GB2026795A - Control of stepper motors - Google Patents

Abstract

Windings 23, 24 of a variable reluctance stepper motor are alternately energised by respective transistor bridges A-D, E-H controlled by a processor receiving the outputs of comparators 77-80, each of which receives a signal synthesized by the processor to have an unperturbed waveform corresponding to the winding voltage when the motor is stationary and a signal of sensed winding voltage having a perturbed waveform related to the motor movement, whereby the processor first confirms that the motor is moving and then energises a winding reversely to its previous state. The signal waveform intersections define two crossing points dependent on the motor load, the processor respectively using the first point or the second point, Figs. 8A and 9B (not shown), to energise the windings according to whether optimum acceleration or deceleration is required. Load variations during driving automatically vary the crossing point and energisation instant being used, further variation occurring in dependence on motor position or velocity when the circuit is included in a programmed closed loop control system. Constructions are described, Figures 1 to 4 (not shown) of linear and rotary cylindrical or disc motors providing the characteristics of Figures 8A and 8B. Also described is a method of fabricating the stator and bearing system of the linear motor. <IMAGE>

Description

SPECIFICATION Incremental motion drive system The present invention relates to incremental motion drive systems comprising reluctance motors and, more particularly, variable reluctance stepper motors and novel controller for said motors.

It is well known that stepping motors of all kinds exhibit instabilities at certain combinations of drive, load inertia and operating frequency. These instabilities result from the fact that the force/displacement characteristic at each cardinal position of the stepper is like a spring constant which, acting on the inertia mass of the moving part, results in a highly undamped mechanical resonance.

Operation of the stepper at the resonant frequency or at harmonics of this frequency will often result in erratic performance. While there are timing methods which will uniformly accelerate and decelerate a stepping motor through its resonance frequencies, these methods are all subject to the requirement that the load must be nearly constant. A well-conpensated stepping motor drive system which smoothly accelerates, slews and decelerates a given load will usuallly perform very badly if the load is doubled or halved.

Manufacturers and users of stepping motors have developed various techniques for controlling stepper motors in a closed-loop manner. Feedback stepper controls may be classified into two groups: (1) veiocity feedback systems, in which a signal indicative of mechanical stepping rate is developed and used to modify the drive frequency; and (2) pulse position or timing feedback systems, in which an output is derived from either the motor itself or a separate transducer and used directly to control stepper drive switching. Velocity feedback is implicit in the latter systems and the response of the stepper to time varying loads is much more rapid. The most successfully known method of feedback control involves the addition of an external position measuring device such as an electro-optical transducer.Signals from the transducer are used to confirm and count steps and in some systems the transducer output is used directly to time driving pulses to the motor.

Investigators have tried to derive feedback signals directly from the windings of a stepper motor.

The principal advantage of this approach would be lower costs. A secondary advantage in high performance systems would be the elimation of the inertia of a separate transducer, which can be a signigicant part of the total load. The problems most frequently encountered are that the windings of most stepper motors have a high degree of cross-coupling and the feedback signals are small compared with drive voltages. In conventional steppers, as the motor speed changes the relative magnitudes of these voltages vary significantly. The most successful known system is one which measures average motor current which is indicative of average motor speed because the motor back EMF reduces motor current. At least one such closed loop motor control system is commercially available.The response of such a system to load transients is extremely poor, however, because the averaging process involves a long time constant.

It has been discovered that novel variable reluctance stepping motors of the type disclosed hereinafter are characterized by the production of a motion dependent electrical signal that can be employed in the incremental motion motor controller also herein after disclosed and forming part of the present invention, to time the drive pulses in a optimum fashion so as to achieve reliable stepper operation during acceleration, slewing and deceleration under widely varying load conditions.

A reluctance motor makes use of the dependence on position of energy in a magnetic circuit to develop mechanical force in the direction of least reluctance.

One known variable reluctance stepper motor employs a toothed rotor/stator combination in which rotation of the rotor causes a cyclic variation in the reluctance of the magnetic circuit, which includes the rotor and stator teeth and the gap therebetween. The gap changes dimension as the rotor and stator move relative to one another. A motor capable of providing continuous stepping motion is comprised of two or more such sets of rotor/stator teeth, as well as separate magnetic circuits extending therethrough, which circuits are capable of being selectively energized. The different rotor/stator teeth are staggered in relative angular positions.By selective energization of the magnetic circuits, the rotor is caused to assume successive positions of least reluctance for the respective magnetic circuits, depending on the magnetic and mechanical variables designed into the motor and the method of control. In conventional variable reluctance stepper motors, the rotor and stator teeth are of the same or nearly the same width. This configuration produces the greatest possible difference between maximum and minimum reluctance.

The incemental motion drive system of the present invention comprises a variable reluctance stepper motor and a controller for said motor, said motor having at least two windings, characterized by no-motion signals having unperturbed waveforms and motion-dependent signals having perturbed waveforms; and said controller comprising waveform generator means for synthesizing waveforms modeled after said no-motion signals; comparator means for comparing said synthesized waveforms with said motion-dependent waveforms; energization of said windings in response to said comparison.

The present invention involves as part of the incremental motion drive system a novel variable reluctance stepper motor which minimizes undesirable restoring forces and produces a more efficient stepper motor of higher sensitivity.

The said variable reluctance stepper motors are characterized by such a motion-dependent signal and generally comprise cooperating fixed and moving structures having tooth-like patterns of equal pitch but with the fixed and moving teeth having different lengths, measured in the direction of movement. The smaller teeth are divided into groups which are offset from one another by fractions of a tooth pitch to provide a bi-directionai motor capable of being stepped from one position to the next with the teeth tending to produce force in the desired direction carrying essentially all of the flux and the teeth tending to produce force in the opposite direction carrying essentially no flux.

One embodiment of a linear variable reluctance stepper motor characterized by such a motion dependent signal comprises a cylindrical slider and a rod-shaped stator. The slider comprises two poles separated by a permanent magnet. Each pole comprises two sets of one or more spiral teeth separated by a winding. Each winding is continuously energized by a direct current the direction of which is controlled. The stator comprises a toothed member having uniformly spaced spiral teeth having a pitch P and a width equal to P/2. The spiral slider teeth have a pitch P and a width equal to P/4. The slider tooth sets on each pole are offset from each other by an amount equal to (n + 1/2)P, n being an integer.

The poles of the slider are offset from each other by an amount equal to (m + 1/4)P, m being an integer.

One embodiment of a disk, rotary variable reluctance stepper motor characterized by such a motion dependent signal comprises a rotor and a stator having two poles. Between the stator poles is a disk-shaped rotor having uniformly spaced radial teeth having an angular pitch P and an angular width equal to P/2. Each stator pole comprises two sets of radial teeth, the locus of each set describing a circle with a different radius. The stator teeth have an angular pitch P and an angular width equal to P/4.

Associated with each stator pole is a permanent ring magnet and a winding. The sets of teeth in each stator pole are offset from each other by an angular amount equal to (n + 1/2)P, n being an integer. The stator poles are offset from each other by an angular amount equal to (m + 1/4)P, m being an integer.

Each winding is continuously energized by a direct current, the direction of which is controlled.

