WO1994014234A1

WO1994014234A1 - Method and apparatus for determining constants of functions expressing characteristics of controlled system

Info

Publication number: WO1994014234A1
Application number: PCT/JP1993/001825
Authority: WO
Inventors: Toshiaki Yamane; Noriyuki Nagae; Shigeru Futami
Original assignee: Kabushiki Kaisha Yaskawa Denki
Priority date: 1992-12-16
Filing date: 1993-12-15
Publication date: 1994-06-23

Abstract

A method and apparatus for determining exactly the characteristics of a controlled system, such as the inertia, and the coefficient of viscous friction of a mechanical device in which an electric motor is incorporated. In the same controlled system, different kinds of control systems are set up in order to measure the response time. In accordance with the differences in the results of the measurement, the characteristics of the controlled system are determined.

Description

Specification

Method and apparatus for identifying constant of function representing characteristic of controlled object

〔Technical field〕

The present invention relates to a method for identifying a constant, such as inertia, a coefficient of viscous friction, etc., representing characteristics of an electrically driven machine in which an electric motor or the like is incorporated, or an apparatus for implementing these methods. .

(Background technology)

When using a control device with a built-in motor to control a controlled object, it is necessary to accurately identify the characteristics of the controlled object, such as load inertia and viscous friction coefficient.

As for the identification of the load inertia, a method disclosed in Japanese Patent Application Laid-Open No. Sho 61-244 286 has been known.

That is, a speed command * of a certain time function is added to the control system, and the speed at a certain time is obtained as a table corresponding to various values of inertia, and the speed command of the certain time function is actually obtained. ω ₂ * is added to the control system to determine the speed ω ₂ at the elapse of the time, and the inertia data corresponding to (ω ₂ * / ω ι *) · ω ₂ is determined from the table.

There was a problem that it was difficult to make a difference in speed after a certain period of time when the force command and the speed command were changed. The following methods have been known for identifying the coefficient of viscous friction.

For a controlled object with viscous friction, the viscous friction coefficient is identified based on the equation of motion for the controlled variable. For example, the behavior of the angular velocity ω when the torque Tq is applied to a motor having inertia J and viscous friction coefficient D is described by the following equation of motion.

Τς-Ό ω = 3 άω / dt-(1)

A certain angular velocity ω. When the torque is set to 0 at the time tu rotating at ω (t) = ω. 'exp (-D / J-(t-t.)))' ”(2) The method of measuring this angular velocity change over time and applying it to equation (2) to identify the viscous friction coefficient D is widely used. Have been.

However, in the above method, as is clear from Eq. (2), the time change of ω is an exponential function, and the change width decreases with time, so the SZ Ν ratio decreases. There is a possibility that the measurement resolution may be insufficient and the measurement accuracy may be degraded.

SUMMARY OF THE INVENTION An object of the present invention is to provide a method and an apparatus capable of accurately identifying characteristics of a controlled object such as an inertia, a viscous friction coefficient, and the like.

[Disclosure of the invention],

The present invention is to construct a plurality of different types of control systems on the same control target, measure the time response, and identify the characteristics of the control target based on the difference in the measurement results. Here, the different types of control systems refer to control systems whose transfer functions are essentially different, such as ΡI control system and IΡcontrol system, for example, and the coefficient of the same Ρ Ιcontrol system. Those that simply change the value of are excluded. The difference referred to here includes not only the subtracted difference but also the divided ratio.

[Brief description of drawings]

FIG. 1 is a block diagram of one embodiment of the present invention, FIG. 2 is a block diagram showing a ΡI control system, FIG. 3 is a block diagram showing an IΡ control system, and FIG. 4 is a diagram showing a step response of the ΡI control system. Fig. 5 shows the step response of the IΡ control system, Fig. 6 shows the step response delay time of the IΡ control system and the IΡ control system, and Fig. 7 shows the I 応答 control system and the IΡ control system. FIG. 8 is a block diagram of another embodiment of the present invention, FIG. 9 is a block diagram showing a ΡI control system having viscous friction on a control target, and FIG. Block diagram showing an I I control system with viscous friction in the object.Figures 11, 11, and 13 are block diagrams showing the principle of compensating for viscous friction of a controlled object with viscous friction. FIG. 10 is a block diagram of another embodiment of the present invention.

