JPS6240501A - Gain setting device for digital servo-control device, and its method - Google Patents

Abstract

PURPOSE:To easily design a control device by prescribing a state variable and an evaluation function, applying an optimum regulator, and deriving each coefficient (each gain of a proportionor, an integrator and a differentiator) kP, kI and kD of a servo-system of a PID type. CONSTITUTION:A continuous-time state equation setting part 121 sets a continuous-time state equation, when a gain G of a controlled system has been inputted. A discrete-time state equation setting part 122 converts the continuous-time state equation to a discrete- time by a sampling time T, and sets a discrete-time state equation. An integral type state equation setting part 123 sets an integral type state equation, based on the discrete-time state equation. An optimum regulator solution-deriving part 124 solves an optimum regulator problem, based on an input R for showing the solidity of a servo, and derives coefficients kI, kp and kD. A target value (r) is inputted, added 112 to an output (feedback quantity) of a controlled system 110 which has been brought to sampling by a sampler 111, and its error (e) is outputted. In this state, each coefficient which has been derived as mentioned above is inputted to an integrator, a differentiator and a proportionor, and a servo-system control of a PID type is executed.

Description

[Detailed Description of the Invention] [Table of Contents] Overview Industrial Field of Application Conventional Technology Problems to be Solved by the Invention Means for Solving the Problems (Fig. 1) Work/Example of Use (a) Digital・Explanation of the servo system (Figures 2 to 9) Φ) Detailed explanation of the present invention (Figure 10) (C) Actual example of the present invention (Figures 11, 12, and 13) Invention Effect [Summary] Like a DC motor, the transfer function P (S): G/S”
In a PID type digital servo control device that performs proportional-integral-derivative control on a controlled object expressed as .

Instead of determining the integrator gain, proportionality gain, and differentiator gain by trial and error, each of these gains is obtained by a mechanical procedure by using optimal regulator theory.

[Industrial application field]

For example, the present invention can be applied to a digital current-controlled DC motor.
Transfer function P(S) such as a servo device: For a servo device to be controlled expressed as G/82, an optimal regulator and a finite setting observer are applied, and an integrator (1) is generated from only the motor position signal. This invention relates to a digital servo device that uses a proportional device η and a differentiator 0 to constitute a stable digital and servo system that does not produce steady-state deviations.

Servo control of DC motors traditionally uses operational amplifiers.

It consisted of an analog system that combined resistors, capacitors, etc., but because it was an analog system, there were problems such as operational inaccuracies due to variations in elements and temperature drift, and there was also a limit to the miniaturization of the device.

Therefore, recently, digital servo systems using digital elements such as microprocessors have begun to be adopted.

[Conventional technology]

There are various ways to configure a digital servo system.

For example, as shown in Fig. 14, a servo system is used which is equipped with an integrator 205 because it does not generate steady-state deviations, and a velocity feedback or differentiator 207 to further stabilize the system. However, in this type of conventional servo system, the integrator 20
5. Proportionator 206. Gain kI of the differentiator 207, etc.

It is not clear how to set kp and kd, and even if appropriate values are determined through experience and trial and error, it is not easy to set the gains in these coefficient sections 202 to 204, and this takes a lot of effort and time. Gakakashi.

Furthermore, it has been difficult to maintain sufficient stability against unknown disturbances and parameter fluctuations of the controlled object.

On the other hand, among the achievements of modern control theory, there is optimal regulator theory, which is a method of designing a control system that eliminates the trial-and-error factor and minimizes a given quadratic evaluation function. However, optimal regulator theory uses state variables,
There is a lot of freedom in how to decide the state variables and the evaluation function.If you do not choose an appropriate combination of state variables and evaluation function,
The control system has become complicated, and the physical meaning of the evaluation function has become vague, making it difficult to construct the desired control system. Furthermore, the optimal regulator provides feedback from the overall state, but in reality, it is often impossible to know the entire state (internal state) of the controlled object, so an observer etc. is used to generate the internal state from the output. It's coming out. This makes the entire control system extremely complex. Furthermore, since it is expressed as state feedback, the physical meaning of the control system may become unclear, making it difficult to improve the control system.