One embodiment of a cylindrical, rotary variable reluctance stepper motor characterized by such motion dependent signal comprises a rotor and a stator having two poles. The rotor is cylindrical and has longitudinally extending teeth with grooves therebetween, the rotor teeth having an angular pitch P and an angular width equal to P/2. The stator is cylindrical and surrounds the rotor. The stator has two annular poles separated by an annular magnet. Each stator pole has two sets of equally spaced, longitudinally extending teeth having an angular pitch P and an angular width equal to P/4. The sets of teeth in each stator pole are offset from each other by an angular amount equal to (n + 1/2)P, n being in integer. The two stator poles are offset from each other by an angular amount equal to (m + 1/4)P, m being an integer.The sets of teeth in each stator pole are separated by an annular winding which is continuously energized by a direct current, the direction of which is controlled.

Thus, the variable reluctance stepper motors suitable for use with the incremental motion motor controller of the incremental motion drive system of the present invention comprise a pair of windings continuously energized by direct currents the direction of which is controlled. The motion dependent signal employed in the incremental motion controller of the present invention is derived from that end of the winding which has most recently switched to the lower (e.g., ground) voltage. In the absence of any motion, the voltage will exhibit an unperturbed waveform which, in the case of a linear variable reluctance stepper motor, may be of the type V=a( 1 ebt), where a and b are constants.When the stepper motor is allowed to move, however, the change in reluctance induces a transient voltage in the winding which is superimposed on the unperturbed waveform and results in a perturbed waveform. In the case of a linear variable reluctance stepper motor the perturbation may be such as might be caused if "b" in the expression V=a(1e-bt) were not constant but, for some time, t > O, b = b(t), first decreasing and then increasing in value. See, e.g., the lower curves in Figures 8A and 8B.As described in greater detail hereinafter, the incremental motion motor controller of the present invention compares the motion induced (perturbed) signal with a synthesized signal which is modeled after the no-motion (non-perturbed) waveform and which is offset from the no-motion waveform in the direction of perturbation so as to control the timing of the drive pulses and achieve stepper operation during acceleration, slewing and deceleration under widely varying load conditions.

In a preferred method for fabrication a stator and bearing system for a linear variable reluctance stepper motor, threads are cut in an ion rod to produce alternating regions of high and low reluctance.

The threaded rod is then tin flashed. Next a tinned strip of electrically conducting, non-magnetic material is fitted into a groove. The rod is next dip soldered-and then ground to slightly less than the desired diameter. The rod is then copper flashed and chromium plated to form an extremely hard surface of the desired diameter. A bearing of softer material, which forms a part of the slider, rides on the hard stator surface.

Figure 1 is a simplified view in section of a linear, variable reluctance stepper motor for use with the motor controller in the incremental motion drive system of the present invention.

Figure 2 is a simplified plan view, partially sectioned, of a cylindrical, rotary, variable reluctance stepper motor for such use.

Figure 3A is a simplified view in section of a disk, rotary, variable reluctance stepper motor for said use.

Figure 3B is a simplified view of the tooth arrangement of the motor of Figure 3A.

Figure 4A is a simplified view in section of a slider element for the motor of Figure 1.

Figure 4B is a simplified partial plan view of a stator for use in the spiral slider element of Figure 4A.

Figure 5 is a functional block diagram of one embodiment of the incremental motion motor controller of the incremental motion drive system of the present invention.

Figure 6 is a schematic diagram of one embodiment of the motor drive circuit of Figure 5.

Figure 7 is a schematic diagram of one embodiment of the function generator and comparator circuits of Figure 5.

Figures 8A, 8B and 8C are graphical representations of typical waveforms associated with one embodiment of the incremental motion controller of Figure 5.

Figures 9A, 9B and 9C are flow diagrams of one embodiment of the programs for the processor of Fig. 5.

One embodiment of a linear variable reluctance motor useful with the incremental motion motor controller of the incremental motion drive system of the present invention is illustrated in Fig. 1. Linear variable reluctance motor 10 comprises a cylindrical stator 11 and an annular slider 14. Stator 11 has teeth 12 and interspersed grooves 13. The teeth have a pitch P and a width P/2. Stator 11 is preferably formed from 2.5 % silicon iron. Annular slider 1 4 slides along stator 11 on support bearings 1 5. Slider 1 4 comprises poles 1 6 and 1 7 separated by ring permanent magnet 18, preferably a samarium cobalt magnet. Pole 16 comprises two annular slider elements 1 9 and 20 while pole 17 comprises two annular slider elements 21 and 22.Slider elements 19 and 20 are separated by winding 23 while slider elements 21 and 22 are separated by winding 24. Between ring permanent magnet 1 8 and poles 1 6 and 17 are flux "regulators" 25 and 26. The slider elements and flux "regulators" are also formed of 2.5 % silicon iron. Annular rings 27 and 28, also of 2.5 % silicon iron, provide flux paths between slider elements 1 9-20 and 21-22, respectively.

Whereas stator teeth 12 have a pitch and a width equal to P/2, slider teeth 29 have a pitch P and a width equal to P/4. In addition, the teeth in slider elements 19 and 20 (as well as the teeth in slider elements 21 and 22) are offset from each other by an amount equal to (n + 1/2)P, n being an integer.

The teeth of poles 1 6 and 17 are offset from each other by an amount equal to (m + 1/4)P, m being an integer. Motor 10 is "stepped" from one linear position to the next by reversing the direction of current in one of the two control windings 23 and 24, both of which are continuously energized.

There is no tendency for the slider to move in the wrong direction. The direction of motion is dependent solely upon which winding current is reversed. Also, selectively inactive teeth do not set up any forces which conflict with the direction of the desired forces created by the magnetic energization of the active teeth. Thus, the design of Fig. 1 enables the motor to be stepped in either direction and with good stability.

One embodiment of a cylindrical rotary variable reluctance motor useful in the incremental motion drive system of the present invention is illustrated in Figure 2. Motor 40 comprises a cylindrical rotor 41 having longitudinally extending teeth 42 with grooves 43 therebetween. Teeth 42 have an angular pitch P and an angular width equal to P/2. Grooves 43 maybe filled with a non-magnetic material so that rotor 41 presents a smooth outer periphery. Stator 44 is provided with two poles, 44a and 44b. Associated with each of stator poles 44a and 44b are two sets of longitudinally extending stator teeth 4546 and 47-48. Positioned between statorteeth 45-46 and 47-48 are control windings 49a and 49b, respectively.Stator teeth 45, 46, 47 and 48 have an angular pitch P and an angular width equal to P/4.

Stator poles 44a and 44b are separated from each other by ring permanent magnet 49. Stator teeth 45 and 46 (as well as stator teeth 47 and 48) are displaced from each other by an angular amount equal to (n + 1/2)P, n being an integer. Stator poles 44a and 44b are offset from each other by an angular amount equal to (m + 1/4)P, m being an integer.

Control windings 49a and 49b are continuously energized by direct currents of a magnitude sufficient to create an MMF equal to that developed by permanent magnet 49, the direction of current being selected to cause the magnetic flux developed by the control winding either to aid or oppose the magnetic flux of permanent magnet 49. The four possible combinations of current direction establish flux paths through the rotor and stator teeth which are analogous to those created in the linear stepper motor of Fig. 1. The rotary stepper motor is stepped by changing the direction of current of one of control windings 49a or 49b.