[Best mode for carrying out the invention] FIG. 1 shows an embodiment of the apparatus of the present invention.

1 is an input signal setting means that can set an arbitrary input signal.2a and 2b are a plurality of different types of controls that input the input signal set by the previous and human power signal setting means and output the operation amount to the control target. A computing unit, 3 is a switching unit for enabling one of the control computing units, 4 is an output value storage unit for storing an output value of an output of the controlled object 5, and 6 is a parameter of the controlled object 5 based on the output value. It is a control object that identifies the control object (the constant of a function that represents the characteristics of the control object).

Reference numeral 7 denotes a viscous friction compensating unit that, when the controlled object has viscous friction, identifies the coefficient of the viscous friction and then closes the switch 8 so that the compensating function works during control. At the time of identification of the viscous friction coefficient, the switch 8 is open, and the viscous friction compensation unit 7 does not function.

FIG. 2 is a diagram illustrating the principle when the control target 5 is a servomotor and a load, the control calculation unit 2 is a PI speed control system, and FIG. 3 is an IP speed control system. In the figure, J to be controlled is the sum of the rotor inertia of the servomotor and the load inertia. Kv and Ti of the controller are control constants, which are a proportional gain and an integration time constant, respectively.

A method for identifying J from the difference in time response between the PI control system and the IP control system is described. In Figs. 2 and 3, the transfer function from the speed command to the command torque is given by the transfer function _GTPI (s) of the PI control system as follows:

The transfer function G _TIP (s) of the IP control system is given by the following equation.

As a result, the difference between the command torque response to the speed command of the PI control system and the IP control system is

Becomes Hereinafter, for simplicity, let A be the denominator on the right side of equation (5).

When the speed command signal is Vref (s), the steady-state value Ω of the n-order integrated value of the difference in the response of the command torque is given by the final value theorem at t → (ie, steady state).

J · Kv, Ti · s ² 1

Ω = lira s Vref (s) · ——… (6) s → 0 A s ⁿ

Becomes

Note that the act of setting the difference in the response of the command torque to the nth order integration is equivalent to integrating the response of the command torque to the nth order and taking the difference. Hereinafter, the description “n-order integrated value of command torque difference” shall mean “difference of n-order integrated value of command torque”.

This processing of n steps includes the case where n = 0, that is, the case where integration is not performed, and the case where n is negative, that is, the case where differentiation is performed. J can be identified by integrating an arbitrary speed command signal whose coefficient is known by the rank at which the difference in the response of the command torque converges.

In practice, there is no need to wait until t → oo, and the time t becomes steady state when the natural period of the control system is about 3 to 5 times, and converges sufficiently to the value of equation (25).

The following is an example of a method for identifying J using the above method when six types of signals are used as speed commands.

[Example 1: Step signal]

As speed command signal

0 t <0

f (t) = au (t), u (t) (7)

1 t≥ 0

When the step signal is given, the difference between the command torque and the steady-state value Ω

J · Kv · Ti · s ² a 1

Ω = lim s —— · —— = J · Ti-a-(8) s → 0 A ss ²

Converge to the value [Example 6: Lamp signal]

As speed command signal

f (t) = at… (17)

And the steady-state value Ω of the integral of the difference between the command torques is

Converge to the value

[Example 2: Parabolic signal]

As speed command signal

f (t) = at ² ,

Given a parabolic signal, the steady-state value Ω of the command torque difference is

J-KvTi 2a

Ω = lira s 2 J ♦ Ti (10) s → 0 A

Converge to the value

[Example 9: Sine wave signal]

As speed command signal

f (t) = asin (cot)… (11)

Given a sine wave signal, the constant value Ω of the third-order integral of the difference in command torque is

J-Kv · Ti a ω J · Ti

Ω = lira s (12) s → 0 AS ² + 0) ^:

Converge to the value

(However, depending on the machine, damage may be caused by a sine wave signal command, so care must be taken when applying this example.)

