JPS6344203A - Control constant determining device for digital follow-up control system - Google Patents

Abstract

PURPOSE:To improve rapid responsiveness guaranteeing stability, by expressing a controlled system by developing expression from a transfer unction to a differential equation, and further to a difference equation by applying a discrete processing, and constituting and calculating an expanded deviation system based on the above expression. CONSTITUTION:A control constant deciding device in a digital follow-up control system is constituted of a dynamic characteristic input part 11, a dynamic characteristic expression conversion part 12, a sample control cycle setting part 13, a discrete arithmetic part 14, an expanded deviation system constituting part 15, a design parameter setting part 16, an equation solving part 17, a control constant arithmetic part 18, a time response arithmetic part 19, and a decision part 20. And a digital controller is used in the device, and the control constant of a control system in which a sample controlling cycle is considered, can be decided. Thereby, the control constant arithmetic part 18 can output the state feedback coefficient, and the integration coefficient of the control constant, based on the maximal solution obtained at the equation solving part 17, and the result of the discrete arithmetic part 14. Furthermore, it is possible to handle the controlled system expressed as a system with direct attaining part.

Description

[Detailed Description of the Invention] [Object of the Invention] (Industrial Application Field) The present invention is directed to a digital tracking system that realizes the determination of control constants in the design of a tracking control system, especially when a digital control device is used as a control device. This invention relates to a control constant determination device for a control system.

(Prior Art) A PID control method is typical as a control method for single-person output. Proportional (K, ), integral (Kl/8), differential (KD8
), and a number of methods have been proposed for determining these control constants, but these cannot be directly applied when the controlled object is a multi-input/output system.

A follow-up control method based on modern control theory is being considered as a control method when the controlled object is a multi-input/output system. This control method is shown in Figure 4.

The controlled object is expressed in the form shown in block 1a, and the characteristics are improved by multiplying this state variable x (t) by a constant matrix ~ and feeding it back. Within the range where the manipulated variable u (t) does not saturate, You can improve the connectivity as much as you like.

Moreover, since the controller 2 has a structure in which the integral operation works as long as there is a difference between the target value r (t) and the control i Y (t), it is possible to configure a follow-up control system with no offset and excellent responsiveness.

Regarding this control method, for example, "General method for linear multi-input/output optimal tracking control system" (Proceedings of the Society of Instrument and Control Engineers, Vol. 1)
4, No. 4, August 1978), it is possible to configure a tracking control system even for a control target with multiple inputs and outputs. However, from a practical standpoint, there are some points that should be improved as follows.

l) Although the use of digital controllers has become common with the development of microprocessors,
It is only possible to determine the control constants when using an analog controller as shown in block 2 of FIG. It is desired to be able to determine the control constants of a digital controller by a simple method that takes into account the sample control period.

2) The controlled object cannot be handled unless it is expressed as a multi-input/output system as shown in block 1 of FIG. Therefore, even if the control target is to be expressed as a system with a direct result, the design formula cannot be used unless the direct result is approximated by a fast system and expanded. In this case, the order of the state variables becomes large, which not only increases the amount of arithmetic processing required for design, but also degrades calculation accuracy.

Therefore, even if the controlled object is expressed as a system with a direct effect component, it is desirable to be able to handle it as is, with terms expressing the direct effect component.

(Problems to be Solved by the Invention) This invention has been made to satisfy the above-mentioned requirements for the conventional design method. An object of the present invention is to provide a device for determining control constants of.

[Structure of the invention]

(Means for Solving the Problem) The present invention converts a controlled object from a transfer function expression to a differential equation expression, discretizes this based on a sample control period and converts it into a difference equation expression, and based on this, expands the Control constants of a digital tracking control system configured to configure a system, calculate a control law that minimizes a given evaluation function in this expanded deviation system, and calculate a state feedback coefficient and an integral coefficient from this calculation result. It is a decision device.

(Operation) According to the present invention, it is possible to determine control constants for a follow-up control system that can improve coordination while guaranteeing stability and can also eliminate offsets.

At this time, using a digital controller, it is possible to determine control constants of the control system in consideration of the sample control period. Conventionally, only control constants for analog controllers could be obtained, so when trying to realize this with a digital controller, the only way to achieve this was to use the control constants as they were or approximate discretized values, and set a fine sample control period. Ta.