One embodiment of a disk, rotary variable reluctance motor useful in the incremental motion drive system of the present invention is illustrated in Figures 3A and 3B. Motor 50 comprises a rotor 51 mounted on a non-magnetic, preferably stainless steel, shaft 51 a by means of a central collar 51 b, which may be made from an epoxy resin, upon which is mounted an integral soft iron ring 51c. Two stator poles 52 and 53 are disposed on opposite sides of rotor 51. Stator pole 52 comprises two sets of radial, wedge-shaped teeth 54, 55, the locus of each set describing a circle with a different radius.

Stator pole 53 comprises two sets of similar stator teeth 56, 57. Associated with stator poles 52 and 53 respectively are permanent ring magnets 57 and 58 preferably of samarium cobalt. Surrounding ring magnets 57 and 58 respectively are coils 59 and 60 having leads 59a-59b and 60a-60b adapted for connection to sources of current whose direction is controllable.

Rotor 51 comprises equally spaced, wedge-shaped radial teeth 61. Rotor teeth 61 and stator teeth 54-56 are preferably made from vanadium permendur. Rotor teeth 61 have an angular pitch P and an angular width P/4. Stator teeth 54, 55 (as well as stator teeth 56, 57) are offset from each other by an angular amount equal to (n + 1/2up, n being an integer. Stator poles 52 and 53 are offset by an angular amount equal to (m + 1/4)P, m being an integer. Fig. 3B shows the spatial relation between rotor teeth 61 and stator teeth 54 and 55. Both the rotor and stator teeth are preferably embedded in epoxy rings.

The direct current continuously applied to control windings 59 and 60 is of a magnitude substantially equal to the MMF of ring-shaped permanent magnets 57 and 58, either aiding or opposing. Incremental stepping of the disk-type stepping motor is controlled by switching current direction as described earlier. Although not shown for purposes of simplicity, it should be understood that stator halves 52, 53 are typically enclosed within a non-magnetic housing.

Figs. 4A and 4B show a spiral slider element and stator for use with the linear variable reluctance stepper motor of Fig. 1. Spiral slider element 1 9 is comprised of a hollow cylindrical shell 1 9a having an outwardly extending circular flange 1 9b provided for mounting purposes. The hollow interior is provided with a tooth pattern comprised of teeth 29 arranged in a regular helix, each tooth having a pitch P and a width equal to P/4. Grooves 30 are three times as wide as teeth 29. Four spiral slider elements are employed in each motor 10 (elements 1 9, 20, 21 and 22 of Fig. 1). Fig. 4B shows the stator 11 having interspersed teeth 12 and grooves 13. Teeth 12 and grooves 1 3 have a pitch P and a width equal to P/2.Teeth 12 of the stator form a continuous helix and have square threads.

In a preferred method for fabricating stator 11 an iron bar, preferably 2.5 % silicon iron, is machined in a lathe and helical threads of the desired depth are cut therein. The threaded bar is then tin flashed with a very thin electro-deposit of elemental tin so as to make soldeering material to the threaded bar possible. Next a tinned strip of electrically conducting, non-magnetic material is fitted into the groove 13 extending the length of the bar. This material may, for example, be copper or aluminum.

The strip may be secured to the bar by a screw 11 a. After the strip has been placed in groove 13 the bar is soldered, for example by dipping, so as to fill up the space around the tinned strip with solder. Next the bar is ground to a diameter slightly smaller than the desired finished diameter. It may, for example, be ground to a diameter 0.002 inches less than the desired finished diameter. The ground rod is now preferably copper flashed with a very thin copper coating a fraction of a thousandth of an inch thick. The rod is now plated with, for example, a thin layer of a non-magnetic material such as chromium to produce a very hard finish. When chromium is used for plating it is necessary to go through the step of copper flashing. When other plating materials such as nickel are used, the copper flashing step may be omitted.

In the finished structure support bearings 1 5 ride on stator 11 (See Fig. 1). Where the plating on stator 11 is hard, support bearings 1 5 are of a softer material. Conversely, where the surface of stator 11 is soft, the support bearing material is harder. For example, where the surface of stator 11 is very hard, e.g., chromium, support bearings 1 5 are preferably of an oilite sintered bronze material.

Alternatively, support bearings 1 5 may be eliminated and the grooves between teeth 23 of the slider elements may be filled with a Teflon loaded material called "Delrin" or with a nylon loaded material called "Rulon" and employed directly in lieu of bearings 1 5. Where stator 11 is plated with a material which is not quite as hard as chromium, such as nickel, then support bearing 1 5 may be made from aluminum treated with the "Tufram" process of General Magnaplate which has the effect of oxidizing the aluminum to make polycrystalline alumina after which the voids are impregnated with Teflon. This is a very hard bearing material which has a low coefficient of friction.

It should be understood that the tooth arrangements heretofore described may be reversed in that the wide teeth or the narrow teeth may be provided on the fixed or on the moving part, the opposite tooth configuration being placed on the moving and fixed parts respectively. In addition, the permanent magnets, although preferably formed of samarium cobalt, can be formed of any suitable material.

Alternatively, they may be electromagnets. Magnetic paths may be either solid or laminated and the coils may be located as shown or wound directly around the teeth to provide different coupling for their MMF's. In the linear embodiment, the cross section of the inner member need not be round but may be square, hexagonal or any other desired shape. An inner member having a round cross section is preferred because it is easier to manufacture.

The number of teeth employed and, therefore, the size of motion increments, is not limited by any ratio or formula involving pole and slop counts as is the case with vernier steppers. If the desired number of rotary steps is divisible by four, a motor can be designed to provide directly this capability. If the desired number of steps is divisible by two but not by four, then the motor must have two electrical steps per design step. To provide an odd number of steps per revolution of the motor, the motor must be designed with four electrical steps per design step. In most cases, however, one to three steps can be added to the design value to simplify the design. On the other hand, linear motors can be designed to have any pitch within the practical limits of physical size and gap tolerances. Although gap tolerances should be close, they fall well within practical ranges.

Figure 5 is a functional block diagram of one embodiment of the incremental motion controller for use in the incremental motion drive system of the present invention. It comprises a processor 70, motor drive circuits 71 and 72, waveform generators 73, 74, 75 and 76 and comparators 77, 78, 79, 80. The motor drive circuits continuously supply direct current to the motor windings which may, e.g., be windings 23 and 24 of the linear variable reluctance motor of Fig. 1. Processor 70 may, e.g., be a Rockwell 6502 microprocessor. Motor drive circuit 71 may, for example, be of the type shown in Fin. 6.

Waveform generator 74 and comparator 80 may, e.g., be of the type shown in Fig. 7.

