GB2294784A - Method for compensation for the starting friction of a drive - Google Patents

Abstract

A method is proposed for determination of a starting friction compensation signal (FK) for compensation for the starting friction in a drive. It is connected to the drive control signal when the movement of the drive starts from a stationary position. According to the method, the compensation signal (FK) is composed of an initialization compensation signal (Ko, Knew) and a correction signal ( DELTA K) which is formed by linking at least two characteristic variables (TR, SR) which describe the starting friction. The determination of the correction signal ( DELTA K) includes the following steps in this case: - determination of association values (zero, small, medium, large) for the characteristic variables (TR, SR) to form predefined association functions which describe the characteristic variables linguistically, - linking of the determined association values (zero, small, medium, large) in accordance with a predetermined control procedure to form proposed values ( DELTA F/Fo) - linking of the proposed values ( DELTA F/Fo) in accordance with a predetermined algorithm to form the correction signal ( DELTA K).

Description

Method for compcnsation for the starting friction of a drive Prior art The invention is based on a method of the generic type of the main Claim. Methods of this type are typical - ly used in machine tools which are designed for high accuracy. A regular requirement of such machine tools is that a required contour which is predetermined for a workpiece corresponds precisely with the actually pro duced contour. Maintenance of this correspondence is particularly difficult if processing requires the rever sal of the movement direction of a drive. Such a situ ation occurs, for example, if a tool which moves along two shafts each having their own drive is intended to carry out a circular path.As a result of the starting friction force, which always exists in the case of mechanical systems and counteracts the movement, the respectively affected drive in this case briefly sticks in an a adhesion phase whenever the direction is changed.

It does not tear itself free until the moment acting on the shaft is greater than the breaking-free moment which is governed by the friction. As a result of this behaviour, undesirable dynamic path deviations occur at the direction change points. In order to avoid such path deviations, it is known for a compensation signal, which compensates for the starting friction, to be connected to the drive control loop. The main difficulty in the case of this arrangement is the determination of a suitable compensation signal. Known solutions, such as that from EP-A 460 224, are based on the principle of a closed control loop, that is to say the value of the friction compensation results from a fed-back output variable from the drive control loop.An unsatisfactory feature of this solution is that the effect of the drive friction compensation depends on the adjustment of the drive control loop. Drive friction compensation and control loop adjustment must therefore be carefully matched to one another. Since drive friction compensation comprises a non-linear action in the control loop, even small changes in the control loop adjustment can change the effect of the drive friction compensation in a longlasting manner.

One option for avoiding the difficulties which result from including the drive friction compensation in the drive control loop is to carry out characteristicbased drive friction compensation which manages without variables fed back from the control loop for determination of the drive friction compensation signal. The compensation result in this case depends, however, in principle on the quality of the characteristic used.

The object of the invention is to specify a method which allows simple determination of a speed/ compensation force characteristic.

This object is achieved by a method having the characterizing features of the main Claim. The method according to the invention can advantageously be carried out in the course of automatic starting up. It allows very good compensation for the starting friction. The method is in consequence particularly suitable for ultraprecision machines, advantageously in conjunction with anticipatory control. A major advantage of the method according to the invention is, furthermore, that it manages without a process model of the drive control loop. In consequence, it can be used for drives which are structured in any desired manner in terms of the control technology. This also allows, in particular, retrofitting to existing drive systems.

It is advantageous to repeat the proposed method iteratively until the determined compensation signal no longer changes when repetition is repeated. The stationary time of a drive in the reversal position and the maximum path error in the reversal positions are expediently used as the required characteristic variables to describe the starting friction which occurs without complete compensation. These characteristic variables are advantageously determined using a so-called "reverse" test. In this case, the machine tool carries out a "cosine"-shaped path with a predetermined amplitude and predetermined speed. In one particularly advantageous refinement of the proposed method, the association function values, which are linked in accordance with fuzzy rules, have the fuzziness removed simply by forming the mean value.Finally, it is advantageous to connect the determined compensation signals directly to the current control loop.

An exemplary embodiment of the proposed method is explained in more detail in the following text, with reference to the drawing.

Drawing Figure 1 shows a flow diagram of the proposed method, Figure 2 measurement curves, recorded in a 'reverse" test, for the speed behaviour and the path deviation, Figure 3 association functions for the stationary time and the maximum run-on error, Figure 4 a multi-value control procedure for fuzzy linking of the stationary time and the maximum path error to form a compensation signal, and Figure 5 a block diagram of a drive system which is suitable for carrying out the proposed method.

