JPS62219002A - Servo controller - Google Patents

Abstract

PURPOSE:To obtain a servo controller requiring no complicated adjusting works easy to mistake by inputting various numerical values to a weight coefficient included in the evaluation function in the secondary form of an optimum regulator logic to set a state feedback gain automatically. CONSTITUTION:A function generator 7 generates a signal corresponding to an ideal state variable of the output from a controlled system 1 and a signal corresponding to an ideal manipulated variable as a feed forward quantity. An adder 3 adds the feedback quantity outputted from a feedback element 2 and the fed forward quantity from the function generator 7 to obtain a manipulated variable and operates the controlled system 1 by the manipulated variable. A feedback gain control means 10 consists of a feedback gain determining means 11 and a keyboard 12 as a weight coefficient input means, and the feedback gain determining means 11 consists of a Riccati's equation solving part 13 and a gain calculating part 14. The Riccati's equation solving part 13 obtains P of Riccati's equations, and the gain calculating part 14 obtains a state feedback gain (f).

Description

[Detailed Description of the Invention] [Summary] The state feedback gain is adjusted by inputting an arbitrary value to the weighting coefficient of the evaluation function of the optimal regulator theory, making it easy to adjust quickly and accurately with a minimum of parameter settings. It is a servo control device that can perform

[Industrial application field]

The present invention relates to a servo control device used in robots, NC (numerical control) devices, etc., and specifically controls the current flowing through a motor etc. so that state variables such as position and speed follow changing target values. The present invention relates to a servo control device that determines and controls a quantity.

[Conventional technology]

Conventionally, there has been a servo control device shown in FIG. 11 that controls a controlled object such as a robot arm.

The device is composed of a feedback element 2, an adder 3, a function generator 7, and a feedback gain input means 6. The feedback element 2 detects state quantities such as the position and acceleration of the controlled object 1, and sends out a feedback quantity based on a state feedback gain determined by optimal regulator theory. The function generator 7 outputs an ideal state quantity that serves as a reference for comparison with the state quantity of the controlled object l, and an ideal manipulated variable that serves as a feedforward quantity. Further, the adder 3 adds the feedback amount, which is the output of the feedback element 2, and the feedforward amount, which is the output of the function generator 7, and outputs the result as the manipulated variable of the controlled object 1. Furthermore, the feedback gain input means 6 has a feedback gain f
is input and set in the control system.

The feedback element 2 further includes an observer calculation means 4 that estimates the state quantity of the controlled object l by simulation calculation, and a state feedback gain f set by the state quantity estimated by the observer calculation means 4 and the feedback gain input means 6. The state feedback section 5 outputs a feedback amount.

A digital servo system that represents this servo control device in a discrete time system will be described. Assume that the controlled object l moves according to the linear discrete-time state equation (1). Here, W(k) is an n-dimensional vector whose components are state quantities such as the rotational speed and rotational angle at the time, and u(k) is the operation such as the current applied to the motor to operate the controlled object 1. A is an nXn constant matrix, and b is an n-dimensional constant vector. Hereinafter, equation (1) will be expressed as an error system indicating the deviation from the ideal state quantity 1(k) as the reference value set by the function generator 7 and the ideal manipulated variable '1(k) as the feedforward quantity. Expressed as: i(k+1)=Ax(k)+Tou(k)
(2), where ni (k) = electric (k) - yu (k) π (k) = u (k) - stone (k). This servo control device calculates the value from this reference value. The purpose is to operate the controlled object l so as to minimize the deviation, and at that time, the amount of feedback supplied to the control element 3 is π(k) = −f'; t(k)
(3) is obtained from the state feedback section 5. Here, the state feedback gain f is selected so as to minimize the quadratic form evaluation function according to the optimal regulator theory, and is specifically obtained by solving Hirikachi's equation (5). Here, Q is an n×n constant matrix and R is a constant, each representing a weighting coefficient, which is conventionally specified to an appropriate value in advance. T indicates a transposed matrix.

Generally, the state quantity 1(k) is difficult to observe, so instead of observation, it is estimated by the observer calculation means 4 through simulation calculation using the following equation.

Here, H is a constant matrix of nXm, and 9(k) is 1 that represents the state quantity of the observable output of the controlled object 1, such as the rotation angle or rotation speed of the motor, in an error system.
The next vector is y(k)=clid(k) (8
). Here, C is an mXn constant matrix.