Therefore, the purpose of the present invention is to solve these problems by using the optimal regulator theory.
PI that is easy to configure mechanically, eliminating the trial and error factor
The purpose is to configure a D-type control system.

[Means for solving problems]

In order to achieve the above object, the present invention includes an integrator 105. as shown in FIG. Proportionator 106. The coefficients of each coefficient section 102 , 103 , 104 of the differentiator 107 are automatically determined based on the output of the gain setting device 101 . This gain setting device 101 has a tap T at the time of sampling, a constant R9 indicating the stiffness of the servo, an in G for the gain of the controlled object (G = 7 for a motor; ICr is a torque constant).

J is the inertia factor J) applied to the motor.

As described later, the coefficient parts 102 to 104 O coefficient kI l kPI k according to the optimal regulator theory.
Dt - Can be determined mechanically.

[For production]

According to the present invention, by using the optimal regulator theory, trial and error factors are eliminated and the coefficients kr, k are automatically calculated.
Easy to configure PID that can calculate p, kD, etc.
It is possible to construct a shape control system.

〔Example〕

The configuration of the PID type servo system according to the present invention and its theoretical background will be explained.

(a) Description of digital servo system First, we will explain a general system not limited to DC motors, and then apply the results to DC motors to construct the PID type servo system of the present invention. show.

The object of control is generally expressed as a continuous time system of one person's output by the following equation.

x(t) = kcλ(t) + Ibc u(t)
...""Song..."...(1)y (t) =喀＊(
t) ・・・・・・・・・・・・・・・・・・
...(2) Here, X(t) : State variable n-th vector u(t) : Manipulated variable (input) Scalar AC diistem matrix nXn matrix Movement C: Control matrix N-th vector @ : Output matrix First-order vector : Time differential Ma : Transpose (The transpose of the vector, i.e., flX1 matrix is I
It becomes an Xn matrix. The following symbols all indicate the transposition of matrices and vectors. ) to express.

A block diagram of this system can be expressed in FIG.

In FIG. 2, 1 is a control matrix, 2 is a block showing integration, 3 is an output matrix, and 4 is a system matrix.

I/8 is a Tubulus transformation meaning integration, and 1 is an identity matrix.

When formula (1) and (2) are made into a discrete time with sampling time T.

1t(k+x) = A cold(k) + b u(k
) , , , , , , , , , , , (3) y(k
)=c'χ(k) ・・・・・・・・・
・・・・・・・・・・・・ It can be expressed as (4). However, χ[exist]>, u(k), y()c) is the time ox(tL u(tL y(t))! D, A, and To are each of the system of the following formula% formula% As shown in FIG. 3, the block diagram is the same as in FIG. 2 with a zero-order hold 6 and a sampler 9 added.

If this is further expressed in a discrete time system, it will be as shown in FIG. In FIG. 4, 2' is a block sb that delays one sampling time, and z-1 is a Z transformation that delays one sampling time.

Now, for this system, an ideal unification (k+1
)=Δcondition(g))+bu(k) ・・・・・・・・・
・・・・・・(7) r (k) = exposure i(k>
・・・・・・・・・・・・・・・・・・・・・(E
S) and the error system that deviates from this ideal system due to disturbance etc. (k+t)=^()C)+l)α(k)...
・・・・・・・・・・・・ (9) 5F(k)=a'rt
example) ··············
・ (Consider II. The real system is a linear combination of the two, 1t(k) = z(k)1) ・・・・・・・・・
・・・・・・・・・・・・αDY(k)=Y(g))
+r(k) ・・・・・・・・・・・・・・・
・・・・・・αriU(g))=ff(g))+[(S)
) ・・・・・・・・・・・・・・・・・・・・・
・It is 0. Here r (k) is a target value.