Description Figure 5 shows as a block diagram in simplified form the design of a drive arrangement for which the proposed method is also conceived. It has, on the one hand, a known control loop with the elements position/ rotation speed control 52, current regulation 55 and drive 53. The position/rotation speed control 52 is supplied on the input side with required values for the rotation speed v,,g and the position xreq. Furthermore, the actual values, which occur at the output of the drive 53, for the rotation speed vact and the position xact are fed back to it.On the basis of the respectively occurring control differences for the rotation speed vreq Vact and the position xreq - xact, the position/rotation speed control 52 determines an instantaneous required value which it supplies via its instantaneous position 54 to the current regulation 55. The signal which is picked off in the drive 53 for the actual current value IaCt is furthermore fed back to said current regulation 55.

In addition to the drive control loop, the arrangement which is illustrated in Figure 5 furthermore has a compensator 51 for compensation for the drive friction as well as a start-up device 50. The actual values, which occur at the output of the drive 53, for the rotation speed Vact and the position xact are fed back on the input side to the start-up device 50. On the output side, it is connected on the one hand to the required rotation speed vreq and required position xreq inputs of the position/rotation speed control 52. It is furthermore connected, via a further output, to a compensator 51 for transmission of a determined compensation signal k. In addition to the signal k from the start-up device 50, the required value signals for the rotation speed Vrq and position xreq are likewise fed to the compensator 51. On the output side, the compensator 51 is connected to the moment interface 54.

The drive control loop 52 to 55 is driven in a known manner. In order to avoid path errors which are governed by the adhesion friction which counteracts the start of a movement, a compensation signal FK at the moment interface 54 is connected to the drive control loop at path points where a drive changes from a stationary position into a movement. The magnitude of the compensation signal FK which is respectively to be connected is determined by the compensator 51 using a compensation signal characteristic which assigns a compensation moment to each required value Vreq or Xreq.

This is determined with the aid of the start-up device 50.

Figure 1 shows as a flow diagram the essential steps of the method according to the invention for determination of a required-value compensation moment characteristic. In the first method step 10, suitable parameters for carrying out the compensation signal determination method are determined first. In this case, the amplitude, frequency and duration of the test signals which are required for the determination of the characteristic values are defined, in particular. Furthermore, if possible and necessary, the limit frequency for filtering of the measurement curves obtained is predetermined, expediently such that a robust, automatic start-up can be carried out. Furthermore, an initialization compensation signal Ko is defined. The nominal moment which is predetermined for the drive is expediently used for initialization.This is typically between 5% and 20% of the rated moment of the drive. A value of, for example, 10% of the value of the rated drive moment is therefore used as a rule as the presetting for Ko.

In the following step 11, at least two characteristic variables are determined which describe the starting friction effect which occurs with the initialization compensation signal Ko. This is expediently done using a "reverse" test. This is considered to be a known measurement method for investigation of the feed properties of a drive during a reversing movement, there being an illustration, for example, in the project report "Untersuchung von hochgenauen, langsam laufenden Vorschubantrieben für den Submikrometerbereich" [Investigation of high-precision, slowly running feed drives for the submicrometre range] from the Forschungsgemeinschaft Ultrapräzisionstechnik [Ultraprecision Technology Research Association], DE, Aachen 1990.A carriage which is moved by two drives is moved along a "cosine"-shaped path during the "reverse" test. The corresponding required path values vreq and xreq are produced by the start-up device 50 and are supplied to the position/ rotation speed control 51. They are furthermore recorded by the start-up device 50. During the movement of the carriage, the start-up device 50 furthermore detects the actual values vact and xact which occur, and likewise records them. At least two characteristic variables for describing the drive friction effect which has occurred are then determined by analysis of the recorded path data. The determination of two characteristic variables which are particularly highly suitable for this purpose is illustrated in Figure 2. The upper part of the Figure shows the detected actual speed vact with respect to the measurement time t.A stopping time TRv or TRr which is dependent on the existing starting friction force can be read from the measurement curve in a simple manner, in each case in conjunction with a zero crossing of the speed profile. TRv and TRr each correspond to a time within which the carriage virtually does not move in the reversing positions. The speed measurement signal is evaluated by software in order to determine these times numerically. Speed thresholds of small magnitude are in this case defined around the value vact = O. The values of TRV and TRr define the leaving of the negative threshold and the re-entry into the positive threshold of the measured speed signal. A low-pass filter having a limiting frequency of at least five times the known signal frequency of the test signal expediently smooths the measurement signal.

The path deviation xact - xreq which occurs is shown with respect to the measurement time t in the lower part of Figure 2. In this case, the maximum path errors SRVT SRr can be read directly from the measurement curve.

