GB2264369A

GB2264369A - Method and device for positioning an adjusting mechanism in a motor vehicle

Info

Publication number: GB2264369A
Application number: GB9302697A
Authority: GB
Inventors: Chi-Thuan Cao
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 1992-02-12
Filing date: 1993-02-11
Publication date: 1993-08-25
Anticipated expiration: 2013-02-11
Also published as: GB2264369B; GB9302697D0; DE4204047A1; DE4204047C2; JP3305392B2; JPH0628037A

Description

2264369

- 1DESCRIPTION METHOD AND DEVICE FOR POSITIONING AN ADJUSTING MECHANISM IN A MOTOR VEHICLE

The present invention relates to a method and device for positioning an adjusting mechanism in a motor vehicle.

A method for carrying out the adaptive position control in the case of electro-mechanical drives which are affected by friction is known from DE 37 31 984 A. With this method, the time graph of the amount of frictional force is determined by means of a nonlinear observer which is supported by a model. The sign digit of the frictional force detected in a different manner is subsequently added to the amount. In order to compensate for the frictional force detected in this way, a device is connected in parallel with a governor and the output signal of the device is combined with the output signal of the governor. The control system is influenced by the signal produced this way.

A disadvantage of this method exists in the fact that a model must be found which as accurately as possible describes a control system in order to obtain good control characteristics. The more accurately the control system needs to be described, the more comprehensive and the more complicated is the model -2used for the description. This makes it difficult to transfer the control process to different systems and to seek and remove errors.

A control system for an adjusting mechanism affected by friction is known from DE 40 12 577 C1. With this control system, a two-position controller is connected downstream of a position controller. The hysteresis width of the two-position controller can be adjusted dependent upon the operating conditions. This arrangement enables the influence of the friction to be reduced, in order to improve the dynamics of the system. A disadvantage of this control system exists in the fact that as a result of the control process by means of the two-position controller, the adjusting mechanism fluctuates constantly about the desired position. This leads to an increased amount of wear and increased energy consumption of the adjusting mechanism. Moreover, it is not possible to limit the deviation to a permanently low value, rather the deviation remains oscillating with respect to time between zero and half of the hysteresis width.

A similar control device is known from DE 32 07 863 Al, wherein a twoposition controller is connected downstream of a non-linear controller. The number of switching actuations of the two-position controller is limited by means of a limiter stage.

A system for controlling the velocity of a motor vehicle by means of fuzzy logic is known from US 5 005 133. In this case. the actual value of the velocity is determined and a desired value is established taking into consideration the wishes of the driver. Suitable associated functions are selected depending upon the driving condition (e.g. the gear engaged). Based on the associated functions located in this way and the desired value and actual value of the velocity, a correcting variable for controlling an adjusting mechanism is determined using fuzzy rules.

The above-mentioned method and devices have the disadvantage, that it is not possible to carry out an optimum control under all operating conditions.

An object of the invention is to render it possible to position an adjusting mechanism precisely and quickly in a motor vehicle. in so doing, the deviation between the desired value and the actual value should be maintained as low as possible under as many as possible operating conditions and the control characteristics should remain stable even in extreme cases. In particular, small deviations should also be ruled out reliably despite any existing friction or other non-linearities.

In accordance with a first aspect of the present invention there is provided a method for positioning an adjusting mechanism by means of a control loop, wherein a deviation (1) between a desired value (L#) and an actual value (y) is determined and fed as an input variable to a controller having at least one of the control characteristics P, If D, which controller supplies a first correcting variable (A,), and a fuzzy controller lies in parallel with the controller or can be switched and/or alternatively switched in to the controller, the fuzzy controller is fed the derivative with respect to time (el) of the deviation and the deviation (e) as input variables and the fuzzy controller supplies a second correcting variable (312).

In accordance with a second aspect of the present invention there is provided a device for positioning an adjusting mechanism by means of a control loop, wherein a means for determining a deviation (e) between a desired value (La) and an actual value (y) of a signal in association with the position of the adjusting mechanism and a controller is provided, the controller having at least one of the control characteristics P, If D, receives the deviation (1) as an input variable and supplies a first correcting variable (A,), wherein a fuzzy controller lies in parallel to the controller or can be switched and/or can be alternatively switched in to the controller, receives the derivative with respect to time (el) of -5the deviation as an input variable in addition to the deviation (e) and supplies a second correcting variable (22).