Each motor drive circuit comprises an H-bridge which drives its winding with essentially constant current in one of two directions. The feedback signal used to control stepper timing is derived from the end of the winding which has been most recently switched to the lower in the case (ground) voltage. At the moment of switching the winding produces an EMF that causes the diode in parallel with the lower switching transistor to conduct, and the voltage reaches apprnximately-1 .0 volts. As the energy in the winding inductance is dissipated, this voltage rises above ground and approaches a positive voltage equal to the IR drop of the winding current through the forward resistance of the drive transistor and the resistance of the 1.5 ohm current limiting resistor.In the absence of any motion produced EMF, the voltage will exhibit an unperturbed waveform which, in the case of a linear variable reluctance stepper motor of the type shown in Fig. 1, may be of the form V=a( 1 -bt), where a and b are constants. Such waveforms are shown, e.g., in the upper curves in Figures SA and 8B.

If, however, the stepper is allowed to move in response to the condition described above, then the reluctance change at the end of the motor controlled by this winding will produce a momentary EMF, superimposed on the unperturbed waveform. In the case of a linear variable reluctance stepper motor of the type shown in Fig. 1 , the perturbation may be such as might be caused if "b" in the expression V=a(1e-bt) were not constant but, for some time t > O, b = b(t), first decreasing and then increasing in value. Such perturbed waveforms are shown, e.g., in the lower curves of Figures SA and 88. The lower curve in Fig. 8A, which is typical of the motion voltage produced with light load.If the stepper is more heavily loaded, however, the motion voltage will resemble that shown in the lower curve in Fig. 88. The motion voltage occurs later, indicating a slower mechanical response to the reversal of winding current.

In the incremental motion motor controller of the motion drive system of the present invention a signal is synthesized in waveform generators 73-76 which is modeled after the no-motion (non perturbed) waveform and is offset from the no-motion waveform in the direction of the perturbation.

The motion induced (perturbed) signal is compared with the synthesized signal using comparators 77-80. In the case of linear variable reluctance stepper motor of the type shown in Fig. 1, the synthesized and perturbed waveforms, together with the comparator output are shown graphically in Fig. 8C. The first crossing, indicated by the comparator output going to its low output voltage, occurs at the time which is nearly optimum for acceleration switching. The second crossing, indicated by comparator output going to its higher output voltages, occurs at a nearly optimum time for deceleration switching. Depending on the desired program of motion, one of these transitions can be used to cause reversal of the winding current at the other pole so that the next mechanical state is selected.That winding, in turn will produce a motion control voltage which can be used to time the next reversal of the first winding current, and so on.

As will be readily appreciated by those skilled in the art, the waveform of the no-motion signal and the motion induced signal is heavily dependent on the physical construction of the motor. In the case of other linear embodiments or in the case of rotary embodiments of the variable reluctance stepper motors disclosed herein, those waveforms may or may not be exponential in character. They might, for example, be parabolic or hyperbolic. They may even take a form which does not readily lend itself to mathematical expression. Nevertheless, such waveforms can still be synthesized in waveform generators using, e.g., piecewise linear approximations, read only memories (ROM's), microprocessors or a combination thereof.

It will also be understood by those skilled in the art that if the stepper motor encounters a hard stop or an excessive load, then the motion voltage and resulting comparator outputs will not be produced and the next state of the windings will not be selected. This condition can be used to signal an overload or to stop counting and indicate the actual position reached by the stepper. A correct response to a hard stop or an excessive load is possible only with a step-by-step feedback technique.

With a large but not excessive load, the timing of the first crossover at the comparator input will be delayed, as shown in Figs. 8A and 88, and switching to the next state will be automatically delayed.

The stepper will, therefore, automatically slow down in response to increasing load and speed up when the load is decreased or removed, and this response will occur on a step-by-step basis.

While an incremental motion motor controller could be used to control stepper motion directly, without the counting of steps, by a system which connected the comparator outputs directly to winding controls, most actual systems will require a means of step counting and a method for commanding the stepping motor to move to various positions according to a fixed or adjustable sequence. A flexible control device which can produce this type of response is a microprocessor, incorporating control programs which select the winding states and feedback signals, providing full positioning performance.

The flow charts for one suitable program are shown in Fig. 9A, 9B and 9C, with Figs. 98 and 9C showing the "STEPS" and "DELCSN" subroutines.

The value POSNOW is the present position of the step per motor, counted up and down as the stepper actually moves. POSCOM is the commanded new position, set at a new value before entering the program from the Monitor. The program starts by computing the difference between POSNOW and POSCOM, the flag indicating the sign of this difference is DIRFLG. The absolute difference is OFFSET, a quantity which will be counted down to zero as positioning proceeds. If OFFSET is initially zero the routine returns to Monitor. If not, the first step is taken by subroutine STEPS. After this, the program checks whether two steps remain and, if so, switches to a deceleration routine. If more than two steps remain, the DELSCN subroutine examines the selected feedback comparator for a motion signal. When it occurs the next step is taken.

The deceleration routine uses subroutine DELSCN also. But when the comparator has made a transition to zero, the routine continues by examining the same comparator for a transistion to one.

When that occurs, the next step is taken and this routine repeats until OFFSET=(b.

The STEPS subroutine corrects the value of POSNOW by adding DIRFLG, which is either +1 or -1. The lowest order 2 bits of POSNOW are now masked and used to select the state of output windings to cause motion to the position POSNOW. This is done by using the low order bits of POSNOW as part of an index. After a delay, the same bits are used to construct another index which selects the generator for the comparason transient. Finally, the OFFSET is decremented, and the subroutine exists.

The DELSCN subroutine initially delays action to allow the winding current transient to die down.

Then, an index is computed to select the proper input for feedback. The input is repeatedly scanned by a loop whose iterations are counted. If no feedback has occurred by the time initial value LOOPCT has been decremented to zero, the program exists to Monitor because the stepper has taken too long to move. In so doing, it must correct the stack pointer (SP) because it is jumping out of a subroutine.

When the input from the comparator is found to be zero, the subroutine exists normally.

The program described is, and will usually be, part of an overall control program which communicates with a source of commanded positions and may feed back condition reports to this source. The routines described are sufficient to provide positioning response to a digital command, however, and comprise only 180 bytes.

Tests with a linear variable reluctance stepper motor of the type shown in Fig. 1 have demonstrated that under closed loop control reliable stepping rates of about 400 steps/second are readily achieved even though in an open loop mode the motor will not reliably step at over about 1 50 steps/second. Under closed loop control the motor has been shown to be quite intensive to load, running from 400 steps/second down to less than 50 steps/second with increasing load, and always indicating actual steps completed after a hard stop.

While the variable reluctance stepper motor and incremental motion motor controller of the motion drive system of the present invention has been described in detail in connection with such linear variable reluctance stepper motor it will be appreciated by those skilled in the art that it is equally applicable to rotary disk and cylindrical rotary embodiments as well. In addition, while the program disclosed in Figs. 9A to 9C and in the Appendix adjusts the timing of current switching on the basis of position, it will be appreciated by those skilled in the art that the timing of current switching may also be adjusted on the basis of a velocity signal, derived from the time between steps. Even higher speeds may be attained by a control system which commands a position more than one step away from the dynamic position.This technique may be particularly effective where the delay in energizing windings becomes a significant limiting factor in stepper performance. Under these circumstances, the feedback signal will have to be measured on the other winding and a delay adjustment may be necessary to avoid producing reverse forces or torques.