[Example 4: Exponential signal 1]

As speed command signal

f (t) = ae— ^τ '… (13) , The steady-state value Ω of the third-order product-minute value of the difference between the commanded torques is J · Kv · Ti · s ² a 1 J 'ΤΊ · a

Ω = lim s • (14) s → 0 A s + T T

Converge to the value

[Example 5: Exponential signal 2]

As speed command signal

f (t) = ate- ^{T t} (15)

When the signal is given, the steady-state value Ω of the 3rd order value of the difference of the command torque is

Converge to the value

As described above, there is actually no need to wait until t → 、, and the time t is 3 to 3 times the natural period of the control system.

At about five times, the values converge sufficiently to the values of Eqs.

In Equations (8), (10), (12), (14), (16), and (18), the values of a, Ti, T, and ω are known, so that the value of J can be calculated therefrom. In the embodiment shown in FIG. 1, it is automatically calculated by the control target parameter overnight identification calculating unit 6. In addition, since the difference is taken, the influence of Coulomb friction is eliminated, and the value of J can be obtained with high accuracy.

7 shows a second embodiment of the present invention. In Figs. 2 and 3, the transfer function from the speed command to the speed is given by the following equation, which is the transfer function G _VP1 (s) of the PI control system.

The transfer function G _VIP (s) of the IP control system is given by the following equation.

These are expressed in the form of second-order standard systems as follows. 2-ζ-ω-5 + ω '

G vp I (s) ⁼ • (19 ')

s ² + 2-ζ-ω-s + ω '

Where (19 ') (20')

Kv

ω-natural angular frequency

(T iJ)

The step response of the system represented by these is as shown in Fig. 4 and Fig. 5, respectively. Paying attention to the delay time (time when the response reaches 50% of the command), which is one of the temporal features of these responses, the PI control system decreases as ^ increases as shown in Fig. 6. In the IP control system, the force increases as ^ increases. Its absolute value changes with the value of ω. However, when the ratio between the value in the ΡI control system and the value in the IΡ control system is taken, as shown in Fig. 7, it changes depending only on the value of ^ regardless of the value of ω. By using the relationship between the ratio of the delay time and the value of ^, the value of ^ can be easily obtained, and J can be identified.

In other words, Kv and T i are set to appropriate values, the step response is measured in both the P I and I P control systems, and the delay time ratio is taken. Then, the value of ^ is obtained by comparing the value with a table that associates the value of し with the delay time ratio calculated in advance. From the value and the definition of ^ in equations (19 ') and (20'), the value of J can be identified.

In the embodiment shown in FIG. 1, the identification is performed automatically by the control target parameter identification calculation unit 6.

Hereinafter, a case will be described in which a time response measured by only one type of control system and a time response equivalent to the time response of another type of control system by performing signal processing on the time response are used. In Figs. 2 and 3, the transfer function of the PI control system from the speed command to the command torque G _TPI (s) : The relationship between Eq. (1) and the transfer function G _T (s) of the IP control system: Eq. (.2)

GTP. (S) = (Ti · s + 1)-GTIP Since (S)-(21), the response of the command torque of the IP control system is 1 It is equivalent to the value multiplied by (Ti · s + 1). This operation is equivalent to inputting to a first-order lag system having a time constant equal to the integration time constant of the PI control system and obtaining its output. In other words, as shown in Fig. 8, a PI control system is constructed for the control target, the time response of the command torque is measured by giving a speed command, and at the same time, the time response is input to the first-order lag system described above. As an output, a time response equivalent to the time response of the finger torque of the IP control system is obtained.

