JP2733881B2 - Adaptive sliding mode control method based on PI control loop - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a servo motor control system for various machines driven by a servo motor such as a robot and a machine tool, and more particularly to a sliding mode control.

[0002]

2. Description of the Related Art Conventionally, various sliding mode controls have been used for servomotor control of various machines driven by servomotors in order to improve disturbance rejection and obtain a servo system having good followability to commands. Kaihei 2-297
611, Japanese Patent Application No. 1-253767, etc.). However, in the case of the above-described conventional sliding mode control, P control (proportional control) is conventionally used for position loop control and PI control (proportional / integral control) is used for speed loop control. Sliding mode control, which has no relation at all, is applied, and therefore, there is a drawback that the technique of linear control of P control and PI control that has been conventionally trained cannot be used at all. Therefore, the introduction of the sliding mode control and the selection of various parameter values take a very long time, and are not efficient.

The inventor of the present invention has applied sliding mode control to linear control PI which has been practiced for many years, and has taken advantage of the technology and know-how of the PI control that has been cultivated up to now. A servo motor control method for performing PI control and sliding mode control has been proposed (see Japanese Patent Application No. 3-140656).

[0004] On the other hand, it is known that a combination of sliding mode control and adaptive control can provide a device having extremely high robustness and high utility value. That is, it is known that since the disturbance rejection is high and the parameter is not largely changed, a device having a high use value can be obtained. However, also in this case, unlike the conventional PI control, there is a problem that it is difficult to introduce the control into the servomotor control, and it is very difficult to perform parameter adjustment and the like.

[0005]

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to combine the sliding mode control and the adaptive control based on the PI control to utilize the PI control technology and know-how cultivated in the past. Another object of the present invention is to provide a servomotor control method having high robustness.

[0006]

According to the present invention, a position loop control is a proportional control, a speed loop is a proportional integral control, and a torque command obtained by the linear control is divided by an integral gain of the speed loop. As the phase plane of the Lyapunov function, assuming that the inertia of the controlled object, the dynamic friction coefficient, and the estimated value of the gravitational term are taken into account, so that the differential value of the Lyapunov function is always negative, each gain of the linear control is set, In addition, an auxiliary input which is added to the torque command value from the linear control and serves as a torque command to the servomotor is determined.

The position gain of the position loop is represented by Kp, the integral gain of the velocity loop is represented by K1, the proportional gain is represented by K2, the position deviation is represented by ε, and the velocity deviation is represented by dots on ε. Jhat
, The coefficient of kinetic friction is A, the estimated value is Ahat, and the gravitational term is Gr.
The estimated value is represented by Grhat, the values of the adjustment parameters for determining the adaptive speed are represented by α, β, γ, the phase plane Suf of the sliding mode is represented by Expression 9, and the Lyapunov function is represented by Expression 10
The position gain Kp, the integral gain K1 of the speed loop, and the proportional gain K2 are determined so that the differential value of the Lyapunov function is always negative. Since the control is performed by determining the auxiliary input as the torque command to the servo motor, the servo motor can be controlled by combining the sliding mode control and the adaptive control based on the conventional position / speed loop control.

[0008]

(Equation 9)

[0009]

(Equation 10) In particular, the relationship between the position gain Kp, the integral gain K1, the proportional gain K2, and the maximum inertia Jmax of the controlled object is set such that the following equation 11 is satisfied:

[0010]

[Equation 11] Also, the acceleration of the movement command θr is represented by adding two dots on θr, the speed feedback value from the servo motor is represented by adding dots on θ, and the switching input is represented by τ1.
And the input τ to the servo motor is represented by Expression 12.

[0011]

(Equation 12) The values of the adjustment parameters that determine the adaptation speed are α, β,
As γ, the estimated value of the inertia Jhat is expressed by Equation 13, the estimated value of the dynamic friction coefficient Ahat is expressed by Equation 14, and the estimated value of the gravity term is Grh.
while changing at as in Equation 15,

[0012]

(Equation 13)

[0013]

[Equation 14]

[0014]

(Equation 15) When the value of the phase plane Suf is equal to or greater than “0”, the switching input is set to τ1 as the expected maximum disturbance torque.
The servomotor is controlled by a combination of sliding mode control and adaptive control based on a PI control loop that controls the servomotor by setting the expected minimum disturbance torque.