[Problem that the invention seeks to solve]

By the way, according to the optimal regulator theory, in order to construct a control system that is always stable, it is necessary to set the weighting coefficients Q and R included in the quadratic form evaluation function equation (4) to appropriate amounts. When Q is fixed, the smaller the weighting coefficient R related to the operation amount reduction (k) as the feedback amount, the larger the state feedback gain amount, the wider the frequency band of the servo control system, and the better the coordination. Furthermore, according to control theory, the control system should be stable no matter how small R is given. However, in reality, as the weighting coefficient R is made smaller, it usually becomes unstable and oscillates. The reason for this is that the controlled object is not actually according to equation (1), but rather (1)
) is an approximation formula that ignores the high frequency range, so if the band of the system is raised, the system will oscillate above the resonance frequency ignored in formula (1).

Also, if the weighting coefficient R is small, the manipulated variable π(k) as a feedback amount becomes large, but in reality the manipulated variable is reduced (k).
There is a limit to the value, and the system becomes unstable when it saturates at a certain value.

In this way, the selection of Q and H does not necessarily follow the theory, so conventionally, when certain Q and R are selected, the feedback gain f at that time is calculated and set in the control system by the feedback gain input means 6, If the desired performance cannot be obtained, it is necessary to perform adjustment work such as recalculating the feedback gain f and setting it again in the control system. However, since the feedback gain f has dimensions equal to the number of states to be controlled, this adjustment is quite complicated, and if even one value is incorrectly set, the system becomes unstable and the adjustment work becomes difficult. It had

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a servo control device that does not require complicated and error-prone adjustment work.

[Means for solving problems]

FIG. 1 is a principle block diagram of the servo control device according to the present invention. In FIG. 102 and inputting numerical values to the weighting coefficients included in the quadratic form evaluation function of the optimal regulator theory, and determining a state feedback gain based on the weighting coefficient and inputting it to the feedback element 102. Feedback gain adjustment means 11 consisting of feedback gain determination means 111
Equipped with G.

[Operation] The present invention converts the state quantities such as the rotation angle and rotation speed of the controlled object 101 detected by the feedback element 102 into a feedback amount based on the state feedback gain of the optimal regulator theory, and adds it to the controlled object 101 and operates it. .

In this case, in the present invention, the feedback gain adjustment means 110 for adjusting the state feedback gain provided to the feedback element 102 is a weighting coefficient that inputs an arbitrary value to the weighting coefficient included in the quadratic form evaluation function of the optimal regulator theory. It includes an input means 112 and a feedback gain determining means 111 that determines a state feedback gain based on the weighting coefficient. In addition, changing the weighting coefficient can easily change the control system over a wide range from a stable state to an unstable state, making it possible to adjust various parameters without having to perform the complicated work required in the past. Become.

〔Example〕

A servo control device according to a first embodiment will be explained based on FIG.

The device is composed of a feedback element 2, an adder 3, a function generator 7, and a feedback gain adjustment means 10.

Feedback element 2 detects the state quantity such as the rotation angle of the DC motor, which is the output from the robot arm using the DC motor as the controlled object l, and converts it based on the state feedback gain determined by the optimal regulator theory. The data is sent to the adder 3 as a feedback amount, and includes an observer calculation means 4 and a state feedback section 5. The observer calculation means 4 calculates the state quantity (k) which is difficult to observe based on the state quantity which is the output from the detected observable controlled object l and the feedback quantity U(k) inputted to the adder 3. This is estimated by simulation calculation. The state feedback unit 5 converts the state quantity i (k) by the state feedback gain f, and inputs the feedback quantity π (k) to the adder 3.
get.

It is something that

The function generator 7 generates a signal corresponding to an ideal state quantity F (k) which is an output from the controlled object l and an ideal state quantity F (k) as a feedforward quantity.

Reference numeral 3 denotes an adder, which adds the feedback amount output from the feedback element 2 and the feedforward amount output from the function generator 7, and operates the controlled object l as a manipulated variable.

Reference numeral 10 denotes a feedback gain adjustment means, which is composed of a feedback gain determination means 11 and a keyboard 12 as a weighting coefficient input means. Furthermore, the feedback gain determining means 11 is composed of a Hikatchi equation solving section 13 and a gain calculating section 14. In the Riccati equation solving section 13, the preset Q, keyboard 1
R1 input in step 2 and A, b of formula (1) or (2)
P is calculated using equation (6) based on the following. In addition, the gain calculation unit 14 calculates the state feedback gain amount from equation (5) based on P, R, A, and b. The function generator 7, feedback gain adjustment means 1O, etc. are configured by microcomputer software.