This has the advantage, that the above-mentioned disadvantages are overcome.

The rapid transient characteristics and the good disturbance handling characteristics of the controller have a particularly advantageous effect. The compensation for friction enables the desired value to be adjusted precisely. A further advantage is the robustness of the controller even in extreme conditions. The adaption principle of the control process renders it possible to adapt it, without any problem, to suit the actual area of application without interfering with the structure of the controller.

Both standardised and also non-standardised variables are used in connection with the illustration of the invention. For the purpose of differentiationy the symbols for the non-standardised variables are underlined in each case.

By way of example only specific embodiments of the present invention will now be described with reference to, and as illustrated in, the accompanying drawings, in which:

Fig. 1 is a block diagram of the control loop with a fuzzy controller constructed in accordance with one embodiment of the invention; Fig. 2 is the schematic illustration of the structure of a simple fuzzy controller; Fig. 3 is the schematic illustration of the structure of an adaptive fuzzy controller; Fig. 4 illustrates the associated functions for the standardised deviation e, the standardised derivative with respect to time el of the deviation and the standardised correcting variable u; Fig. 5 is a phase plane for the standardised deviation e and the standardised derivative with respect to time e' of the deviation; Fig. 6 is a table for the allocation of areas of the phase plane into categories of the standardised correcting variable u; Fig. 7 is a listing of fuzzy rules; and Fig. 8 is a graph illustrating the application of fuzzy rules.

The structure and the method of functioning of the invention are described by way of an example for use in connection with a fuel metering system in a diesel internal combustion engine. In this example, the invention provides signals for controlling the electro-magnetic adjusting mechanism of a fuel injection pump which meters the fuel.

Referring to Fig. 1, a block 10 makes available a desired value w of the position of an electro-magnetic adjusting mechanism of a fuel metering system as a first input signal for a summation point 11. An actual value y of the adjusting mechanism position is entered into the summation point 11 as a further input signal. The actual value y is subtracted from the desired value w at the summation point 11. This gives the deviation e. The deviation e is fed to the controller 12 which determines a correcting variable ul from the deviation and passes the correcting variable to a further summation point 13. The summation point 13 receives as a further input signal a correcting variable 22 determined from a fuzzy controller 14 and supplies the total from ul and 22 as an output signal u. The fuzzy controller 14 is disposed in parallel with the controller 12 and comprises two inputs. The deviation e, determined by means of the summation point 11, lies at the first input and the derivative with respect to time el of the deviation e which is determined from the deviation A by means of a differentiating stage 15 lies at the second input.

The output signal u of the summation point 13 is fed to the electromagnetic adjusting mechanism 16 of the fuel metering system and the fuel metering system meters the fuel accordingly. A sensor 17 connected to the adjusting mechanism 16 determines the actual position y of the adjusting mechanism and reports back to the summation point 11 by means of a feedback line 18.

Depending upon the area of application, the controller 12 comprises at least one of the components P.. I, D (proportional, integral, differential). It is designed in such a way that in the case of the friction of the adjusting mechanism 16 being neglected, an optimum control is renderad possible. The influence of the friction is compensated for by means of the fuzzy controller 14. The fuzzy controller 14 is designed in such a way that it becomes heavily involved in the control process, i.e. it supplies a high amount M2 to the correcting variable u especially in the case of small deviations, where the frictional forces particularly cause interference. In this way, permanent deviations which mostly occur in the same situation with conventional controllers are prevented. In the case of extremely large deviations, the influence of the fuzzy controller 14 is comparatively small and the control characteristics are mainly determined by means of the controller 12.

In a further embodiment, the fuzzy controller 14 can be switched in and/or alternatively switched in to the controller 12 in the case of small deviations e. The switching and/or alternatively switching in of the fuzzy controller 14 is carried out if a predeterminable value of the deviation e is not achieved and upon exceeding this value the process is reversed. In so doing, it can prove to be advantageous that the switching process is only carried out if the switching requirement has existed at least for a predetermined period of time.

Methods known from the prior art can be used in order to determine the desired position w of the electro-magnetic adjusting mechanism 16 by means of block 10. Normally, the desired position w of the adjusting mechanism 16 is determined from various operating parameters taking into consideration the wishes of the driver and by means of characteristic curves and characteristic fields.