According to the present invention, control constants for a digital controller can be optimally determined by explicitly considering the sample control period. The burden on the computer can be reduced compared to the conventional method.

Furthermore, according to the present invention, it is also possible to handle a controlled object expressed as a system with direct components. That is, in the conventional method, the direct result could only be approximated by a fast system and treated as an expanded system, which not only increased the calculation processing required for design but also degraded calculation accuracy. According to the present invention, it is possible to design with direct components intact. Moreover, contrary to the above case, when dealing with a controlled object consisting of a fast-responsive system and a slow-responsive system, it is also possible to reduce the dimensionality by approximating the fast-responsive system as a direct component. becomes. In either case.

The present invention makes it possible to reduce the burden on computers.

(Example) Hereinafter, the present invention will be explained in detail according to examples.

FIG. 3 shows the configuration of a digital follow-up control system that can be designed using the control constant determination device according to the present invention, and shows the coupling relationship between the controlled object 1b and the digital controller 3. The digital controller 3 is the sampler 4
It consists of a digital control calculation section 5 and a holder 6, and performs calculations and other processing every sample control period.

The sampler 4a samples the state variable x(t) of the controlled object 1b and inputs it to the calculation unit 7 as %x(kτ).

The calculation unit 7 multiplies the value of x(kτ) by a control constant and outputs the result.

On the other hand, the adder 8 uses the target value r (t) and the control amount Y (t)
The result is sampled by the sampler 4b, and e(kτ) is input to the calculation unit 9. In the calculation section 9.

Based on this sample value e(kτ), calculation processing of an integral operation is performed and the result is output.

Based on the outputs of the calculation units 7 and 9, an adder 10 calculates a control signal u(kτ) for each sample period, inputs this to the holder 6, and outputs u(t) from the holder 6 to the controlled object 1b. used as the manipulated variable.

The control constant determination device for a digital follow-up control system according to the present invention is a device for determining control constants used in the digital control calculation section 5 in the control system having the structure described above.

This will be explained below using FIGS. 1 and 2.

An embodiment of a control constant determination device for a digital follow-up control system according to the present invention is shown in FIG. A dynamic characteristic input unit 11 that inputs system data representing the dynamic characteristics of the controlled object, and a dynamic characteristic expression conversion unit that receives the result input in the dynamic characteristic input unit and converts it into a differential equation expression if it is a transfer function expression. a sample control period setting section 12 for inputting and setting a sample control period; and a discrete unit 13 for inputting and setting a sample control period; an expansion calculation unit 14, an expanded deviation system configuration unit 15 that configures an expanded deviation system from the difference equation representation of the controlled object, a design parameter setting unit 16 that inputs and sets design parameters, and a design parameter setting unit 16 that inputs and sets design parameters. An equation solving unit 17 that solves the Riccati type equation based on the expanded deviation system configured by the expanded deviation system component and obtains its maximum group, and based on the result obtained here and the difference equation expression that is the output of the discretization calculation unit. A control constant calculation unit 18 calculates control constants of the digital tracking control system using the control constant calculation unit 18, and a control constant calculated by this control constant calculation unit and a dynamic characteristic differential equation expression of the controlled object which is the output of the dynamic characteristic expression conversion unit. Checks whether the control system designed based on the results of the time response calculation unit 19 and the 1-hour response calculation unit, which compose the digital tracking control system and calculate the time response of the control system and display the results, has achieved the design target. Determine whether

Judgment unit 20 into which the judgment result at that time can be input
It is composed of.

Hereinafter, one embodiment of the present invention will be explained in more detail using FIG. Figure @2 shows the processing steps of this control constant determination device in the form of a flowchart.

The dynamic characteristic input section 11 inputs system data representing the dynamic characteristics of the controlled object in the following format.

or.

Here, the controlled objects are m inputs and m outputs (positive integers of m≧1), and the direct components are represented by a matrix Dc.

The dynamic characteristic expression conversion unit 12 receives the result input by the dynamic characteristic input unit 11, and if it is a transfer function expression (first equation), converts it into a differential equation expression (second equation, third equation), for example. Conversion is performed using the following algorithm. First, transform the first equation into: Here J., J3. ... can be calculated using the following algorithm.