This relationship is illustrated in the block diagrams of FIGS. 5 and 6.

In other words, Fig. 5 shows the difference between the error α(k) of the manipulated variable u (k) and the error 3' (k) of the output y (k) in Fig. 4.
This is a block diagram of a system with input and output as 7.
and 8 are adders. FIG. 6 is a block diagram of a system equivalent to FIG. 5 in terms of input and output.

Then, in (9) above, an optimal regulator is constructed for the error system of equation H. An optimal regulator is a stable feedback system that returns the deviation from the standard state to the standard state. In this case, it acts to return the deviation from the ideal state to the ideal state as shown by (force, (S) 2) above. .

By the way, in the above (9), if there is a disturbance such as kd and 1 gravity, friction, etc. that directly constitutes the optimum regulator in the error system of the α1 equation, a steady deviation may occur. Therefore, (9) above,
The optimal regulator is constructed by adding an integrator to the end of the output of equation α1)' (k).

A block diagram of this optimal regulator is shown in FIG.

In FIG. 7, 10 is a controlled unit, 11 is an integrator, 1
2 is a block that delays one sampling time, 13 is an adder, 14 and 15 are feedback coefficient units, and 16 is an adder.

In other words? Add the integral quantity of (k) to the state variable,
State variable w, (k) as %vI 伽)=? (k)+v4(k-1)...
・・・・・・・・・・・・I"t+t()C)=
)! h (k) (i = 1~n) ”-...
・-” Kasumi and a new state variable W(g)) (n+1 order) are introduced.

However, t)! t(k) is the i-th element of vector g(k).

w++x(k) is the i+th element of the vector W(k).

The new equation of state is Vv (k+ 1) = Aw w(k) + tyw
”(')1 c'A ♂1 = [W example) + (1) law)......as□A tfil, where . indicates a zero matrix whose elements are all zero. In this case, there is an n-by-1 zero matrix, that is, an n-dimensional zero vector.・・・・・・・・・
......Construct an optimal regulator by applying state feedback called wholesale.

Here, the feedback constant is the evaluation function J-4j ((k) + Rt[eclipse]), where R is the weight indicating the balance between the integral 1 town (k) and the manipulated variable ff (k).・
・・・・・・・・・It gives the operation amount α(g)) that minimizes −O to the rice.

am = (R+b, f'bJ'bwFm, ...
・・・・・・・・・・・・It is calculated as 0. Here, r is the solution of Rikkatchi's equation below.

P = Q +lA: P lb(R+
bvP ttJ' Bl)～・・・・・・(1) However, Q
= Archer] The block diagram of the above optimal regulator is shown in Fig. 7. However, =hi+, (i=l~n)...
......Ql) Yes, the 1011th element of vector bO corresponds to the i-th element of the vector.

By the way, the optimal regulator is
However, in an actual system, the only quantity that can be known is the output)' (k) (for example, the angle of the motor).

Therefore, a finite-settling observer is used to know the internal state K(k) of the system (for example, the speed and acceleration of the motor).

The estimated state total weight at time k) and the estimated output y (k) derived from that state are based on the above equations (9) and (11).

Total (k) = A (k-1) + I) α (k-t) ・・
・・・・・・・・・・・・・・・(2) y(k)=s”Q group) ・・・・・・・・・・・・・・・
・It becomes (c).

And the above estimated output y ()c) and the output y of the actual system
By feeding back the difference from (k) using F (R-order vector), the estimated state origin (k) is
+r(5'(k)-'maku)) ・・・・・・・・・・・・
...Correct as t2→.

Observer here! ! The following formula (c) is used for r.

An optimal regulator using the above observer is shown in FIG.

In FIG. 8, numeral 17 is a model part of the controlled object, which is related to the error amount away from the ideal state, and is similar to that in FIG. 6, and numeral 20 is an observer, which simulates the model part 17. be.

In this observer, 21 is a control matrix.

22 is a block that delays one sampling time.