Although two waveform generators are shown in Fig. 5 for each winding, it will be appreciated by those skilled in the art that where the no-motion waveform produced when one end of a winding is switched to the lower potential is substantially the same as when the other end of the winding is switched to the lower potential, then only a single waveform generator is needed for each winding.

Similarly, only one comparator would be required for each winding, if it were time shared. When employing integrated circuits, however, it is often simpler to avoid time sharing and to use multiple components, the additional size and cost being nominal.

Although unnecessary to enable persons skilled in the art to make and use the present invention, a complete program for both open loop and closed loop positioning is annexed hereto as an Appendix since that constitutes the best mode contemplated by the applicant of carrying out the invention.

Claims (33)

1. An incremental motion drive system comprising a variable reluctance stepper motor and a controller for said motor, said motor having at least two windings characterized by no-motion signals having unperturbed waveforms and motion-dependent signals having perturbed waveforms; and said controller comprising waveform generator means for synthesizing waveforms modeled after said nomotion signals; and comparator means for comparing said synthesized waveforms with said motiondependent waveforms; and means for controlling the energization of said windings in response to said comparison.

2. The incremental motion drive system of claim 1 comprising a DC variable reluctance stepper motor and a controller for said motor, said motor having first and second windings characterized by nomotion signals having unperturbed waveforms and motion-dependent signals having perturbed waveforms, and a motor controller, said controller comprising a first and second motor drive circuit connected, respectively, to said first and second windings for energizing same; and first waveform generator means for synthesizing waveforms modeled after said no-motion signals produced by said first winding; and second waveform generator means for synthesizing waveforms modeled after said no-motion signals produced by said second winding; and first comparator means connected to said first winding and to the output of said first waveform generator means for comparing the synthesized waveforms modeled after said no-motion signals produced by said first winding with said motion depending waveforms produced by said first winding; and second comparator means connected to said second winding and to the output of said second waveform generator means for comparing the synthesized waveforms modeled after said no-motion signals produced by said second winding with said motion-depending waveforms produced by said second winding; and processor means connected to said first and second motor drive circuits, said first and second waveform generator means and to said first and second comparator means for controlling the energization of said first and second windings in response to said comparisons.

3. The incremental motion drive system as claimed in claim 1 wherein said motor is a variable reluctance, bi-directional stepper motor comprising a first member having a plurality of teeth having a pitch P and a width equal to P/2; and a second member moveable relative to said first member, said second member comprising two poles, each pole having two sets of teeth having a pitch P and a width equal to P/4, the sets of teeth in each pole being offset from each other by an amount equal to (n + 1/2)P, n being an integer, said poles being offset from each other by an amount equal to (m + 1/4)P, m being an integer, each of said poles having associated therewith a winding adapted for connection to a direction current source and constituting one of said windings, said second member having associated therewith at least one magnet.

4. The incremental motion drive system as claimed in claim 3 wherein said first member of said motor is stationary and said second member moves.

5. The incremental motion drive system as claimed in claim 3 wherein said second member of said motor is stationary and said first member moves.

6. The incremental motion drive system as claimed in claim 3 wherein said magnet is a permanent magnet.

7. The incremental motion drive system as claimed in any one preceding claim wherein said processor means for controlling the energization of said windings comprises means for determining the difference between a desired motor position and the present motor position; and means for determining the direction of stepping and means for stepping said motor so as to reduce said difference to zero.

8. The drive system as claimed in claim 7 further including means for decelerating said motor when said difference has been reduced to a predetermined value.

9. The drive system as claimed in claim 7 wherein said first and second motor drive circuits each comprises a four tansistor H-bridge connected across the winding, siad four transistors being selectively energized in pairs under control of said processor means to effect current reversal through the winding and stepping of said motor.

10. The drive system as claimed in claim 7 wherein said first and second waveform generator means each comprises two waveform generators and wherein said first and second comparator means each comprises two comparators.

11. The drive system as claimed in claim 7 wherein said no-motion signals have exponential waveforms.

12. The drive system as claimed in claim 7 wherein said synthesised waveforms are offset in the direction of perturbation.

1 3. The drive system as claimed in claim 7 wherein said exponential waveforms are of the general type V=a(l--e-b') where a and bare constants.

1 4. The incremental motion drive system as claimed in claim 13 wherein said motion-dependent signal has a perturbed exponential waveform of the general type V'=a(1ebt), where for some t > 0, b = b(t), first decreasing in value and then increasing in value.

1 5. The incremental motion drive system as claimed in one or more of claims 2 through 14 wherein said motor is a linear variable reluctance stepper motor and wherein said first member of said motor is a cylindrical motor member having a plurality of regular helical teeth with grooves therebetween; and said second member is a cylindrical motor member surrounding at least a portion of said first member, said second member comprising two annular poles separated by an annular magnet, each pole having two annular elements separated by an annular winding, each element having a set of regular helical teeth with grooves therebetween, said teeth having a pitch P and a width equal to P/4, the sets of teeth in each pole being offset longitudinally from each other by an amount equal to (n + 1/2)P, said poles being offset from each other in the longitudinally direction by an amount equal to (m + 1/4)P.

1 6. The incremental motion drive system as claimed in claim 1 5 wherein said second motor member includes annular flux "regulators" disposed on each side of said magnet and between said magnet and each pole, the cross section of said flux "regulators" narrowing from said magnet toward each of said poles.

1 7. The incremental motion drive system as claimed in claim 1 6 wherein said magnet is a permanent magnet.

1 8. The incremental motion drive system as claimed in claim 1 7 wherein said permanent magnet is a rare earth permanent magnet.

1 9. The incremental motion drive system as claimed in claim 1 5 wherein said grooves of said elements are filled with a Teflon or Nylon loaded material.

20. The incremental motion drive system as claimed in claim 5, wherein said motor is a disc, rotary, variable reluctance stepper motor comprising a disk-shaped rotor mounted on a shaft and having a plurality of wedge-shaped, radially extending equally spaced teeth; and a stator comprising two poles, one disposed on each side of said rotor, each stator pole having two sets of wedge-shaped, radially extending, equally spaced teeth, the locii of said sets of stator teeth describing circles having two different radii, the sets of teeth in each rotor pole being offset from each other by an angular amount equal to (n I 1/2)P, the two stator poles being offset from each other by an angular amount equal to (m + 1/4)P, each stator pole also including an annular magnet and an annular winding constituting one of said windings.

21. The drive system of claim 20 wherein said rotor further includes an annular-shaped iron ring disposed between said shaft and said rotor teeth to conduct flux between said stator poles.

22. The drive system as claimed in claim 18 or 20 wherein said magnet is a permanent magnet and preferably a rare earth permanent magnet.

23. The incremental motion drive system as claimed in claims 1 to 14 wherein the motor is a cylindrical, rotary, variable bi-directional stepper motor comprising a cylindrical rotor having a plurality of longitudinally extending teeth with grooves therebetween, said rotor teeth having an angular pitch P and an angular width equal to 1/2P; and a cylindrical stator surrounding said rotor, said stator having two annular poles separated by an annular magnet, each stator pole having two sets of equally spaced, longitudinally extending teeth having an angular pitch P and an angular width equal to 1/4P, the sets of teeth in each stator pole being offset from each other by an angular amount equal to (n + 1/2)P, n being an integer, the two stator poles being offset from each other by an angular amount equal to (m + 1/4)P, m being an integer, the sets of teeth in each stator pole being separated by an annular winding constituting one of said windings, and adapted for connection to a direct current source.