This embodiment operates as follows. When performing gain adjustment using the feedback gain adjustment means 10 in the flowchart of FIG. 3 (20), first input R using the keyboard 12 (21).

Next, in the Riccati equation solving unit 13, P is obtained by solving Equation (6) through repeated calculations as shown in the flowchart (22). Generally, this repeated calculation converges in about several to several tens of times. Next, the gain calculation unit 14 solves equation (5) based on P thus obtained to obtain the feedback gain f (23).

On the other hand, when the gain adjustment is not performed by the feedback gain adjustment means lO in the flowchart of FIG.
0), the function generator 7 calculates the ideal state quantity τ(k), which is the control reference value, and the ideal manipulated variable π(k), which is the feedforward quantity, and outputs them as signals (24);
Next, the detected state quantity y(k) of the controlled object 1 is input to the feedback element 2 (25), and the detected state quantity y(k
) and the ideal state quantity τ(k) (26)
, Furthermore, the state quantity (k) is determined by the observer calculation means 4.
(27), and then the state quantity -1c(k)
The feedback amount π is determined by the state feedback unit 5 from
(k) is obtained (28), and further, the adder 3 adds the feedforward quantity (k) generated by the function generator 7 and the feedback quantity 1(k), and the control/object 1
Find the manipulated variable u(k) that should be added to (29), and use the thus obtained (k) and (k) to find x (k+1) and y(k+1) in the next discrete time (30)
Repeat the above calculation (31).

Each of the above operations is executed by a microcomputer, including an adder 3, an observer calculation means 4, a state feedback section 5, a function generator 7, and a Riccati equation solving section 1.
3 and the gain calculation section 14 are executed by software inside the microcomputer.

Next, a second embodiment is shown in FIG.

In this embodiment, unlike the first embodiment, the feedback element 32 includes an integrator 33 for removing the steady-state deviation of the state quantity detected from the controlled object l. Also,
The feedback gain adjustment means 40 is comprised of a feedback gain determination means 41 and a keyboard 12 as a weighting coefficient input means, and the feedback gain determination means 41 is comprised of a generator calculation section 42 using an approximate formula and a gain adjustment section 43. In the approximate formula gain calculation unit 42, the relationship between the weighting coefficient R and the state feedback gain f' is determined in advance using an approximate formula, and the state feedback gain f° is calculated based on R input from the keyboard 12 using this approximate formula. do. The f° is further adjusted by a gain adjustment section 43, converted into f, and provided to the feedback element 32.

Below, approximate expressions will be found for a simple model.

Now, the transfer function of the controlled object l is expressed as and applied to positioning control using a current-controlled DC motor as an actuator. Here, G is expressed as G=kT/J using the torque constant kT of the DC motor and the inertia factor J of the load applied to the DC motor. In addition, U (s) is the current u (t) as the manipulated variable flowing through the DC motor, Y(S
) is the Laplace transform of the rotation angle y (t) of the DC motor. Expressing equation (9) as a state equation in a continuous time system, the speed x1(t), position X2 (
t ) is a component of the state quantity vector
10) Denoted as CC.

However, if the sampling time of the discrete time system in equation (1) is T, and it is converted to discrete time using a sampler and a zero-order hold, the state equation becomes i (k+1) == AN
(k) + bπ(k) (11),
However, the quantity Ma obtained by integrating x2(k) by the integrator 33 in order to remove the steady-state deviation. (k) is added as a new component. Regarding this equation of state (12), for example IfT
= 0.0OL, G = lOO, and then solve (5) and (6) for the weighting coefficient Q in equation (4) using a calculator, and then calculate the weights from the 7th
If the relationship between R and each component of fo is linearly approximated using a dashed-dotted line from this graph shown up to the figure, it will be as follows.In addition, although the above calculation is based on G-100, when G is not 100, the gain adjustment unit 43 Therefore, fo in equation (13) is set to 100/G
Note that the servo control device described above is configured by microcomputer software.

This embodiment operates as follows. This embodiment differs from the first embodiment in that, as shown in the flowchart of FIG.
Inputs R (SO).

Then, the gain calculation unit 42 using an approximate formula performs an approximate calculation of fo based on the input H (51), and the gain adjustment unit 43 adjusts fo in case G is not 100 (52), and the adjusted state is obtained. Outputs feedback gain f.