23 is the output matrix, 24 is the system matrix, 25, 26°2
7 is an adder, and 28 is an observer coefficient section.

The control equations for each part in FIG. 8 are summarized below.

? (k) = y(k) −r(k) ・・
・・・・・・・・・・・・Moxibustion (k)=n(k)+f
(y(S))-y example)) ・・・・・・・・・・・・・
...Punishment wt(kI = Wt(k-1) + 7(k)
−・”−=−Ci!19L[(k)=−h
+wt(1c) −k w(k) “'-””
−'−...−翰u(k)=ff(k)+H伽)
・・・・・・・・・・・・・・・ (To)
Total (k+1)=:8X(S))+1bff(g)) ・
・・・・・・・・・・・・・・・Gυ? (k+1) =
a'■(k-H) ・・・・・・・・・・・・
...133 The block diagram of FIG. 8 can be modified as shown in FIG. 9. In FIG. 9, 12' is an integrator, and 29 is an adder, which subtracts the target value r□□□) from the current value and outputs the error.

However, in the digital servo system using a finite observer and optimal regulator as shown in Fig. 9,
Although it is possible to calculate the coefficients of the servo system mathematically without relying on experience and trial and error as in the past, the configuration becomes extremely complicated.

(b) Detailed Description of the Present Invention By the way, when the application of the digital servo system explained in FIG. 9 is limited to DC motors, the following analysis is made.

The current 1 (t) flowing through the DC motor is the manipulated variable.

When the rotation angle θ(1) of the motor is the output, the transfer function p(s) of the DC motor is expressed as P(S,
=l KT I G ・・・・・・・・・
・Song・(to) I, (s) J S2 S” However, G〒¥− θ(S), I(s) can be approximated by the Laplace transform of θ(t) e 1(t).

Therefore, from equation (to), the state equation for the continuous time system uses one rotation position xl (=y) and rotational speed xs (=;t) as state variables.

becomes.

When Equation (2) and Equation I3!19 are made into a discrete time using sampling time T, Equation (5) and Equation (6) above are used.

Here, in order to match the units of xl(k), x, and (k), if Txx□□□) is newly set to X and (k), the equation (to) becomes as follows.

The error system at this time is It is.

The observer coefficient V is obtained from the above equation (c).

Above equation 01), equation 02 (to) equation, (8 of equation 40, To
, a, the observer's estimate is.

Th(k)=2(k-t)+ror1(k-t)
−・・−−−−−−−−−−−(a, so @
Substituting these relationships in equations (40 to (43) into equations.

Men (k) 2 sentences (k) + (field)? Field)) =yF(k) ・・・・・・・・・
......■xa(k)=complete(k)+(magazine)-9(
t)))” = X5(k-1) + T”Gtl(k-
1)+5'()C)-Qt(k-1)-Qz(k
-1) --! −T”G(1(k−1)=magazine)−仝t(
k-1) + -! -T"Gα(k-1)=5'(k
) −? (k-1) + TT”GO(k-1)...
The song becomes...(c).

The state feedback coefficient is determined by the above 0g equation using equation (L6).

In addition, the manipulated variable tl (k) is determined by the four holes (formula 44, (4!1
Substituting equation 9, ■(k) = -hl Wl[exist]) -kt? ()c)
-kt(3'(k)-?(k-1) +-T'Gu(k
-t)), song, becomes p.

Once again, e (g)) = -5' [exist]) = r [exist]) - y (k)
・・・・・・・・・・・・・・・(49w(k)
) = -htWx(k) == w(k-1) +
lb e (k) = -f)Qk! =h
Song・1 song・・←skP: hs: kI
...Song (2) kD := h
s == kg・・・・・・1
Song-ku =-T”G kg...
Assuming the interlude (goods), the above (4gJ formula is ff (k) = mk) + be (k) 10 kD (e (k) -
e (k−x )−Ku 1l(k−t)−・f
p@w(k) = w(k-1) + kt e (k
) ===-p).