Fig. 2 illustrates a schematic illustration of the fuzzy controller 14 which comprises internally three in-line functional elements 20, 22 and 24. These three functional elements are normally designated as fuzzification 20, fuzzy logic 22 and defuzzification 24.

The first functioning element 20 receives the deviation e as an input signal and the derivative with respect to time el of the deviation e. The standardised deviation e and the standardised derivative with respect to time el of the deviation are obtained by standardising the deviation e and its derivative with respect to time e'. Two families of associated functions Me and Me, which are graphically illustrated in Fig. 4 are associated with the variables e and e'. The actual values for e and/or e' are noted in each associated function and the associated-functions are subsequently relayed to the second functional element 22.

The fuzzy rules regarding the associated functions made available by the first functional element 20 are applied in the second functional element 22 and as a result an associated function pu is obtained for the correcting variable. A graphic illustration of this operation which is normally designated as fuzzy logic is illustrated in Fig. 8 described below. The associated function pu is relayed to the third functional element 24 which produces a standardised correcting variable u therefrom. by forming a.mean value. A correcting variable j12 which is adjusted to suit the system in which the fuzzy controller 14 is used is determined from the standardised correcting variable u and made available at the output of the fuzzy controller 14.

Fig. 3 is a further embodiment of the fuzzy controller 14 which comprises an additional means for adapting the fuzzy controller. The actual fuzzy controller is contained in the block illustrated by the broken line, devices for determining a static control basis 32 and from the parameters K,, K2 and K3 are disposed outside the block. These devices can either only be present during the development phase of the controller, or if a constant adaptation is desired, entirely or partially also when the controller is being used. The core of the adaptive fuzzy controller (illustrated here) comprises as does the fuzzy controller of Fig. 2 the functional elements fuzzification 30, fuzzy logic 31, 32 and defuzzification 33. The configuration and method of functioning of functional elements of this type has already been described in the text relating to Fig. 2. The fuzzy logic element differs however from the element illustrated in Fig. 2 in that the fuzzy rules are located separately in a static control basis 32 in order to facilitate the adaption. The rules contained in the control basis 32 are applied in block 31 to the associated functions.

Two stages of adaption are provided in the adaptive fuzzy controller illustrated in Fig. 3. The characteristics of the controller are adapted in a first stage to suit an area of application. The static control basis 32 is influenced accordingly for this purpose by means of an expert knowledge module 34. Among other things the theory of the structure variable systems is exploited to form the fuzzy rules. The expert knowledge which is relevant for all possible areas of application is contained in the expert knowledge module 34.

An adaption to a special control system by selecting suitable parameters for influencing the input and output signals of the adaptive fuzzy controller is carried out in a second adaption stage. The deviation e is multiplied in a block 35 by a parameter K, and the standardised deviation e produced in this way is relayed to the block 30. The derivative with respect to time el of the deviation is multiplied in a block 36 by a parameter K2 and the standardised derivative with respect to time el of the deviation produced this way is relayed to the block 30. The standardised correcting variable u output by block 33 is multiplied in a block 37 by a parameter K3 and the correcting variable U2 produced in this way represents the output signal of the adaptive fuzzy controller.

The parameters K,, K2 and K3 are determined by means of adjusting the module 38 to suit. The data required for the adjustment can be determined either manually with the aid of the expert knowledge module 34 or automatically by evaluating a prediction for the deviation with an evaluating module 39. A block 40 makes the prediction of the deviation e(k+i) to the time k+i at the time k in the knowledge of the desired value w(k+i) and the actual value y(k).

When searching for the parameter K,, the value of the deviation e is determined, after which point it is no longer possible for the controller 12 from Fig. 1 to follow the desired value w. The deviation eo determined in this way should produce exactly half the maximum standardised deviation emax after being multiplied by the parameter K,. The following therefore applies:

K, " emax/2eO The positive and negative limits of the static friction F+s and F-s are required to determine K3. The parameter K3 is dimensioned in such a way that the force to compensate for the friction at emax/2 is at least equal to the maximum from F+s and F-S: K3 k max (2F+s/emax, 2F-S/emax) The parameter K2 is dimensioned in such a way that the dynamics of the fuzzy controller are -14optimised. This enables a deviation e(k+i) to be predicted either manually on the basis of the expert knowledge module 34 or automatically by the above described evaluation.