On the other hand, in the case (20) in which no gain adjustment is performed in the flowchart of FIG. )) as a signal (54)
, Next, input the detected state quantity y(k) (55)
, y (k) and the ideal state quantity r(k) (5
6), the state 7(k) obtained by the error calculation is integrated by the integrator 33 to obtain "x 3(k).Furthermore, the observer calculation means 5 estimates the state quantity 1(k) ( 58), Next, the state feedback unit 5 calculates the feedback amount π(k) from the state amount 9(k) (59), and calculates the feedback amount π(k) and the feedforward amount u (
k) by the adder 3 to add the manipulated variable u (k
) as (SO), the thus obtained π(k)
+'E'E (k), the observers x (k+1) and y (k+1) at the next discrete time are determined by the observer calculation means 4 (61), and the above calculation is repeated (62).

In this embodiment, each time the weighting coefficient R is changed (5),
Since it is not necessary to newly solve Riccati's equation (6), the calculation of the state feedback gain f becomes faster. Moreover, instead of the program (22) for solving Riccati's equation shown in the flowchart of Figure 3, (14)
Since it is only necessary to prepare a program for the formula, it can be easily implemented even on a small-scale microcomputer.

Next, a third embodiment will be explained based on FIG. 9. In this embodiment, unlike the second embodiment, the feedback gain adjusting means 70 is inputted from the feedback gain determining means 71 and the keyboard 12 as a weighting coefficient input means. It is configured. The feedback gain determining means 71 is based on table 7.
2. It is composed of a table correspondence means 73 and a gain adjustment section 43. The table 72 is created by selecting a plurality of weighting coefficients R in advance off-line and determining the state feedback gain f° for each R, and is stored in the memory of the microcomputer. The table correspondence means 73 searches the table 72 for the state feedback gain f° corresponding to the input R and outputs it. Note that if G is not 100, the state feedback gain f' is multiplied by 1007 G in the same manner as in the second embodiment.

This embodiment operates as follows. This embodiment is different from the second embodiment, and as shown in the flowchart of FIG.
When performing gain adjustment (20)
Yoban】R's! tJi! (63), and then the table correspondence means 73 creates the table 72 for the corresponding R.
The corresponding state feedback gain f”
(64).Furthermore, if G is not loo, the state feedback gain f° is multiplied by 100/G and converted to f in the same manner as in the second embodiment (65).
, Thus, compared to the second embodiment, this embodiment can only select the value listed in the table as the value of R, but the calculation of f is faster, and the approximate formula shown in equation (14) is Since even the calculation of This method is inexpensive, and it is advantageous in terms of cost to use more memory than to create a program to calculate equation (14).

Furthermore, this embodiment can be applied even when approximate expressions for R and f cannot be easily obtained.

〔effect〕

According to the present invention, by automatically setting the state feedback gain by inputting various numerical values to the weighting coefficients included in the quadratic form evaluation function of the optimal regulator theory,
The state feedback gain is adjusted. Therefore, compared to the conventional case where many feed centering gains are directly fixed, the setting of a minimum number of parameters is required, and the adjustment is easy, fast, and reliable.

[Brief explanation of drawings]

Fig. 1 is a block diagram of the principle of the present invention, Fig. 2 is a block diagram showing the first embodiment, Fig. 3 is a flowchart according to the first embodiment, and Fig. 4 is a block diagram showing the second embodiment. figure,
5 to 7 are graphs according to the second embodiment, FIG. 8 is a flowchart according to the second embodiment, and FIG. 9 is a diagram showing the third embodiment. 1.101... Controlled object 2.32, 102... Feedback element 3... Adder 10.40, 70, 110... Feed-pack gain adjustment means 7... Function generator 11.41 .71.111...Feedback gain determining means

Claims (1)

[Claims] 1) A feedback element (
102), a servo control device comprising: weighting coefficient input means (112) for inputting a numerical value to a weighting coefficient included in a quadratic form evaluation function of optimal regulator theory; and determining a state feedback gain based on the weighting coefficient. A servo control device comprising a feedback gain adjusting means (110) comprising a feedback gain determining means (111) input to a feedback element (102). 2) The feedback gain determining means (111) includes:
2. The servo control device according to claim 1, wherein the state feedback gain is determined based on a numerical solution obtained directly from Riccati's equation. 3) The feedback gain determining means (111) includes:
2. The servo control device according to claim 1, wherein the state feedback gain is determined based on an approximate expression of a relationship between a weighting coefficient and a state feedback gain determined in advance. 4) The feedback gain determining means (111) includes:
2. The servo control device according to claim 1, wherein the state feedback gain is determined based on a table created in advance that shows the relationship between a plurality of weighting coefficients and the feedback gain.