[0015]

[Action] The phase command of the sliding mode control is obtained by dividing the torque command obtained by the linear control by the integral gain of the speed loop, and the Lyapunov function is obtained by considering the inertia, the dynamic friction coefficient, and the estimated value of the gravitational term of the controlled object. Therefore, the technology and know-how of the linear control that has been conventionally implemented can be applied as it is, and the phase surface of the sliding mode control is proportional to the torque command obtained by the linear control. ,
The Lyapunov function takes into account the inertia, dynamic friction coefficient, and estimated value of the gravitational term of the controlled object, and the estimated values are gradually changed to determine the auxiliary input. Therefore, the torque command issued to the servomotor does not extremely change, so that optimal control can be performed.

[0016]

EXAMPLE A phase plane (switching plane) Suf is represented by the following equation (16).

[0017]

(Equation 16) In Equation 16, ε denotes a position deviation, and the one with one dot added to the position deviation ε denotes the differentiation of the position deviation. In the following, letters with one dot on the character indicate differentiation, and letters with two dots on the character indicate twice differentiation. Also,
Kp is the position gain of the position loop by P control, K
1 and K2 are an integral gain and a proportional gain of the speed loop by the PI control.

It is assumed that the control target is expressed by the following equation (17).

[0019]

[Equation 17] In Expression 17, θ is the feedback amount of the motor position, J is the inertia, A is the dynamic friction coefficient, Gr is the term of gravity, and Dis is the disturbance torque. In addition, the movement command is θr
Then, the movement command θr, the position feedback amount θ,
The relationship of the position deviation ε is as in the following Expression 18.

[0020]

(Equation 18) Therefore, the input τ to the servomotor is represented by the following equation (19).

[0021]

[Equation 19] In Equation 19 above, Jhat is the estimated value of inertia,
Ahat is the estimated value of the dynamic friction coefficient, Grhat is the estimated value of the gravitational term, and τ1 is the switching input. Further, the first and second expressions on the right side of Expression 19 represent the torque command value τ0 (Equation 2) when the position loop control is P-controlled and the speed loop control is PI-controlled.
0), which means that the remaining portion may be used as the auxiliary input τa. That is, the auxiliary input τa
Is the following equation 21, the above equation 19 is obtained by the following equation 22
Becomes

[0022]

(Equation 20)

[0023]

(Equation 21)

[0024]

(Equation 22) Therefore, if a block diagram for obtaining the input τ to the servomotor shown in Expression 22 is drawn, it becomes as shown in FIG. As is apparent from FIG. 1, the input τ to the servomotor is obtained by adding the auxiliary input τa to the output τ0 (torque command) of the conventional linear control in which the position loop is P-controlled and the speed loop is PI-controlled. This facilitates introduction of a combination of the sliding mode control and the application control.

Next, as a Lyapunov function, the following equation (23)
think of.

[0026]

(Equation 23) In Equation 23, α, β, and γ are positive adjustment parameters that determine the adaptive speed. Jbar is the estimation error of the inertia, Abar is the estimation error of the dynamic friction coefficient, and Grbar is the estimation error of the gravitational term.

[0027]

(Equation 24) If an input that always makes the differential value of the Lyapunov function negative is input to the servomotor, the Lyapunov function V is always positive, and the differential is negative. The surface Suf has the minimum value “0”
Converges to As a result, the responsiveness converges to Suf = 0 and moves fixedly without being affected by inertia or disturbance.

The following expression 25 is obtained by differentiating and organizing both sides of the expression 23.

[0029]

(Equation 25) Equation 26 is obtained by differentiating and rearranging both sides of Equation 16.

[0030]

(Equation 26) The following Expression 27 is obtained by substituting Expression 18 into Expression 17 and rearranging it.

[0031]

[Equation 27] Substituting Equation 27 into Equation 26 gives Equation 28 below.

[0032]

[Equation 28] The following Expression 29 is obtained by substituting Expression 28 into Expression 25 and rearranging it.

[0033]

(Equation 29) Also, from Equation 16,

[0034]

[Equation 30] When Equation 30 is substituted into Equation 29 and rearranged, the following Equation 31 is obtained.

[0035]

(Equation 31) The following Expression 32 is obtained by substituting Expression 19 into Expression 31 and rearranging it.

