LL r _ c~ L
.~ V L. ~ C V r ~ 0 n ~- ; r r ~ c ~ ., c ~ _ L Vl L ~f V I ' C C
O ~ r r h r ~ O c L
~ D .. ` ~ r' F c F ~ _ r c L c L ~ C _ -- ~ f L L._ . ~ r, /r ~ _ . c ~, c.
,r. L r IJ ~ L FL V O L ~ L~ O --, F
F ~ h L ~' ~ IL L IJ . _ . ~ V _ r ~ r ~
h ~; ,1 ~ ,. L L ~ L~ L, ~ ~ & C ~ F C _ _ r, L
4 ~ V V 1~1 ~, O L C C Ll ~ IL L .LI F F X .. _ V .~
h c ,a, ~' ~ o ~ ~ r L ~ O Cl 1 a c C c c ~ ~c C; I~ F . _ ~ L` r -- -- . c c r~ _ _ _. v, _ c n n 0 o n v :- . r V! h~ S & ~ r~ C :' h -- ~ Vl C~ -r .S _ C
~ r -- & ~ ~
C1 ~ ~ C r~ .5 - C
a K ,~ Y ~ ~ K :~
~r c K h' J ~ 1-: F-: L- F- LJ j_ h L, i L, 5- o c ~-- * ~ ~ r ~ _ ~ r~ ~- -, c. ~, o r~ ~ ~ ~ h~ * -~ ~ & h & ~- J ~ c~
C h . ~- ~ 3 ~ cl O ,&~1 ~' ~ X " " ~ J ~ &h; h & ~ _ r ~ = r i ~T := ~ U 3, ~ v V.
1-- . 51 ~ X _ ~ 41 c ~ ~ O ~,J ~ h ~ C~ 1-- Cl c 1.. C~ O ~ rc; V~ . ~;,;, ,, ~, O c3 ~h,, rl 3 Ci ~v 3 t, C ~ ti ~ h C _ C a O C ~ 7 t U. ~. a ~ t, O O ~- a a t: .o c 3 c c C ~J c c .I c F- ~- C C F- t, hl r.~ a ~ q. C~ - C :~ 5 ~ t~ ~ a, J C~
O. ~ :- Kj I ~ ~ _ t~ 1- ~ 1- a 1_ ~ 3 K Kj 3 ~ C ~ ~ C ~ D~ C _ a c . ~ . C 3 ir C :t i- :~ ~ _ ~ f- .c L ~ L F- h. 7 C ~Yr -- u, I_ U. ~ t, L t. O ~ C S. S C ~ L U ~ U -- ~1 U. x ~ c t, V.
~ Z
F- 11 _ *
h ., U 1~ Cl * Y
a. C~ C, ia 1~ r t. t, C ~ K ~ = ~. r~
3 r~y h O i_ c~ h C i . O C~

U C\ CJ Y 12: r,c I_ F- C i C~ L C z o C h~ _ r.~ IL h IL Z h . _ .. CJ CC ~ t~ tJ 1-- ~
..

U F~ rc r~ r,~ r r~ C ~ C' L U 5 5 5 C, C C C, rc ~ tC C. ~J
z , CN o O O
hl L! c c. c. o ~J 5 O ~ ~ r ~ tJ t~ rt t O c r h, h r i~
r~ ;' ~ r 1` ` ~ r~l ~J _ C~ :D O o o CD r- L L L~ U hi ~ h W ~ L~ U cr~ L~ f ~ D t- D ^~ L~ r.
Y i~ r O~ rc O ~ ~ ~ r L~ W N ~ r~ L~ L~ h _ ~ c ~: h: 0 i~ ~ Ul r ~r a Ll h' h. C <x ~ U 5 L~ h~ ~
W O ~ 1 .I C ~ ,C ~1 ~ C C C a .C a c c c ~ C, i ~ .1 ~ .S C a c ~ ~ ~ u~ c a .Ir ~r ~ c ~ t ~ a, ~ ~r cC OOOOOO~O::10oOOO OOOOOO~O~O::1OO~OOOOOOOOOOOOOOO
V W _ N ~ O--r,~ N ~ C r u~ o _ r~ r ~ r~ : t~ c _ r~ o r CD 0. 0 _ N ro ~r r ~r ~ o 0~ ~
U Z r i~ r-- 1~ r- r 1-- r ~ O _ _ t~ I CC D ~ ~ C ~ CJ 5~ ~ C~ tO m t~ ~ CJ ~ ~ 1~1 m C D C~ ~ D ~ t~ CD IC CC
J _ r C~ h~
W