Based on the difference between the time response equivalent to the response of the IP control system obtained in this way and the measured time response of the PI control system, it is desirable to identify the characteristics of the control target and finally build a control system based on it. It is possible to set the control constant of the control device so as to show the behavior.

That is, the number of times of measurement is half as compared with the case where both the PI control system and the IP control system are actually constructed and the time response is measured, so that the work efficiency can be improved.

In the embodiment of the present invention, the case where the difference in time response between the PI control system and the IP control system is used has been described.However, the present invention is applicable to the case where various control systems such as the PID control system and the IPD control system are used. Applicable.

In the embodiment of the present invention, the time response is a step response, a ramp response, a parabolic response, a sine wave response, and a function of 時間 (t) = ae— ^Tl and f (t) = ate- ^Tt with respect to time t. The case where a response to a command is used has been described. However, the present invention can be applied to a case where an arbitrary time response such as an impulse response or a response to a trapezoidal command pattern is used.

In the embodiment of the present invention, the case where the delay time of the step response is used as the time response has been described. However, the present invention can be applied to the case where various characteristic amounts such as the rise time and the amount of overshoot are used.

As described below, the technology described above is applied to the case of a controlled object in which viscous friction exists. It can be applied to the identification method of the viscous friction coefficient. Furthermore, after identifying the viscous friction coefficient first, the inertia can be identified.

Fig. 9 shows a PI control system with viscous friction in the controlled object, and Fig. 10 shows an IP control system with viscous friction in the controlled object. In the figure, J is the sum of the inlet and outlet inertia of the servomotor and the inertia of the load, and D is the viscous friction coefficient. Other than the control target, it is the same as described above.

Explain how to identify D from the difference in time response between PI control system and IP control system.o

In Figs. 9 and 10, consider the transfer function from the speed command to the command torque. When the transfer function of the PI control system is _{GTP I} (s), it is expressed by the following equation.

The transfer function of the IP control system G _TIP (s) is given by the following equation.

Here, for simplicity, let B be the denominator of Eq. (22) (also Eq. (23)).

Becomes

Here, for simplicity, let the numerator of equation (24) be E.

When the speed command signal is Vref (s), the steady-state value Ω of the value obtained by dividing the response difference of the command torque by nth order is given by the final value theorem from t → ∞ (that is, steady state).

E 1

Ω = lira s Vref (s) '(25)

s → 0 B s ⁿ

Becomes Note that the above-mentioned act of making the difference between the response of the command torque and the II-order integral equivalent to the n-order integration of the response of the control torque and taking the difference. Hereinafter, the description “n-order integrated value of command torque difference” shall mean “difference of n-order integrated value of command torque”.

This n-order integration process includes the case where n = 0, that is, the case where no integration is performed, and the case where n is negative, that is, the case where differentiation is performed.

D can be identified by integrating with any speed command signal whose coefficient is known by the rank at which the response difference of the command torque converges.

In practice, there is no need to wait until t → oo, and the time l¾t is about 3 to 5 times the natural period of the control system, and a steady state is reached, and the value converges sufficiently to the value of equation (25).

The following is an example of a method for identifying D using the above method when six types of signals are used as speed commands.

[Example 1: Step signal]

As a speed control signal

(0 t <0

f (t) = a · n (t), n (t) = \… (26)

¹ 1 t≥ 0

When the step signal is given, the steady value Ω of the integrated value of the difference between the command torques is

E a 1

Ω = l ira s = D-Ti a (27)

s → 0 B

Converge to the value

[Example 2: Lamp signal]

As speed command signal

Vref (t) = at (28)

Given a ramp signal, the steady-state value Ω of the command torque difference is

E a

Ω = l ira s = DTia (29)

s → 0 B

Converge to the value < [Example 3 ··· Parabolic signal]

As speed command signal

Vref (t) = at ² … (30)