[0036]

(Equation 32) Further, when Equation 24 is substituted into Equation 32 and rearranged, Equation 3 is obtained.
It becomes 3.

[0037]

[Equation 33] As a result, if the derivative of the Lyapunov function is always negative,
What is necessary is just to make the above equation 33 always negative, and for that purpose, the switching input τ1 and the estimated values Jhat, Ahat and Grhat may be changed so that the above equation 33 is always negative. First, in order to make the first expression on the right side of Expression 33 negative, Kp <(K2 / J)-(K1 / K2) only needs to be satisfied. For that purpose, Kp <(K2 / Jmax)-(K1 / K2) ), The position gain Kp and the integral gain K
1. The proportional gain K2 may be selected and set. Note that Jma
x is the expected maximum inertia of the controlled object.

Next, the second expression on the right side of Expression 33 is "0".
To Then, the following Expression 34 is established.

[0039]

(Equation 34) Assuming that Jbar = J-Jhat and the change of the inertia J is very small and its differential value can be regarded as "0", the following equation 35 is established, and the above equation 34 is expressed as the following equation 36.

[0040]

(Equation 35)

[0041]

[Equation 36] Similarly, the third and fourth expressions on the right-hand side of Expression 33 are also set to “0”, and the changes in the dynamic friction coefficient A and the gravitational term Gr are very small. Equations 37 and 38 hold.

[0042]

(37)

[0043]

(38) As shown by the above Expressions 36, 37, and 38, it can be seen that the adjustment parameters α, β, and γ determine the changing speed of each estimated value and determine the adaptive speed. In the fifth expression on the right side of Expression 33, in order to always make the value negative, Suf · (Dis−τ1) <0, and when Suf ≧ 0, Dis−τ1 <0 should be satisfied. = Dismax. Note that Dismax is the maximum value of the disturbance torque.

When Suf <0, Dis-τ1> 0 may be satisfied, and τ1 = Dismin may be satisfied. In addition, Dis
min is the minimum value of the disturbance torque.

From the above, in order to determine the auxiliary input τa so that the derivative of the Lyapunov function is always negative, the unknown estimated values Jhat, Ahat, and Grhat in Equation (21) are obtained by integrating Equations (36), (37), and (38). The value of the phase surface Suf can be obtained by dividing the output of the linear control (P control of the position loop and PI control of the speed loop) τ0 by the proportional gain K2 as shown in Expressions 16 and 20. You can ask. The switching input τ1 is the phase plane Suf
The maximum value Dismax or the minimum value D of the disturbance torque depends on the sign of
Switch to ismin.

FIG. 2 is a block diagram of a main part of a servo motor control of a machine which implements an embodiment of the present invention. In the drawing, reference numeral 20 denotes a higher-level CPU such as a numerical control device for controlling the machine; A shared memory for receiving various commands to the servo motor and outputting it to the processor of the digital servo circuit 22. A digital servo circuit 22 includes a processor, a ROM, a RAM, and the like. 24, processing of position, speed and current control. 23 is a servo amplifier composed of a transistor inverter or the like, 24 is a servomotor, 25 is a position for detecting the rotational position and speed of the servomotor 24 and feeding it back to the digital servo circuit 22.
It is a speed detector.

The above configuration is the same as the configuration of a known digital servo circuit in controlling a servomotor of a robot, a machine tool, or the like.

FIGS. 3 and 4 are flow charts of feedforward processing, position loop processing, speed loop processing, sliding mode processing and adaptive control processing performed by the processor of the digital servo circuit 22 of this embodiment.
The processor executes the processing shown in FIGS. 3 and 4 every predetermined period (position / speed loop processing period) T.

First, the upper CPU through the shared memory 21
A movement command θr for each position / speed loop is obtained from the movement command sent from the controller 20 and the position / speed feedback values output from the position / speed detector 25 are read (step S1). Then, a value obtained by subtracting the position feedback value θ from the movement command θr is input to a register R (ε) that stores the position deviation ε, and the position deviation ε in the cycle is input.
Is obtained (step S2).