~2~ 3 o . ~ , ,, .. U
~F ~ _ ; c, ~, _ F
CC (r G G _ F ~; L
U L G ,, ~ V _ r r ~r u c u . _ -- ~ r, T F C U ~ ~ ~ ~ r "~n u U o ~ L. L. L. ~ ~
~ ~^ a c - ~ ~ _ a r Vl ' ~ r ~
D ~ ~ u :r _ 'A u ~ _ ., _ .~ ., _ ., .~ .~ * * D
C 1-- ~ ~ ~ ~ h e I ~- ~ C 7 _ C ~ C, ~ U h- ~
-- h IJ 1~ ~) n ~_ h ~ hl ~ r ~ --1 ~~ ~ 7 ~ ~ C_ C~ C, .~ Y.
r. ~ r_ - . * * c ., ~ o c ~ c e~ n a. .s ;:~ O c * t W r ~ h~

5~, C ~ ~o ~ ~ X _ ~ r ~ y; r ~r V 5 ~ S- Ib a. V~ V. ~_ 7 L 11 ~ ~ 1-5 1~ U _ " ~; V ~f ,n~ n y w ~ r~ 5 r ~ ~ ~ h C ~ ~ D ~ n ,~", _ X
v. ~ c ~ v~ n ~ C * ~ C v, ~ Z ~ _ ~ Z L ~ C ~ V~ V ~ C ~ S ~: C C C * - ~ . 5 O r ~ * U ~ -~ ~ r~. ~ ~ Li ~ h' Z
C~ * ~ ~ C ~ * h. ~ ~ h, C ~ * c F~ * ~ h; hi _ U h -C ~. C~ C C~ 5 a ~:C c~ C C C c. c~ ¢ ~ C, a ¢ r, C
-e C
O C~ h~ O Cl O

C~ _. r~ r~ ti W ai r~ C C a cc e a. C~ Y a r~ C~ a _ _ c, 1 C Ir e C _ v N N N C 0~ hW ~ " 1,, W h h~ ~L O ~ W ~ _ ~ N ~ ~ r~ N N N Ll N L
0~ C ~ In 1~ ~r. ¢~ h~ C _ ~ V~ r r~ W ~. C _ ~ e~ VJ ~ ~ c ~J h1 C ~ I~ ~ L e .a ~ r~ ~ ~D e rr ~.
W ~ IJ 1~ O C~ Q O C~ O O C~ C~ h1 W W W hl W W W W W l_ h~ h~ h~ h~ h~ ~ h~ h~ O O O O O 111 a .t O ~ o O O o O O o O O o o~ o o o C~ ~ C. o o o o ~ C~ o o o o o o C o < - ~r r~ r~ n ¢
V~ ~ Ul V V~ V~ ) L~l ~nC _ N ~~ ~ V~ ~ a ~ ` ~ ~ ~ ~ ~ ~ r~ ~ ~ e ~ r r al ~ ~ ~ ~ ~ v~ r O E
v. _ 0 n v /~7

Claims (29)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. In a system for controlling rotary means having a periphery, wherein the periphery includes indicia printing means, and wherein the periphery is adapted for feeding a sheet having a leading edge in a path of travel, an improvement in the system comprising:
a) first means for sensing a time interval during which the leading edge of the sheet is linearly displaced a predetermined distance in the path of travel;
b) a d.c. motor coupled to the rotary means for rotation thereof;
c) second means for sensing angular displacement of the rotary means and, d) computer means coupled to the first and second sensing means and to the d.c. motor, the computer means comprising:
i) means for providing successive sampling time periods;
ii) means responsive to the first sensing means for providing respective counts representative of desired angular displacements of the rotary means during successive sampling time periods, iii) means responsive to the second sensing means for providing respective counts representative of actual angular displacements of the rotary means during successive sampling time periods, and iv) means for compensating for the difference between desired and actual counts and generating a d.c.
motor control signal. for controlling rotation of the motor to cause the indicia printing means to initially engage the sheet in the path of travel a predetermined marginal distance from the leading edge of the sheet.

2, The improvement according to Claim 1, wherein the first sensing means comprises first and second electro-optical sensing devices spaced apart from each other a predetermined distance for sensing arrival of the leading edge of the sheet at each of two spaced apart locations.

3. The improvement according to Claim 1, wherein the motor has an output shaft, and the second sensing means comprises quadrature encoder means coupled to the output shaft.