Associated functions are illustrated in Fig. 4. In order to define the associated functions. the value ranges of the standardised deviation e, of the standardised derivative with respect to time el of the deviation and the standardised correcting variable u are allocated in each case to several categories, wherein each category qualitatively describes the position of a sub-range within the value range. The strength of the allocation of each individual value of a value range to a category is determined by an associated function. For example, the strength of the allocation of the standardised deviation e to the category "negative small" is described by the associated function Me designated "NES" as shown in Fig. 4a.

Fig. 4 illustrates the associated functions for the categories "negative big" (NB), "negative small" (NS), 91positive small" (PS) and "positive big" (PB). The standardised variables e (Fig. 4a). e' (Fig. 4b) and u (Fig. 4c) are plotted on the x coordinates in each case for the range from a minimum value emin, e'min and/or umin to a maximum value emax, e'max and/or umax -15and the associated functions Pe (Fig. 4a), Pel (Fig. 4b) and pu (Fig. 4c) for the various categories are plotted on the y-axis. The associated functions assume in each case values between 0 and 1. The value 0 indicates that there is no associated function in the category under consideration and the value 1 indicates a complete associated function. In the example described here, the associated functions of the standardised deviation e (see Fig. 4a) and the standardised derivative with respect to time el of the deviation (see Fig. 4b), are identical to those for the same category. In principle, however, it is also possible to select different associated functions for each of these two variables. Depending upon the application, it is also possible to select other function graphs than those illustrated in Fig 4.

Fig. 5 illustrates a phase plane for the standardised deviation e and the standardised derivative with respect to time el of the deviation which renders it possible to derive in an efficient and clear manner the fuzzy rules for the purpose of determining the standardised correcting variable u from the standardised deviation e and the standardised derivative with respect to time el of the deviation. The standardised deviation e is plotted on the x-axis and the standardised derivative with respect to time -16el of the deviation is plotted on the y-axis. The phase plane is divided into several areas which are designated with the alphabetic letters A to H. The straight line lle+el=011 extends from top left to bottom right diagonally through the phase plane. The fuzzy rules are produced with reference to the phase plane in which in each case a category of the standardised correcting variable u is associated with an area or a combination of several areas.

Fig. 6 illustrates in a table form the arrangements between the areas of the phase plane (left-hand column) and the categories of the standardised correcting variable u (centre column). These arrangements provide the fuzzy rules (right-hand column), in that the areas of the phase plane are described by means of the logical summation of the categories for the standardised deviation e and the standardised derivative with respect to time el of the deviation.

Fig. 7 illustrates a list of fuzzy rules (Rl to R8). A set of rules for each of the two ranges of phase plane "e'>-e" (Rl to R4) and llel:S-ell (R5 to R8). Each fuzzy rule is introduced by the word "IF",, followed by a premise. The premise is followed by the word "THEW and a consequence. The premise comprises a category input or several category inputs summated -17by means of logical operators for the standardised deviation e and/or the standardised derivative with respect to time e' of the deviation. The variable to which the respective category input refers lies here between the two abbreviations for the category, e.g. NEB means that the standardised deviation e is "negative big". The consequence contains a category input for the standardised correcting variable u, e.g. "NUB".

Fig. 8 is the application of fuzzy rules for the example values eo of the standardised deviation e and e'o of the standardised derivative with respect to time el of the deviation. Four fuzzy rules are illustrated which are defined for the range Ilel>-ell of the phase plane (Rl to R4). Other fuzzy rules are applied according to the same scheme. The associated functions Per Me. and pu from Fig. 4 are illustrated in the upper part of Fig. 8. The application of the fuzzy rules R1 to R4 are included in the illustration. wherein the application of each individual rule is to be read from left to right, in other words, the results of the applications of the rules are in each case illustrated on the right-hand side of Fig. 8. The results of the applications of the rules are superimposed from the top to the bottom and produce the final result which is illustrated in the bottom right-hand corner in Fig. 8.