24. A method for fabricating one member of the bi-directional, linear, variable reluctance stepper motor as claimed in claim 15, comprising the steps of (a) cutting helical threads into the outer periphery of an iron rod; (b) tin flashing said threaded rod; (c) fitting an electrically conducting, non-magnetic tinned strip of material into the helical groove in said threaded rod; (d) soldering said threaded rod with said tinned strip fitted therein; (e) grinding said soldered rod to a diameter approximating the desired finished diameter; and (f) plating said ground rod to produce a hard surface thereon.

25. The method as claimed in claim 24 including subsequent to grinding and prior to plating the step of copper flashing the ground rod.

26. The method as claimed in claim 25 wherein said copper flashed rod is plated with chromium.

27. The method as claimed in claim 26 wherein said ground rod is plated with nickel.

28. The method for controlling incremental motion by controlling a variable reluctance stepper motor having first and second windings characterized by no-motion signals having unperturbed signals and motion-dependent waveforms having perturbed waveforms, said method comprising the steps of (a) synthesizing waveforms modeled after said no-motion signal; (b) comparing the synthesized waveforms with the motion-dependent waveforms; and (c) controlling the energization of said windings in response to said comparison.

29. The method as claimed in claim 28 further including the step of offsetting the synthesized waveforms in the direction of perturbation.

30. The method as claimed in claim 28 wherein said synthesized waveforms are exponential waveforms.

31. The method as claimed in claim 30 wherein said exponential waveforms are of the general type V = a(1e-bt), where a and b are constants.

32. The method as claimed in claims 28 to 31, said method comprising the steps of (a) determining the difference between a desired motor position and the present invention; (b) determining the direction of stepping; (c) synthesizing waveforms modeled after said no-motion signal; (d) comparing the synthesized waveforms with the motion-dependent waveforms; (e) controlling the energization of said windings in response to said comparisons; and (f) stepping said motor so as to reduce said difference to zero.

33. The method as claimed in claim 32 further including the step of decelerating said motor when said difference has been reduced to a predetermined value.