Next, the value of the register R (θr) for storing the previous cycle of the movement command is subtracted from the movement command θr to obtain the feedforward amount (the speed of the movement command θr) (differentiation of the movement command in FIG. 1). (Step S3). Next, the acceleration of the movement command is obtained by subtracting the value of the register storing the feedforward amount of the previous cycle from the obtained feedforward amount (step S4). Steps S1 and S2 are respectively stored in a register for storing a movement command and a register for storing a feedforward amount for use in the next cycle.
Then, the movement command and the feedforward amount obtained in step S3 are stored (step S5).

Next, the feedforward amount is added to the value obtained by multiplying the position deviation ε obtained in step S2 by the position gain Kp, and the value Vr obtained by subtracting the speed feedback value read in step S1 is obtained (step S2).
6) Then, the value Vr is added to the accumulator I to obtain an integral value (integration processing in the speed loop processing of FIG. 1) (step S7). Further, the value obtained by multiplying the value of the accumulator I by the integral gain K1 and the value Vr are proportional to the proportional gain K2.
Are added to obtain a torque command τ0 by linear control (conventional position loop P control with feed forward, speed loop PI control processing) (step S).
8).

As described above, the position gain Kp, the integral gain K1, and the proportional gain K2 are Kp <(K2
/ Jmax)-(K1 / K2) so that
The adjustment parameters α, β, γ and the assumed maximum value Dismax and minimum value Dismin of the disturbance torque are also set in advance by parameters, and are stored in the memory of the digital servo circuit. Shall be.

Next, the value of the phase surface Suf is obtained by dividing the torque command value τ0 of the linear control obtained in step S8 by the proportional gain K2 in the speed loop control (step S8).
9). Next, the value of the second derivative of the movement command θr obtained in step S4, the value of the position deviation ε obtained in step S2, the value of the accumulator I obtained in step S7, the position gain Kp, the integral gain K1, and the proportional gain The value of Q is obtained by performing the following equation 39 from the value of K2 (step S10). The value of Q is the estimated value of inertia Jha
It is for preparing in advance to obtain t and the like.

[0054]

[Equation 39] Next, a register R for storing the estimated inertia value Jhat
(Jhat) is multiplied by a value obtained by dividing the value of the phase surface Suf obtained in step S9 by the parameter α, by the value of Q obtained in step S10, and further added by a value obtained by multiplying the value by the period T of the position / velocity loop processing. Stored in the register R (Jhat) (step S11). That is, the process of step S11 is a process of integrating the mathematical expression 36 to obtain the estimated inertia value Jhat. The register R (Jhat) and registers R (Ahat) and R (Grhat), which will be described later, are set to "0" by default. Then, this register R (J
hat) is multiplied by the value of Q obtained in step S10 and stored in the register R1 (step S12). As a result, the auxiliary input τa shown in Expression 21 is stored in the register R1.
The value of the first expression on the right side of Expression 21 is stored.

Next, the value of the phase surface Suf obtained in step S9 is divided by the value β of the adjustment parameter into the register R (Ahat) storing the estimated value Ahat of the dynamic friction coefficient, and the result is multiplied by the value of the speed feedback. Further, a value multiplied by the cycle T of the position / velocity loop processing is added to obtain an estimated value A of the dynamic friction coefficient.
hat is obtained (step S13). This step S13
Processing integrates Equation 37 to estimate the dynamic friction coefficient Ahat
Is a process for obtaining The value obtained by multiplying the estimated value Ahat of the dynamic friction coefficient by the speed feedback amount is stored in the register R.
2 (step S14). As a result, the register R
2 stores the value of the second expression on the right side of Expression 21. Further, the value obtained by dividing the value of the phase surface Suf obtained in step S9 by the value γ of the adjustment parameter is stored in a register R (Grhat) storing the estimated value Grhat of the gravity term.
Are added and stored (step S15). The process of step S15 is a process of obtaining the estimated value Grhat of the gravitational term by integrating the equation (38).
rhat) stores the value of the third expression on the right side of Expression 21.

Next, the phase plane Suf obtained in step S9
Is determined to be greater than or equal to “0”, and if negative, the switching input τ1 is set to the expected minimum disturbance torque Dismin; if “0” or positive, the switching input τ1 is set to the expected maximum. The disturbance torque Dismxx is set (steps S16 to S18).

Then, the registers R1, R2, R (Grha
The auxiliary input τa is determined by adding the value of t) and the switching input τ1 determined in step S17 or S18 (step S19), and the determined auxiliary input τa is determined in step S8.
Is added to the torque command value τ0 in the linear control obtained in step (1), and is output to the current loop as a torque command τ to the servo motor (step S20).