A fuzzy rule is applied in the following manner:

The category inputs of the premise (e.g. R3: PEIS AND NES) are evaluated first, in that the value of the associated functions Me and/or Pel for the variables e and/or el designated by the category input is determined with respect to each category at the position of the example value eo and/or elo (vertical, broken line) (black dots). If the premise comprises several category inputs, then the largest function value of the category inputs summated by "OR" and/or the smallest function value of the category inputs sununated by "AND" are selected successively. The function value determined in this way is plotted (broken horizontal lines) on the category input of the consequence (e.g. R3: PUB), in that the corresponding associated function yu of the standardised correcting variable u is intersected horizontally at the level of the function value, so that the shaded areas illustrated in Fig. 8 are obtained. In the case of rules Rl and R2, the level of intersection was zero so that no areas remained here.

This process is carried out for each rule and subsequently the combined quantity of all associated functions pu (shaded areas) obtained in this way of the standardised correcting variable u is formed. A numerical value u2 for the correcting variable is -19obtained by forming a mean value regarding the assoociated function (shaded area) obtained by means of the combining operation of the standardised correcting variable u (illustrated bottom right). A correcting variable u2 is obtained from U2 by carrying out an adjustment to suit the control system by means of the parameter K3 (see Fig. 3) and the said correcting variable u2 is superimposed on the correcting variable ul of a conventional controller (see Fig. 1).

In addition to the area of application described here, the invention can be used particularly advantageously in a motor vehicle for controlling an electrically motorised or hydraulic adjusting mechanism of a steering mechanism of a front or rear axle or of a throttle adjusting mechanism in a motor vehicle. It is also possible to use the invention outside a motor vehicle, e.g. in machine tools or robots.

Claims

-20CLAIMS

1. A method for positioning an adjusting mechanism by means of a control loop, wherein a deviation (e) between a desired value (w) and an actual value (y) is determined and fed as an input variable to a controller having at least one of the control characteristics P, I, D, which controller supplies a first correcting variable (a,), and a fuzzy controller lies in parallel with the controller or can be switched and/or alternatively switched in to the controller, the fuzzy controller is fed the derivative with respect to time (el) of the deviation and the deviation (e) as input variables and the fuzzy controller supplies a second correcting variable (R2)'

2. Method according to claim 1, wherein when the controller and fuzzy controller are in parallel or when switching the fuzzy controller, the correcting variables (111, 112) which are determined by the controller and by the fuzzy controller are added together.

3. Method according to one of the preceding claims, wherein the fuzzy controller is switched and/or alternatively switched in if the deviation (e) is less than a selectable value for a selectable period of time.

4. Method according to one of the preceding claims, wherein the fuzzy controller is adjusted to suit an area of application by changing the fuzzy rules.

5. Method according to one of the preceding claims, wherein the input and output signals of the fuzzy controller are multiplied by the parameters and the fuzzy controller is adjusted to suit the control system by manually or automatically changing these parameters.

6. Method according to one of the preceding claims, wherein:

the value ranges of the standardised deviation (e), of the standardised derivative with respect to time (el) of the deviation and the standardised correcting variable (u) are allocated in each case to several categories, each category qualitatively describes the position of a sub-range within the value range, each category has access to an associated function which determines the strength of the allocation of each individual value of the value range to this category.

7. Method according to claim 6, wherein the associated functions (Pe and Pel) of the standardised deviation (e) and the standardised derivative with respect to time (e') of the deviation reduce from 1 to 0 for a category "negative big", if the standardised deviation (e) and/or the standardised derivative with respect to time (e') of the deviation pass through the range from a minimum value (emin and/or e'min) to of rise from 0 to 1 for a category "negative small", if the standardised deviation (e) and/or the standardised derivative with respect to time (el) of the deviation passes through the range from a minimum value (emin and/or e'min) to of reduce from 1 to 0 for a category "positive small", if the standardised deviation (e) and the standardised derivative with respect to time (el) of the deviation passes through the range from 0 to a maximum value (emax and/or e'max)f rise from 0 to 1 for a category "positive big", if the standardised deviation (e) and/or the standardised derivative with respect to time (el) of the deviation passes through the range from 0 to the maximum value (emax and/or e'max)

8. Method according to claim 6, wherein the associated function (MU) of the standardised correcting variable (u) initially rise from 0 to 1 for a category "negative big" and then reduces again to 0, if the standardised correcting variable (u) passes through 1 -23the range from a minimum value (umin) to 0, rises from 0 to 1 for a category "negative small", if the standardised correcting variable (u) passes through the range from half of the minimum value (umin) to of reduces from 1 to 0 for a category "positive small", if the standardised correcting variable (u) passes through the range from 0 to half of a maximum value umax)r and initially rises from 0 to 1 for a category "positive big" and then reduces again to 0, if the standardised correcting variable (u) passes through the range from 0 to the maximum value (umax)

9. Method according to one of the preceding claims, wherein the fuzzy controller determines the standardised correcting variable (u) by applying the fuzzy rules to the standardised deviation (e) and the standardised derivative with respect to time (el) of the deviation and subsequently superimposes the results from the application of these rules by forming a mean value.