In this four equations, the first term represents the integral of the error, the second term represents the proportionality of the error, and the third term represents the differential of the error (difference in error), and a fiPID type servo system can be constructed using these. I understand.

A block diagram at this time is shown in FIG.

In Fig. 10, 102' is a coefficient part that creates summer in the coefficient of the integral term shown in formula (l), 103' is a coefficient part that creates a coefficient kF of the proportional term shown in formula (b), and 104' is a set of This is a coefficient section that creates the coefficient kD of the differential term shown. Each of these coefficients can be calculated using equation (1).

105 is an integrator, 107 is a differentiator, and 108 is an adder.

109 is a zero-order hold; 110 is a controlled object represented by the above equation; and 2 is, for example, a transfer function section of a DC motor, a model of a DC motor; 111 is a sampler that samples y (t) at a sampling time T; 112 is an adder which subtracts the target position r (k> and the current value to obtain the error value e
113 is an adder that outputs (k) and adds the feedforward amount U (k) for making the ideal system follow the target position and the operation amount due to error ■□□□),
- outputs the manipulated variable u (k), 114 is a coefficient section that creates the coefficient shown in the equation (Kan), and 115 is 1
This block delays the sampling time.

As a result, when the transfer function of a DC motor under Mi current control is given by the above Ta equation, AV of (40 equation and (4η equation).

By ToW, the state feedback coefficient is calculated mechanically from υ(11 equation, (2Q equation), and based on this, equation 〜(
Each coefficient kI v kD , kP t
Find ku.

In this way, the PID type digital servo device shown in equation (1) can be easily constructed as shown in FIG.

(C) Examples of the present invention An embodiment of the present invention will be explained with reference to FIG.

In FIG. 11, the same reference numerals as in other figures indicate the same parts.

The gain setting device 101 sets the coefficients kI, kp, k
D is set mechanically, and the continuous time state equation setting section 121. Discrete-time state equation setting section 122. Integral type state equation setting section 123. Optimal regulator solver 1
It is equipped with 24 mag.

The continuous time state equation setting unit 121 determines the gain G of the controlled object.
When inputting , as shown in formulas (b) and (g) above,
(G):=Toe, w(10)==a', and outputs bc and a'.

The discrete-time state equation setting unit 122 converts the continuous-time state equations shown by the equations (1) and (c) obtained from the continuous-time state equation setting unit 121 into discrete time at the sampling time T, and converts the continuous-time state equations obtained from the continuous-time state equation setting unit 121 into the above-mentioned equations (to). Set. Then, [expansion] is set to = σ'(\'' TzG), = 1, and these A, b and α': (10) output from the continuous time equation of state setting section 121 are sent out.

The integral type equation of state setting section 123 sets the equation of state of the α0 formula based on A+To+'' sent from the discrete time equation of state setting section 122.

The optimum regulator solving unit 124 solves the optimum regulator problem Eq. 9 and Eq. ~ coefficient kI according to the set
, kp, kD. If R is set small, the servo will be stiff, and if R is set large, the servo will be loose.

Therefore, the target value r is input, and the feedback amount obtained by sampling the output of the controlled object 110 by the sampler 111 is added by the adder and the error value e is output. As described above, since the mechanically optimal coefficients kI, kP, k are obtained, a very stable PID type control system is obtained.

Note that in this first embodiment, −T”GtI(k−
This is an example in which the term t) is ignored, but this is possible when ti saQ, and can also be approximately ignored when ku<<10. Furthermore, the feedforward ring n is also ignored.

Next, a second embodiment of the present invention will be described based on FIGS. 12 and 13.

In the first embodiment, (-T"Gn(k-1 in equation 42)
), but the second embodiment also takes this term into consideration.

FIG. 12 is a schematic diagram of the second embodiment, and FIG. 13 is a detailed diagram thereof.

In FIG. 12, parts with the same symbols as in other figures indicate the same parts, and 131 is a gain setting device and a coefficient kI.