APPENDIX Memory Instruction Location Mnemonic Mode Opcode Comments 0400 00 OPSELL 0401 04 OPSELH 0402 CF STDEL 0403 00 POSCOM 0404 00 POSNOW 0405 00 DIRFLG 0406 00 OFFSET 0407 00 DELIND 0408 7F INDLD 0409 1F SENDEL 040A FF SENCNT 0408 08 SCMASK 040C 20 GOADRL 040D 05 GOADRH 040E 00 TWOFLG 040F 00 TWOPS1 0410 32 TOPS 2 0411 03 SEVIND 0412 F8 SEVPS 1 0413 9A SEVPS2 0414 90 SEVPS3 0415 50 SEVPS4 0416 13 SEVPS5 0417 09 SEVPS 6 0418 00 SEVPS 7 0419 7F EXPDEL 041A 0418 041C 041D Memory Instruction Location Mnemonic Mode Opcode Comments 041E 041F 0420 CC Final Drive State 1 0421 99 Final Drive State 2 0422 33 Final Drive State 3 0423 66 Final Drive State 4 0424 04 Feedback Sensing Mask 1 0425 08 Feedback Sensing Mask2 0426 01 Feedback Sensing Mask 3 0427 02 Feedback Sensing Mask 4 0428 04 Feedback Sensing Mask 1 0429 03 2 Step Delay 042A 04 3 Step Delay 1 0428 03 3 Step Delay 2 042C 04 4 Step Delay 1 042D 05 4 Step Delay 2 042E 03 4 Step Delay 3 042F 04 5 Step Delay 1 0430 05 5 Step Delay 2 0431 06 5 Step Delay 3 0432 03 5 Step Delay 4 0433 04 6 Step Delay 1 0434 05 6 Step Delay 2 0435 06 6 Step Delay 3 0436 07 6 Step Delay 4 0437 03 6 Step Delay 5 0438 04 7 Step Delay 1 0439 05 7 Step Delay 2 043A 06 7 Step Delay 3 Memory Instruction Location Mnemonic Mode Opcode Comments 0438 07 7 Step Delay 4 043C 05 7 Step Delay 5 043D 03 7 Step Delay 6 043E 04 8 Step Delay 1 043F 05 8 Step Delay 2 0440 06 8 Step Delay 3 0441 07 8 Step Delay 4 0442 07 8 Step Delay 5 0443 04 8 Step Delay 6 0444 03 8 Step Delay 7 0445 29 Delay Address Offset 1 0446 29 Delay Address Offset2 0447 2A Delay Address Offset3 0448 2C Delay Address Offset4 0449 2F Delay Address Offset 5 044A 33 Delay Address Offset6 0448 38 Delay Address Offset 7 044C 3E Delay Address Offset 8 044C B7 0-OP Reset Counters 044E C2 1-OP Step Slow + 044F CD 2-OP Step Slow 0450 D8 3-OP Step Fast + 0451 EO 4--OP Step Fast 0452 E8 5-OP Two Positions 0453 EB 6-OP Seven Positions 0454 EE 7-OP Feedback On 0455 F6 8-OP Feedback Off Memory Instruction Location Mnemonic Mode Opcode Comments 0456 83 9-OP Unused 0457 6C Intermediate Drive State 1-F 0458 C9 Intermediate Drive State 2-F 0459 93 Intermediate Drive State 3-F 045A 36 Intermediate Drive State 4-F 0458 9C Intermediate Drive State 1-R 045C 39 Intermediate Drive State 2-R 045D 63 Intermediate Drive State 3-R 045E C6 Intermediate Drive State 4--R 045F 0460 LDA IMM A9 Initialization Entry 0461 FF 0462 STA ABS 8D Designate Port B - Outputs 0463 01 0464 17 0465 LDA IMM A9 0466 CC 0467 STA ABS 8D Set Output - Final State 1 0468 00 0469 17 046A CLD IMP D8 0468 LDA IMM A9 046C OC 046D STA ABS 8D Designate Port A - Inputs 046E 03 046F 17 Memory Instruction Location Mnemonic Mode Opcode Comments 0470 STA ABS 8D Set IRQ L.S.B.= 00 0471 FE 0472 17 0473 LDA IMM A9 0474 IC 0475 STA ABS 8D Set IRQ M.B.S. = 1C 0476 FF 0477 17 0478 LDY IMM AO Initialize RAM i780-179F 0479 20 047A LDA ABY 89 Loop to load RAM from PROM 0478 00 Loop to load RAM from PROM 047C 04 Loop to load RAM from PROM 047D STA ABY 99 Loop to load RAM from PROM 047E 80 Loop to load RAM from PROM 047F 17 Loop to load RAM from PROM 0480 DEY IMP 88 Loop to load RAM from PROM 0481 BNE REL Do Loop to load RAM from PROM 0482 F7 (-9) Loop to Load RAM from PROM 0483 LDA IMM A9 Monitor Entry Display POSNOW 0484 7F 0485 STA ABS 8D Initialize Display 0486 41 0487 17 0488 LDX IMM A2 Memory Instruction Location ' Mnemonic Mode Opcode Comments 0489 11 048A LDA ABS AD Fetch POSNOW 0488 84 048C 17 048D LSR IMP 4A Shift 4X to Display 048E LSR IMP 4A Upper byte 048F LSR IMP 4A 0490 LSR IMP 4A 0491 JSR ABS 20 Jump to KIM display subroutine 0492 48 0493 1F 0494 LDA ABS AD Fetch POSNOW 0495 84 0496 17 0497 AND IMM 29 Mask lower byte for display 0498 OF 0499 JSR ABS 20 Jump to KIM display Routine 049A 48 0498 1F 049C STX ABS 8E 049D 42 049E 17 049F LDA IMM A9 04A0 00 04A1 STA ABS 8D Turn off display 04A2 41 04A3 17 04A4 JSR ABS 20 Jump to KIM Subroutine GETKEY 04A5 Memory Instruction Location Mnemonic Mode Opcode Comments 04A6 1F 04A7 CMP IMM C9 04A8 OA 04A9 BCS REL BO Loop if key not 0--9 04AA D8 (-40) (Abs = 0483) 04AB NOP EA 04AC NOP EA 04AD TAX IMP AA Transfer Key No. to Index 04AE LDA ABX BD Fetch lower byte of address 04AF 4D for selected operation 0480 04 04B1 STA ABS 8D Store in OPSELL 0482 80 0483 17 0484 JMP IND 6C Jump to selected operation 0485 80 0486 17 0487 LDA IMM A9 O-OP Reset Counters 0488 OC 0489 STA ABS 8D set POSCOM = O 04BA 83 0488 17 048C STA ABS 8D Set POSNOW = O 048D 84 048E 17 048F JMP ABS 4C Return to MONITOR 04C0 83 04C 1 04 04C2 LDA IMM A9 1-OP Step Slow it Memory Instruction Location Mnemonic Mode Opcode Comments 04C3 CF 04C4 STA ABS 8D Set STDEL Maximum 04C5 82 04C6 17 .04C7 INC ABS EE Add 1 to POSCOM 04C8 83 04C9 17 04CA JMP ABS 4C Go to STEPCT Routine 04C8 FB 04CC 04 04CD LDA IMM A9 2-OP Step Slow 04CE CF 04CF STA ABS 8D Set STDEL Maximum 04D0 82 04D1 17 04D2 DEC ABS CE Subtract 1 from POSCOM 04D3 82 04D4 18 04D5 JMP ABS 4C Go to STEPCT Routine 04D6 FB 04D7 04 04D8 LDA IMM A9 3-OP Step Fast + 04D9 18 04DA STA ABS 8D set STDEL Minimum 04DB 82 04DC 17 O4DD JMP ABS 4C Finish with 1-OP 04DE C7 04DF 04 04EO LDA IMM A9 4-OP Step Fast Memory Instruction Location Mnemonic Mode Opcode Comments 04E1 18 04E2 STA ABS 8D Set STDEL minimum 04E3 82 04E4 17 04E5 JMP ABS 4C Finish with 2-OP 04E6 D2 04E7 04 04E8 JMP ABS 4C 5-OP Two Position 04E9 05 04EA 06 04EB JMP ABS 4C 6-OP Seven Position 04EC 1E 04ED 06 04EE LDA IMM A9 7-OP Turn on Feedback 04EF 58 04FO STA ABS 8D Load GOADRL 04F1 8C 04F2 17 04F3 JMP ABS 4C Return to MONITOR 04F4 83 04F5 04 04F6 LDA IMM A9 8-OP Turn OFF Feedback 04F7 20 04F8 JMP ABS 4C Finish with 7-OP 04F9 FO 04FA 04 04FB LDA ABS AD STEPCT Entry-Load POSCOM 04FC 83 04FD 17 Memory Instruction Location Mnemonic Mode Opcode Comments 04FE SEC IMP 38 04FF SBC ABS ED Subtract POSNOW 0500 84 0501 17 0502 BEQ REL FO OFFSET=O? Exit 0503 19 (+25) 0504 BCS REL 80 OFFSET ? 0505 OC (+ 12) 0506 EOR IMM 49 Complement 0507 FF 0508 ADC IMM 69 Correct 0509 01 050A LDX IMM A2 0508 FF 050C STX ABS 8E Set DIRFLG=-1 050D 85 050E 17 050F JMP ABS 4C 0510 17 0511 05 0512 LDX IMM A2 0513 0514 STX ABS 8E Set DIRFLG = + 1 0515 85 0516 17 0517 STA ABS 8D Store OFFSET 0518 86 0519 17 051A JMP IND 6C Jump'to Feedback or Non-Feedback 051B 8C Control Routine 051C 17 Memory Instruction Location Mnemonic Mode Opcode Comments 051 D JMP ABS 4C Exit to next Position Delay 051E F7 051F 05 0520 CMP IMM C9 NON-FEEDBACK Entry-Offset > 8? 0521 09 0522 BCS REL 80 Go to Long Move Routine 0523 15 (+ 21) 0524 TAX IMP AA Prepare index for DELIND fetch 0525 LDA ABX BD Fetch address of first Delay 0526 44 0527 04 0528 STA ABS 8D Store DELIND 0529 87 052A 17 0528 JSR ABS 20 Go to STEPS Sub routine 052C 7F 052D 05 052E BEQ REL FO Exit if OFFSET=0 052F ED 0530 JSR ABS 20 Go to DELAY Sub routine 0531 JSR ABS 82 0532 05 0533 INC ABS EE Increment DELIND 0534 87 0535 17 0536 JMP ABS 4C Loop until OFFSET = 0 0537 28 0538 05 Memory Instruction Location Mnemonic Mode Opcode Comments 0539 LDA IMM A9 Long Move Entry 053A 3E 053B STA ABS 8D Store DELIND = initial value for 8 step move 053C 87 053D 17 053E JSR ABS 20 Go to STEPS Sub-routine 053F 7F 0540 05 0541 JSR ABS 20 Go to DELAY Sub-routine 0542 B2 0543 05 0544 INC ABS EE Increment DELIND 0545 87 0546 17 0547 LDA ABS AD Load new DELIND 0548 87 0549 17 054A CMP IMM C9 Midpoint Delay? 054B 41 054C BNE REL DO Loop until midpoint delay reached 054D FO (-16) 054E JSR ABS 20 Go to STEPS Sub-routine 054F 7F 0550 05 0551 CMP IMM C9 4 Steps remaining? 0552 05 0553 BCC REL 90 Do last 4 steps de crementing DELIND 0554 DB (-37) offer each step Abs = 0530 0555 JSR ABS 20 Go to DELAY Sub-routine 0556 B2 Memory Instruction Location Mnemonic Mode Opcode Comments 0557 05 0558 JMP ABS 4C Loop until 4 steps remain 0559 4E 055A 05 055B CMP IMM C9 Feedback Entry OFFSET 2? 055C 03 055D BCC REL 90 If OFFSET < 2, switch to NON-FEEDBACK 055E C5 (-59)control routine 055F JSR ABS 20 Go to STEPS Sub-routine 0560 7F 0561 05 0562 CMP IMM C9 OFFSET=2? 0563 02 0564 BEQ REL FO Go to DECEL Routine 0565 06 (+6) 0566 JSR ABS 20 Go to DELSON Sub-routine 0567 C4 0568 0 0569 JMP ABS 4C Loop until OFFSET = 2 056A 5F 056B 05 056C JSR ABS 20 DECELERATION--Go to DELSCN, if input = O return 056D C4 056E 05 056F LDA ABS AD Load SCMASK 0570 8B 0571 17 0572 AND ABS 2D AND SCMASK with Input Memory Instruction Location Mnemonic Mode Opcode Comments 0573 02 0574 17 0575 BEQ REL FO Continue scanning until Input= 1 0576 F8 (-8) 0577 JSR ABS 20 Go to STEPS Sub-routine 0578 7F 0579 05 057A BEQ REL FO If OFFSET = 0, branch to Next Po sition DELAY 057B 7B (+ 123) ABS 4C 057D 6C 057E 05 057F LDA ABS AD STEPS Subroutine- load POSNOW 0580 84 0581 17 0582 CLC IMP 18 0583 ADC ABS 6D Use DIRFLG to modi fy POSNOW 0584 85 0585 17 0586 STA ABS 8D Store new POSNOW 0587 84 0588 17 0589 AND IMM 29 Mask two lower hits 058A 03 0588 LDY ABS AC Test DIRFLG 058C 85 058D 17 058E BPL REL 10 Branch if N = O or Dl RFLG + Memory Instruction Location Mnemonic Mode Opcode Comments 058F 03 (+3);if-,increase index by 4 0590 CLC IMP 18 0591 ADC IMM 69 Add 4 to Index 0592 04 0593 TAX IMP AA Final Index 0594 LDA ABX BD 0595 57 0596 04 0597 STA ABS 8D Set intermediate output state 0598 00 0599 17 059A LDA ABS AD Load Exp.Delay Value 059B 99 059C 17 059D TAY IMP A8 059E DEY IMP 88 Loop to Delay Start of 059F BNE REL DO Synthesized Ex ponential OSAO FD (-3) 05A1 TX-A IMP 8A 05A2 AND IMM 29 05A3 03 05A4 TAX IMP AA Prepare index for Final Drive State 05A5 LDA ABX BD 05A6 20 05A7 04 05A8 STA ABS 8D Set Final Output State 05A9 00 05AA 17 Memory Instruction Location Mnemonic Mode Opcode Comments 05AB DEC ABS CE Decrement OFFSET 05AC 86 05AD 17 05AE LDA ABS AD Load new OFFSET 05AF 86 05B0 17 05B1 RTS IMP 60 05B2 LDA IMM A9 DELAY Subroutine load DELVAL 05B3 40 05B4 SEC IMP 38 05B5 LDX ABS AE Load DELIND 0586 87 05B7 17 05B8 LDY ABS AC Load INDLD--Outer Delay Loop 05B9 88 05BA 17 05BB DEY IMP 88 Inner Delay Loop 05BC BNE REL DO Inner Delay Loop 05BD FD (- 3) Inner Delay Loop 05BE SBC ABX FD 05BF CO OSCO 04 05C1 BPL REL 10 05C2 F5 (- 11) Outer Delay Loop 05C3 RTS IMP 60 05C4 LDX ABS AE DELSCN Subroutine Load SEN DEL 05C5 89 05C6 17 05C7 DEX IMP CA Loop of Delay Scanning of Inputs Memory Instruction Location Mnemonic Mode Opcode Comments 05C8 NOP EA Loop to Delay Scanning of Inputs 05C9 NOP EA Loop to Delay Scanning of Inputs 05CA BNE REL DO Loop to Delay Scanning of Inouts 05CB FB (- 5) Loop to Delay Scanning of Inouts 05CC LDA ABS AD Fetch POSNOW 05CD 84 05CE 17 05CF AND IMM 29 Mask 2 L.S.B.