10. Method according to one of the preceding claims, wherein a first set of four fuzzy rules is applied, in the case of the standardised derivative with respect to time (e') of the deviation being greater than the negative of the standardised deviation (e), wherein:

-24a first fuzzy rule (R1) states, that the standardised correcting variable (u) is "positive big", if the standardised deviation (e) is "positive small" and a further condition is fulfilled, wherein this further condition is then fulfilled if the standardised derivative with respect to time (e') of the deviation is "negative small" or "positive small". a second fuzzy rule (R2) states the standardised correcting variable (u) is "positive small", if the deviation (e) is "positive small" or "positive big" and a further condition is fulfilled, wherein this further condition is then fulfilled if the standardised derivative with respect to time (e') of the deviation is "positive big" or the standardised deviation (e) is "positive big", a third fuzzy rule (R3) states that the standardised correcting variable (u) is "positive big" if the standardised derivative with respect to time (e') of the deviation is "positive small" and the deviation (e) is "negative small", a fourth fuzzy rule (R4) states that the standardised correcting variable (u) is "positive small" if the standardised derivative with respect to time (el) of the deviation is "positive big" and a further condition is fulfilled, wherein this further condition is then fulfilled if the standardised -25deviation (e) is "negative big" or "negative small", and a second set of four fuzzy rules is applied, if the standardised derivative with respect to time (el) of the deviation is smaller or equal to the negative of the standardised deviation (e), wherein a fifth fuzzy rule (R5) states that the standardised correcting variable (u) is "negative big,If if the standardised deviation (e) is "negative small" and a further condition is fulfilled, wherein the further condition is then fulfilled if the standardised derivative with respect to time (el) of the deviation is "negative small" or "positive small". a sixth fuzzy rule (R6) states that the standardised correcting variable (u) is "negative small" if a first and a second condition is fulfilled, wherein the first condition is then fulfilled if the standardised deviation (e) is "negative small" or "negative big" and the second condition is then fulfilled if the standardised derivative with respect to time (el) of the deviation is "negative big" or the standardised deviation (e) is "negative big", a seventh fuzzy rule (R7) states that the standardised correcting variable (u) is "negative big", if the standardised deviation (e) is "positive small" and the standardised derivative with respect to time (el) of the deviation is "negative small" and an eighth fuzzy rule (R8) states that the standardised correcting variable (u) is "negative small" if the standardised derivative with respect to time (e') of the deviation is "negative big" and a further condition is fulfilled wherein the further condition is then fulfilled if the standardised deviation (e) is "positive small" or "positive big".

11. A device for positioning an adjusting mechanism by means of a control loop, wherein a means for determining a deviation (e) between a desired value (w) and an actual value (M) of a signal in association with the position of the adjusting mechanism and a controller is provided, the controller having at least one of the control characteristics P, I, D, receives the deviation (e) as an input variable and supplies a first correcting variable (311), wherein a fuzzy controller lies in parallel to the controller or can be switched and/or can be alternatively switched in to the controller, receives the derivative with respect to time (jgl) of the deviation as an innut w- - variable in addition to the deviation (A) and supplies a second correcting variable (22).

12. Device according to claim 11, wherein when the controller and fuzzy controller are in parallel, or when switching the fuzzy controller, the correcting variables (111. A2) determined by the controller and by -27the fuzzy controller are added together and are subsequently relayed to the adjusting mechanism.

13. A method for positioning an adjusting mechanism in a motor vehicle, adapted and arranged to operate substantially as hereinbefore described, with reference to the accompanying drawings.

14. A device for positioning an adjusting mechanism in a motor vehicle, constructed, adapted and arranged substantially as hereinbefore described with reference to the accompanying drawings.