Mechanical calculation of kP, kD and 13
2 is a coefficient section, and 133 is a time delay element, which is a block that delays one sample time, and corresponds to 115 in FIG.

The gain setting device 131 is as shown in FIG.

Continuous time state equation setting unit 141. Discrete-time state equation setting unit 142. It includes an integral state equation setting section 143, an optimal regulator solving section 144, a manipulated variable feedback gain setting section 145, and the like.

Here, the continuous time state equation setting section 141 is similar to the continuous time state setting section 121 in FIG. The integral type equation of state setting unit 143 is similar to the integral type equation of state setting unit 1 described above.
It is similar to 23. The optimum regulator solving section 144 is also similar to the optimum regulator solving section 124, except that it also outputs kD to the manipulated variable feedback gain setting section.

The operation lid feedback gain setting section 145
and kD(=Ni), the coefficient is determined by the above set.

Therefore, in the case of this second embodiment, it is possible to further add control to the term (-T''Gα(k-x) in the small hole).

Further stable control can be performed.

In the above explanation, the configuration of the differentiator is e(k
)−e(k−1), but since the above first-order backward difference format generally tends to emphasize noise, *s(e(k)+36(k−1)−36(k
-2) -e (k-3)) can also be adopted and improved.

In the above description, the DC motor is assumed to have a G/8'' transfer function, but the present invention is not limited to this.

〔Effect of the invention〕

According to the present invention, by defining state variables and evaluation functions and applying an optimal regulator, the coefficients kp, kx, kD of the conventional PID type servo system are determined by trial and error, but instead of 9 It is possible to configure the control system mechanically, and VC1 has a simple configuration that has been familiar to designers.
An ID type control system will be obtained. That is, by configuring a PID type control system with a simple configuration using mechanical procedures that eliminate ambiguity, the control system can be easily designed and sufficient stability can be maintained. Furthermore, since the physical meaning is clear, it becomes easier to improve the control system.

[Brief explanation of drawings]

FIG. 1 is a detailed explanatory diagram of the present invention. FIG. 2 is a block diagram of a general controlled object. FIG. 3 is a block diagram that converts a continuous time system into a discrete time system. FIG. 4 is a block diagram representing FIG. 3 in a discrete time system. FIG. 5 is a block diagram of a system in which inputs and outputs are the error 0(k) of the manipulated variable u (k) and the error y(g) of the -output y (k) in the system of FIG. 4. FIG. 6 is a block diagram of a system equivalent to FIG. 5 in terms of input and output. Figure 7 is a block diagram of an optimal regulator with an integrator. FIG. 8 is a block diagram of an optimal regulator with an integrator using a finite setting observer. FIG. 9 is a block diagram of a general servo device equivalent to FIG. 8. FIG. 10 is a logical configuration diagram of the present invention. FIG. 11 is a configuration diagram of a first embodiment of the present invention. FIG. 12 is a schematic diagram of a second embodiment of the present invention. FIG. 13 is a configuration diagram of a second embodiment of the present invention. FIG. 14 shows a conventional example. 1... Control matrix 2... Block showing integration 3... Output matrix 4... System matrix 5... Adder 6... 0th order hold 7... Adder 8... Addition Instrument 9...Sampler 10...Controlled object 11...Integrator 12...Block 13 that delays one sampling time
... Adder 14 ... Feedback coefficient section 15 ... Feedback coefficient section 16 ... Adder 17 ... Controlled object model section 20 ... Observer 21 ... Coefficient section that creates a control matrix 22... Block 23 that delays the sampling time by 1
... Output matrix 24 ... System matrix 25 ... Adder 2t ... Adder 27 ... Adder 28 ... Observer coefficient section 29 ... Adder 101 ... Gain setting device 102 . . . Coefficient section 103 . . . Coefficient section 104 . . . Coefficient section 105 . . . Integrator 106 . ...Controlled object 111...Sampler 112...Adder 113...Adder 114...Coefficient section

Claims (1)