4. The improvement according to Claim 1, wherein the computer means includes means for comparing counts representative of the desired and actual angular displacements and generating an error signal representative of the difference therebetween, and the compensation means utilizing said error signal for generating the motor control signal.

5. The improvement according to Claim 1, including power amplifier means for coupling the computer means to the d.c. motor.

6. The improvement according to Claim 1, wherein the apparatus comprises a postage meter, the rotary means includes a postage meter drum, the drum has a cycle of rotation, and the motor control signal accelerating the periphery of the drum to the linear velocity of the sheet substantially coincident with the periphery of the drum engaging the leading edge of the sheet.

7. The improvement according to Claim 2, wherein the apparatus comprises a postage meter, the rotary means includes a postage meter drum, and the first sensing means comprises a mailing machine including said first and second sensing devices.

8. The improvement according to Claim 3 including counting means for coupling the quadrature encoder means to the computer means.

9. The improvement according to Claim 4, wherein the motor control signal comprises a pulse width modulated control signal.

10. The improvement according to Claim 4, wherein the motor control signal comprises a function of a regressive mathematical expression.

11. The improvement according to Claim 4, wherein the motor control signal comprises a function of the error signal and a prior error signal.

12. The improvement according to Claim 4, wherein the motor control signal comprises a function of the error signal and a prior motor control signal.

13. The improvement according to Claim 6 including the motor control signal decelerating the drum from said velocity thereof to rest subsequent to disengagement of the drum and sheet.

14. The improvement according to Claim B, wherein the counting means comprises means for providing an output signal for the computer means which is representative of the angular displacement and direction of rotation of the motor drive shaft.

15. The improvement according to Claim 12, wherein the prior motor control signal comprises a function of a prior error signal.

16. In a system for controlling rotary means, wherein the rotary means includes a periphery having indicia printing means and is constructed and arranged for feeding a sheet having a leading edge in a path of travel, a process for controlling rotation of the rotary means, the process comprising:
a) providing means for providing successive sampling time periods;
b) sensing a time interval during which the leading edge of the sheet is linearly displaced a predetermined distance in the path of travel and providing counts representative of respective desired angular displacements of the rotary means during successive sampling time periods;
c) providing a d.c. motor for rotating the rotary means;
d) sensing angular displacement of the rotary means and providing counts representative of respective actual angular displacements of the rotary means during successive sampling time periods; and e) digitally compensating for the difference between desired and actual counts and generating a motor control signal for controlling rotation of the rotary means to cause the indicia printing means to initially engage the sheet in the path of travel a predetermined distance from the leading edge of the sheet.

17. The process according to Claim 16, wherein step (b) includes the step of sensing arrival of the leading edge of the sheet at each of two spaced apart locations.

18. The process according to Claim 16, wherein step (d) includes the step of sensing the direction of angular displacement of the d.c. motor.

19. The process according to Claim 16, wherein step (e) includes the steps of:
1. comparing counts representative of respective desired and actual angular displacements, 2. generating an error signal representative of the difference between respective desired and actual counts and utilizing said error signal for generating the motor control signal.

20. The process according to Claim 16, wherein step (d) includes the step of accelerating the periphery of the rotary means to the velocity of the sheet substantially coincident with engagement of the periphery and sheet.

21. The process according to Claim 16, wherein step (e) includes the step of calculating the motor control signal from a function of a regressive mathematical expression.

22. The process according to Claim 16, wherein step (b) includes the step of generating respective counts representative of desired angular displacements of the rotary means.

23. The process according to Claim 16, wherein step (d) includes the step of generating respective counts representative of actual angular displacements of the rotary means.

24. The process according to Claim 16, wherein step (e) includes the steps of:
1. generating a pulse width modulated motor control signal, 2. amplifying said pulse width modulated control signal, and 3. applying the amplified pulse width modulated control signal to said d.c. motor.

25. The process according to Claim 20, wherein step (d) includes the step of decelerating the periphery of the rotary means to rest subsequent to disengagement of the periphery and sheet.

26. The improvement according to Claim 1, wherein the compensating means includes means for compensating for an electrical parameter of the system.

27. The improvement according to Claim 1, wherein the compensating means includes means for compensating for a mechanical parameter of the system.

28. The process according to Claim 16, wherein step (d) includes the step of digitally compensating for an elec-trical parameter of the system.

29. The process according to Claim 16 wherein step (d) includes the step of digitally compensating for a mecha-nical parameter of the system.