They each occur in conjunction with a zero crossing of the measurement curve, that is to say in conjunction with a movement reversal point. In order to obtain a parameter which is independent of the unavoidable residual run-on which can also be seen in Figure 2, the difference value SR: = SRV - SRr is introduced according to the method as characteristic variable. This value, which corresponds to the maximum possible overall path error, additionally has the advantage that it changes its mathematical sign in the event of overcompensation.

A correction signal AR is determined in the next step 12 by linking the characteristic variables determined in step 11 in accordance with the fuzzy logic rules, by means of which correction signal AK the initialization compensation signal Ko is corrected in order to achieve a better compensation effect. To this end, the characteristic variables which were obtained in step 11 are assigned to linguistic values, as is illustrated in Figure 3, with the aid of a fuzzy association function which is normalized with respect to 1 and is defined in a non-linear manner. Figure 3 shows two possible association functions for the assignment of the stopping time TR to the linguistic values zero, small, medium, large and of the maximum path error SR to the linguistic values zero, small, medium, large.The association Z, in each case normalized to the value 1, corresponding to 100%, is plotted over the abscissas TR/T and SR/A respectively, likewise expediently normalized, T being the time between two zero crossings of the speed profile of the predetermined movement path, and A the required amplitude of the latter. According to this, all the normalized stopping times TR/T of less than 10% correspond to the linguistic value zero, all the normalized stopping times between 10% and 20% with a variable element correspond to the linguistic values zero and small, all the normalized stopping times between 20% and 50% with the variable element correspond to the linguistic values small and medium, all the normalized stopping times between 50% and 80% with a variable element correspond to the linguistic values medium and large, and all the normalized stopping times which are greater than 80% correspond to the linguistic value large.With respect to the normalized maximum path error SR/A, all values less than 2% correspond to the linguistic value zero, all values between 2% and 10% with a variable element correspond to the linguistic values zero and small, all the values between 10% and 15% with a variable element correspond to the linguistic values small and large, and all values greater than 15% correspond to the linguistic value large. For example, 35% of a normalized stopping time TR/T of 30% corresponds to the linguistic value medium, and 65% thereof to the linguistic value small. 40% of a maximum normalized path error SR/A of 12% corresponds, for example, to the linguistic value large, and 60% thereof to the linguistic value small.

The association values obtained for the characteristic variables are subsequently linked with the aid of linguistically formulated linking rules to form proposed values AF/Fo. The proposed values AF/Fo have the same dimension as the initialization compensation signal; they typically denote a percentage of the rated torque specified for the associated drive. Every possible combination of linguistic association values is in this case assigned a correction signal proposed value AF/Fo.

As a result of the large number of rules resulting from this, said rules are reproduced in the form of a Table in Figure 4. This can be read, by way of example, as follows: - If the normalized stopping time TR/T is zero and the normalized maximum path error SR/A is likewise 0, then the normalized proposed value is AF/Fo = 0 - If the normalized stopping time TR/T is small and the normalized maximum path error SR/A is large, then the normalized proposed value is AF/Fo = 6% - If the normalized stopping time TR/T is large and the normalized maximum path error SR/A is small, then the normalized proposed value is AF/Fo = 4% - If the normalized stopping time TR/T is large and the normalized maximum path error SR/A is likewise large, then the normalized proposed value is AF/Fo = 8%.

A discrete value for the correction variable AK can now be derived in a simple manner - without removing the fuzziness - from the proposed values AF/Fo obtained with the aid of the linking rules according to Figure 4, in that the individual proposed values are each weighted by the product of the association values to form the basic linguistic variables, and the weighted proposed values are subsequently added. This is intended to be explained using an example. 60% of a normalized stopping time TR/T is assumed to belong to the association value small and 40% thereof to the linguistic value medium, 20% of a normalized maximum path error SR/A is assumed to belong to the linguistic value zero and 80% thereof to the linguistic value small.In this case, the linking rules according to Figure 4 produce from the linking of a small stopping time and a zero maximum path error the proposed value AF/Fo = 1%, a small stopping time and a small maximum path error produce the proposed value AF/Fo = 2%, a medium stopping time and a zero maximum path error produce the proposed value AF/Fo = 2%, and a medium stopping time and a small maximum path error produce the proposed value AF/Fo = 3%.Taking account of the association function values assumed above, the result of the linking of the small stopping time, zero maximum path error must be weighted by a factor of 60% x 20% = 0.6 x 0.2 = 0.12, the result of the small stopping time, small maximum path error with a factor 60% x 80% = 0.6 x 0.8 = 0.48, the result of a medium stopping time, zero maximum path error with a factor 20% x 40% = 0.2 x 0.4 = 0.08 and the result of the linking of a medium stopping time and small maximum path error with a factor 40% x 80% = 0.4 x 0.8 = 0.32. Addition of the proposed values weighted by the factors determined in this way gives the correction value AR, in the example: AK = 1% x 0.12 + 2% x 0.48 + 2% x 0.08 + 3% x 0.32 = 2.2%.