05D0 03 05D1 TAX IMP AA Prepare tentative index 05D2 LDY ABS AC 05D3 85 Test DIRFLG 05D4 17 if +, increase index by 1 05D5 BMI REL 30 05D6 01 (+1) 05D7 INX IMP E8 05D8 LDA ABX BD Fetch SCMASK Value 05D9 24 05DA O 05DB STA ABS 8D StoreSCMASK 05DC 8B O5DD 17 OSDE LDX ABS AE Fetch SENCNT 05DF 8A 05E0 17 05E1 LDY IMM AO 05E2 FF 05E3 LDA ABS AD Load SCMASK 05E4 8B Memory Instruction Location Mnemonic Mode Opcode Comments 05E5 17 05E6 AND ABS 2D Read Inout 05E7 02 05E8 17 05E9 BEQ REL FO Branch if Input=0 Take next step 05EA OB (+ 11) 05EB DEY IMP 88 05EC BNE REL DO 05ED F5 (-11) 05EE DEX IMP CA 05EF BNE REL DO 05FO FO (-16) 05F1 PLA IMP 68 Adjust Stock pointer in prep. to abort.

subroutine 05F2 PLA IMP 68 Jump to Monitor 05F3 JMP ABS 4C Jump to Monitor 05F4 83 05F5 04 05F6 RTS IMP 60 05F7 LDY IMM AO Next Position Delay - Entry 0000 05F8 FF 05F9 LDX BAS AE Load STDEL 05FA 82 05FB 17 05FC DEX IMP CA 05FD BNE REL DO 05FE FD (-3) 05FF DEY IMP 88 0600 BNE REL DO 0601 F7 (-9) Memory Instruction Location Mnemonic Mode Opcode Comments 0602 JMP ABS 4C Jump to Monitor 0603 83 0604 04 0605 LDX IMM A2 Two Position Routine Entry OCOE 0606 OO 0607 CPX ABS EC Is TWOFLG = 0 0608 8E 0609 18 060A BEQ IMP FO 060B 05 (+ 5) 060C STX ABS 8E Set TWOFLG = 0 060D 8E 060E 17 060F BNE IMP DO Unconditional 0610 D4 (+ 4) 0611 INX IMP E8 Set X = 1 0612 STX ABS 8E SetTWOFLG = 1 0613 8E 0614 17 0615 LDA ABX BD Fetch next TWOPS, X 0616 8F 0617 17 0618 STA ABS 8D Store in POSCOM 0619 83 061A 17 061 B JMP ABS 4C Go to STEPCT 061C FB 061 D 04 061 E LDX ABS AE Seven Position Routine Entry 0027 061F 91 0620 17 Memory Instruction Location Mnemonic Mode Opcode Comments 0621 LDA ABX BD Fetch next value 0622 92 0623 17 0624 STA ABS 8D Store in POSCOM 0625 83 0626 17 0627 DEX IMP CA 0628 BNE REL DO Is SEVIND = 0? 0629 02 062A LDX IMM A2 062B 06 062C STX ABS 8E Set SEVIND = 6 062D 91 062E 17 062F JMP ABS 4C Go to STEPCT 0630 FB 0631 04