[Claims] 1. For a controlled object where the controlled variable y (output) with respect to the manipulated variable u (input) is expressed by a second-order integral characteristic, that is, a transfer function P(S)=G/S^2 an integrator with a gain k_I that integrates the control deviation e that is the difference between the target value r and the control amount y, a proportional device with a gain k_P that multiplies the control deviation e by a constant, and a differential of the gain k_D that differentiates the control deviation e. In a digital servo control device, the manipulated variable u is the sum of the outputs of the integrator, the proportional device, and the differentiator. (1) The controlled variable y and the time derivative v of the controlled variable y are the state variables. a continuous-time state equation setting unit that sets a second-order continuous-time state equation; (2) a discrete-time state equation setting unit that converts the output of the continuous-time state equation setting unit of (1) into a discrete time at a sampling time T; , (3) Setting the integral amount w of the controlled variable y as a new state variable to set a third-order state equation added to the second-order discrete-time state equation output from the discrete-time state equation setting section in (2) above. an integral state equation setting section; (4) an optimal regulator solving section that solves an optimal regulator problem for the state equation set in (3) above; Let the state feedback gain be the integrator gain k_I, and let the state feedback gain from the controlled variable y be the proportional gain k_
A gain setting device for a digital servo control device, characterized in that the state feedback gain from the differential amount v is the differentiator gain k_d. 2. In the gain setting device for a digital servo control device according to claim 1, the k-1
The manipulated variable u(k-1) at the time of sampling is set as gain k_
For a digital servo device whose manipulated variable u(k) at the k-th sampling point is the amount obtained by subtracting the amount multiplied by u from the sum of the outputs of the integrator, proportionalizer, and differentiator at the k-th sampling point, A gain setting device for a digital servo control device, characterized in that a manipulated variable feedback gain setting section is added that sets a gain k_u to an amount proportional to the differentiator gain k_d of the gain setting device and the gain G of the controlled object. 3. For a controlled object where the controlled variable y (output) with respect to the manipulated variable u (input) is expressed by the second-order integral characteristic, that is, the transfer function P(S)=G/S^2, the target value r and The integrator includes an integrator with a gain k_I that integrates the control deviation e that is the difference in the control amount y, a proportional device with a gain k_P that multiplies the control deviation e by a constant, and a differentiator with a gain k_D that differentiates the control deviation e. In a digital servo control device in which the manipulated variable u is the sum of the outputs of the proportional regulator and the differentiator, (1) a second-order continuous time state in which the controlled variable y and the time derivative v of the controlled variable y are the state variables; (2) Convert the output of this continuous-time state equation into a discrete time at sampling time T to create a second-order discrete-time state equation, and (3) set the integral amount w of the controlled variable y as a new state variable. Establish a third-order state equation in addition to the second-order discrete-time state equation in (2) above, and (4) set the integral amount w to 2 for the system expressed in (3) above.
Define w^2 + Ru^2, which is the product of the amount w^3 multiplied by the amount u^2 obtained by squaring the manipulated variable u, and an amount Ru^2 multiplied by a constant R, and (5) defined in (4) above. Solve the optimal regulator problem so that the integrated quantity is the minimum, and use (3) above.
The system is characterized in that the state feedback gain from the integral quantity of the system expressed by is set as an integrator gain k_I, the feedback gain from the manipulated variable is set as a proportional unit gain k_P, and the feedback gain from the differential quantity v is set as a differentiator gain k_D. How to set the gain of digital servo equipment. 4. In the gain setting method for a digital servo device as set forth in claim 3, the amount obtained by multiplying the manipulated variable u(k-1) at the k-1st sampling time by a gain k_u is set at the k-th sampling. The amount subtracted from the sum of the outputs of the integrator, proportionalizer, and differentiator at the time point is defined as the manipulated variable u(k) at the k-th sampling time point, and is proportional to the gain k_D of the differentiator and the gain G of the controlled object. A gain setting method for a digital servo device, characterized in that the amount is defined as a gain k_u.