A check is now carried out in step 13 to determine whether the obtained correction value AK is within a predetermined tolerance band. It is preferably determined whether, as illustrated in Figure 1, it has the value 0. As an equivalent to this, it is also possible to test whether the change between a correction value AK which was last determined and the currently determined value AK is within a predetermined bandwidth.

If the result of the test in step 13 is negative, the steps 11 to 13 are repeated. To this end, a new initialization compensation signal Renew is initially formed in step 14 by addition of the original initialization compensation signal Ko and the previously determined correction signal AK; in the example mentioned above, for instance, the initialization torque set, if it were, for example, 10% of the rated drive torque, would be corrected to the value 12.2%. The newly formed initialization compensation signal Renew is used instead of the previous Ko in step 15.

If the result of the test in step 13 is positive, the current initialization compensation signal Ko is transferred into the compensator 51 as the compensation signal FK' step 16. The value obtained in this way is then the best achievable for the predetermined operating situation.

While maintaining the concept which is defined by the method steps - determination of at least two characteristic variables which describe a starting friction which occurs with an initialization compensation signal, - derivation of a correction signal for correction of the initialization compensation signal from the characteristic variables by linking the characteristic variables in accordance with the fuzzy logic rules, - repetition of the preceding steps until the value determined for the correction signal no longer exceeds a predetermined tolerance band, a large number of modifications and developments of the proposed method can be found directly. For example, it is of course possible to use further and/or other characteristic variables than those proposed to describe the starting friction which occurs. These characteristic variables can, of course, also be determined in a different manner than by means of a reverse test. Furthermore, "real" fuzzy rules can be used instead of the proposed linking rules which enable direct evaluation, which "real" fuzzy rules initially assign to the linguistic association values a starting variable, which is likewise defined linguistically and is in turn assigned, via an association function to one or more value ranges for the exact value of the starting variable. Removal of the fuzziness, which is known from fuzzy logic, is required in this case. Far-reaching modifications are furthermore also possible in the case of the drive arrangement used as the basis for carrying out the proposed method. For example, the start-up device 50 and the compensator 51 can be combined.

The method gives best-possible compensation signal values FK for one predetermined operating situation in each case. Since it can be carried out a number of times for different operating situations, it can be used in a simple manner for determination of a compensation signal characteristic which is then used in standard operation.

Claims (7)

Claims

1. Method for the determination of a starting friction compensation signal for compensation for the starting friction in the case of a drive which is connected to the drive control signal when the movement of the drive starts from a stationary position, characterized in that the compensation signal (F) is composed of an initialization compensation signal (Ko, Knew) and a correction signal (AK) which is formed by linking at least two characteristic variables (TR, SR) which describe the starting friction, the determination of the correction signal (AK) having the following steps:: - determination of association values (zero, small, medium, large) for the characteristic variables (TR, SR) to form predefined association functions which describe the characteristic variables linguistically, - linking of the determined association values (zero, small, medium, large) in accordance with a predetermined control procedure to form proposed values (EF/FO) - linking of the proposed values (AF/FO) in accordance with a predetermined algorithm to form the correction signal (AK).

2. Method according to Claim 1, characterized in that the characteristic variables (TR' SR) which are used to determine the correction signal (AK) describe the starting friction which occurs with the initialization compensation signal (Ro)

3. Method according to Claim 1, characterized in that the determination of the correction signal (AK) is repeated iteratively, that signal being used as the initialization compensation signal (Ko, Knew) which results by linking the initialization compensation signal (Ko), which is used in the preceding method repetition, with the correction signal (AK) which is determined in this case.

4. Method according to Claim 1, characterized in that the stopping time which occurs on movement reversal of the drive behaviour of the speed and the maximum path deviation which occurs following a movement reversal are used as characteristic variables to describe the starting friction.

5. Method according to Claim 1, characterized in that the characteristic variables are determined with the aid of a reverse test, a carriage which is driven by two shafts following a cosine-shaped path and the required and actual path values being recorded.

6. Method according to Claim 1, characterized in that the determined compensation signal at the moment interface between position/rotation speed control and current regulation (55) is connected to the drive control loop.

7. A method for the determination of a starting friction compensation signal substantially as herein described with reference to the accompanying drawings.