Given a parabolic signal, the steady-state value Ω of the differential value of the command torque difference is

E 2 a

Ω = nm s S = 2DTi-a-(29)

s → 0 B

Converge to the value

[Example 4: Sine wave signal]

As speed command signal

f (t) = asin (o t)… (30)

And the steady-state value Ω of the second-order integral of the difference in command torque is

E a ω 1 DTi-a

Ω = hm s (31)

s → 0 B 5 ² + ω 'ω

Converge to the value

[Example 5: Exponential signal 1]

As speed command signal

f (t) = ae— ^Tt (32)

And the steady-state value Ω of the second-order integral of the command torque difference is

E a 1 D

Ω = hm s (33)

B s + T T

Converges to the value

[Example 6: Exponential signal 2]

As speed command signal

f (t) = ate " ^Tt … (34)

E a 1 D

Ω = lira s (33)

s → 0 B (s + T) ² s ^: Converges to the value

The specific measurement method is to set Kv and Ti to appropriate values, apply the above speed command signals to both the P1 and IP control systems, record the command torque, and record the difference between the values. The number of floors corresponding to the speed command signal type (-1 to 2 times) Integrate.

As described above, the time t becomes a steady state when the natural period of the control system is about 3 to 5 times the natural period, and the integrated value is expressed by Eqs. (27), (29), (31), (33), and (35). Since these values converge, the values of a, Ti, T, and ω in these equations are also known, so that the value of D's identification value D can be calculated from them.

The value of D 'is the coefficient (gain) of the viscous friction compensator in Fig. 1. This is shown in Fig. 11, Fig. 12, and Fig. 13, which are set as shown in Fig. 11. Then, it is apparent that the viscous friction D has finally disappeared as shown in FIG. 13 due to the known deformation of FIG.

After doing so, it is possible to identify the above-mentioned inner caller.

As described above, the method of identifying D when six simple signals are used as the speed command has been described as an example. However, other signals can be used.

In Fig. 9 and Fig. 10, the transfer function of the 指令 I control system from the speed command to the command torque G TP. (S): Equation (22) and the transfer function of the IP control system G _TII > (s): (23) The relation of the expression is

GTP. (S) = (Ti · s + 1) · GT I P (S)… (36)

Therefore, the response of the command torque of the IP control system is equivalent to the value obtained by multiplying the response of the command torque of the PI control system by 1 Z (Ti · s + 1).

Multiplying a signal by 1 Z (Ti · s + 1) is equivalent to inputting the signal to a first-order lag system having a time constant equal to the integral time constant Ti of the PI control system and obtaining the output.

In other words, with the configuration shown in Fig. 14, a PI control system is constructed for the control object where viscous friction exists, and the time response of the command torque is measured by giving a speed command, and at the same time, the time response is reduced by the first-order lag. When input to the system, a time response equivalent to the time response of the command torque of the IP control system is obtained as the output. By identifying the viscous friction coefficient based on the difference in the response obtained for both the PI and 1P control systems obtained in this way, the work efficiency is higher than when measuring the time response of the PI control system and the IP control system individually. Can be improved.

In the embodiment of the present invention, the case where the difference in time response between the PI control system and the IP control system is used has been described. However, the present invention is also applicable to the case where various control systems such as the PID control system are used.

In the embodiment of the present invention, the case where the inertia and the viscous friction are identified in the speed control of the servomotor has been described, but the present invention is not limited to this. In other words, in the case of position control, force control, etc., if there is a gain component from the manipulated variable to the control li and a resistance component proportional to the magnitude of the control variable, identify those coefficients. Applicable for.

In the embodiment of the present invention, the case where the response to six types of input signals is measured as the time response has been described. However, the present invention can be applied to the case where other time responses are used.

Using the value of J obtained as described above, the values of the control constants Kv and Ti are set so that the speed control system performs the desired response.