Hereinafter, the above processing is repeatedly performed for each position / speed loop processing cycle.

In the above-described embodiment, an example in which feedforward control is used for linear control has been described. However, the present invention can be applied to P control for normal position control without feedforward control and PI control for speed control. The invention is of course applicable.

[0060]

According to the present invention, the sliding mode control and the adaptive control can be easily applied without changing the conventional linear control, and the adaptive control is performed by using the estimated values such as the inertia and the dynamic friction coefficient. Therefore, the value of the auxiliary input does not fluctuate sharply, and the torque command to the servomotor does not fluctuate rapidly and vibration does not occur. Therefore, it is possible to obtain servomotor control that is strong in disturbance suppression and strong in parameter fluctuations (fluctuations in inertia, dynamic friction, gravity terms, etc.). In addition, since the conventional linear control is used, the technology that has been conventionally trained in the linear control can be used as it is.

[Brief description of the drawings]

FIG. 1 is a block diagram of one embodiment of the present invention.

FIG. 2 is a block diagram of a main part of servo motor control for implementing the embodiment.

FIG. 3 is a part of a flowchart of a linear control, a sliding mode control, and an adaptive control process performed by a processor of the digital servo circuit in the embodiment.

FIG. 4 is a continuation of FIG. 3;

[Explanation of symbols]

 Kp Position gain K1 Integral gain K2 Proportional gain θr Movement command τa Auxiliary input τ0 Torque command by linear control τ Torque command to servo motor

Claims (3)

(57) [Claims] In a servo motor control method, a position loop control is a proportional control, a speed loop is a proportional integral control, and a torque command obtained by the linear control divided by an integral gain of the speed loop is used for a sliding mode control. As a phase surface, assuming that the Lyapunov function considers the inertia of the controlled object, the dynamic friction coefficient, and the estimated value of the gravitational term, so that the differential value of the Lyapunov function is always negative,
Adaptive sliding mode control based on a PI control loop, wherein each gain of the linear control is set, and an auxiliary input to be added to a torque command value from the linear control to be a torque command to a servomotor is determined. method. 2. In a servo motor control method, position loop control is proportional control, speed loop is proportional integral control, the position loop position gain is Kp, the speed loop integral gain is K1, the proportional gain is K2, and the position deviation is K2. Is ε and the speed deviation is The inertia of the controlled object is J, its estimated value is Jhat, the dynamic friction coefficient is A, its estimated value is Ahat, the gravity term is Gr, its estimated value is Grhat, the adjustment parameter values for determining the adaptive speed are α, β, and γ. Is set to τ1, the phase plane Suf of the sliding mode is set to Expression 1, the Lyapunov function is set to Expression 2, and the position gain Kp, the integral gain K1 of the speed loop, and the proportional gain K2 are set so that the differential value of the Lyapunov function is always negative. An adaptive sliding mode control method based on a PI control loop, characterized in that an auxiliary input for determining a torque command to the servomotor by adding the torque command value to the torque command value by the position / speed loop control is determined. (Equation 1) (Equation 2) 3. In a servo motor control method, when the position loop control is proportional control, the speed loop is proportional integral control, the position loop position gain is Kp, the speed loop integral gain is K1, and the proportional gain is K2. , These gain values are set so that equation 3 holds, and The acceleration of the movement command And the speed feedback value from the servo motor , The estimated value of the inertia of the controlled object is Jhat, the estimated value of the dynamic friction coefficient is Ahat, the estimated value of the gravitational term is Grhat, the switching input is τ1, the phase plane Suf of the sliding mode is expressed by Equation 4, and the input τ to the servomotor is As Equation 5: (Equation 5) Let α, β, and γ be the adjustment parameters that determine the adaptive speed, Equation 6 represents the inertia estimated value Jhat, Equation 7 represents the dynamic friction coefficient estimated value Ahat, and Equation 8 represents the estimated value of the gravity term as Grhat.
And the following equation: (Equation 7) (Equation 8) When the value of the phase plane Suf is equal to or greater than “0”, the switching input is set to τ1 as the expected maximum disturbance torque.
An adaptive sliding mode control method based on a PI control loop that controls a servomotor by setting an expected minimum disturbance torque.