[Industrial applicability]

The present invention is applicable to position control, force control, and the like in addition to the speed control of a servo motor, the speed control of a spindle motor of a machine tool, the speed control of a servomotor for driving a robot, and the like. If there is a resistance component proportional to the magnitude of the gain from the manipulated variable to the control variable divided by the magnitude of the control variable, it can be applied to identify the coefficient.

Claims

The scope of the claims

1. In the method of identifying the constant of a function indicating the characteristics of a controlled object, a plurality of types of control systems having different transfer functions are constructed so as to be switchable for the same controlled object, and time responses to the same human power signal are measured, respectively. An identification method characterized by identifying a constant of a function indicating a characteristic of a control target based on a difference between the measurement results.

2. The identification method according to claim 1, wherein the constant of the function indicating the characteristic of the controlled object is the inertia of the control system.

3. The identification method according to claim 1, wherein the constant of the function indicating the characteristic of the controlled object is a viscous friction coefficient of the control system.

4. The identification method according to claim 1, wherein the difference between the measurement results is a difference.

5. The identification method according to claim 1, wherein the difference between the measurement results is a ratio.

6. The identification of the constant of the function indicating the characteristic of the control object based on the difference in the measurement results is performed by using the final value theorem for any input signal and integrating or differentiating the number of times the steady value converges. 2. The identification method according to claim 1, wherein:

7. The identification method according to claim 1, wherein the identification of the constant of the function indicating the characteristic of the control target based on the difference in the measurement result is performed by using an input signal as a step input and measuring a steady-state response.

8. The identification method according to claim 1, wherein the identification of the constant of the function indicating the characteristic of the controlled object based on the difference in the measurement result is performed by measuring a steady-state response using an input signal as a lamp input.

9. The identification method according to claim 1, wherein the identification of the constant of the function indicating the characteristic of the controlled object based on the difference between the measurement results is performed by using an input signal as a parabolic input and measuring a steady-state response.

10. The identification method according to claim 1, wherein the identification of the constant of the function indicating the characteristic of the control target based on the difference between the measurement results is performed by setting an input signal to a sine wave input and measuring a steady-state response.

1 1. The measurement result? ) Identification of the constant of the function indicating the characteristic of the controlled object due to the difference, 2. The identification according to claim 1, wherein the input signal is a signal indicating a value of ί (t) = ae- ^T 'with respect to time t, and a steady-state response is measured.

1 2. The identification of the constant function showing the characteristics of the controlled object due to the difference of the measurement results, f (t) the input signal with respect to time t = ate "a signal indicating a value of ^{T l,} measuring the steady-state response 2. The identification method according to claim 1, wherein:

1 3. Identification of the constant of the function indicating the characteristics of the controlled object based on the difference in the measurement results is based on the fact that the input signal is used as a step input and the relationship between the ratio of the delay time and the value of the attenuation factor ^ is used. The identification method according to claim 1, wherein the identification method is characterized in that:

1. The M constant of the constant of the function indicating the characteristic of the controlled object due to the difference of the measurement results is the time response measured by only one type of control system, and the time response of the other type of control system by processing the time response. 2. The identification method according to claim 1, wherein a time response equivalent to the response is used.

1 5. The PI control system is used as the control system for measuring the time response, and the signal processing is input to a temporary delay system having a time constant equal to the integral time constant of the PI control system. The identification method according to claim 14, wherein a time response equivalent to a time response in a control system is used.

16. A method for identifying a constant of a function indicating a characteristic of a control target, wherein after identifying a viscous friction coefficient of a control system by the method according to claim 3, the inertia of the control system is identified by the method according to claim 2.

1 7. An input signal setting means capable of setting an arbitrary input signal, a plurality of different types of control calculation units for inputting the input signal set by the input signal setting means and outputting an operation amount to a control target, Switching means for enabling any one of the control calculation units, output value storage means for storing the output value of the control target, and a control target noise identification calculation unit for identifying a parameter of the control target from the output value And a constant identification device for a function indicating a characteristic of a control target.