Ji=~-11J temple, ao, J, -j, O≦i<2t-
1 Formula 5 However, if the subscript is negative, it is set to zero.

Next, using Ji in the fifth equation, create H6, HA in the following equation.

Decompose Ht in the sixth equation into the following form.

Hz=UQV” 248 formula where U,
V is an m L x m L orthogonal matrix Q = diag, (
S, , E3g, ·++, Sn, O, -) The coefficient matrix of the differential equation expression (2nd and 3rd equations) of the controlled object is given by the following equation.

Ac = In, mtU HA VT In, sn
L Formula 9 Bc = In, mL U”HL
IL, mt Equation 10 Bc=Im,
mtHtVT I'n, mt Formula 11 However, T*''p and q are defined by the following formula.

T = diag(1/S, , 1/Ss,...
1/Sn, 1, 1, ”-) 12th formula ■, 9. = (I, O:] 1st
The discretization calculation unit 14 calculates the results calculated by processing three or more equations.
and used in the time response calculation section 19.

The discretization calculation unit 14 converts the dynamic characteristics of the controlled object from a differential equation expression to a difference equation expression using the following method based on the result of the dynamic characteristic expression conversion unit and the sample control period that is the output of the sample control period setting unit 13. do.

First, h is determined by a linear equation based on the sample control period τ inputted in the sample control period setting section 13.

One = Int, (4, OX II Ac, Tl
l ) Formula 14 ms = Int , (l
og, rno+1) 15th formula IT
I! = 2'ig
Equation 16 h=τ/m, 1st
Equation 7~, calculate B* using the following equation.

~=I+ACh+-peh2←(h3+... 1st
Formula 8 Formula % Ad, Bd, Cd, and Dd are determined using the following formula.

ha=4rrX H20 formula%
Formula %1) Cd = Cc 22nd formula D
d=Dc Equation 23 Using these matrices, the dynamic characteristics of the controlled object are described by the following difference equation.

x (k+1r)=Adx (k r )+Bd u
(kr) Equation 24 y(kr)=Cd x(kr
)+Dd u (kr) Equation 25 The expansion system configuration unit 15 configures a first-order expansion deviation system using the calculation results of the discretization calculation unit.

Equation 26, where x(kr) = x(kr)−x,
28th formula u(kr) = u(kr)−u,
Equation 29 y(kr)=y(kr)−r,
Equation 30 v(kr)=u(k+
tr)-u(kr) is the formula 31 and is %
x, , us, r, are the steady values of the state quantity, the manipulated variable, and the target value, respectively. In the design parameter setting section 16,
An optimal regulator that minimizes the following evaluation function for the expanded deviation system is considered, and a weight matrix of the evaluation function is given. Evaluation function.

J(v)=Σ(x(kr)Q?(kr)-1-v'(
kr)Rv(kr)) 32nd: Input and set the values of the weight matrices Q and R. however.

The condition is that these matrices are constant symmetric matrices.

Next, in the equation solving unit 17, the expanded deviation system configuration unit 15
The maximum group of linear equations is determined based on the results of the design parameter setting unit 16.

The control constant calculation unit 18 determines control constants based on the maximum group obtained by the equation solving unit 17 and the results of the discretization calculation unit 14.

First, the optimal control law for the expanded deviation system can be described as follows.

v(kr)=−, x(kr)−, u(kre)
Equation 34 Equation 35 Therefore, the control law for the controlled object 1b is as follows: % u (kr) = -L, x (kt) +z (kr)
Equation 36 Z(k+tτ) = Z(kr)
+L, (r(kr)-y(kr)) Equation 37 The control constant calculation unit 18 outputs the state feedback coefficient - and the integral coefficient.

The time response calculation unit 19 receives the control constants that are the output of the control constant calculation unit 18 and the differential equation expression of the controlled object that is the output of the dynamic characteristic expression conversion unit 12, and configures the digital tracking control system as a simulator. , calculates the time response of the control system to target value changes and disturbance application, and displays the results.

The determination unit 20 evaluates the results displayed by the time response calculation unit 19, and if the designed control system does not reach the design target and its control performance is unsatisfactory, the sample control cycle setting unit 13 or the design parameter setting unit 16 You can return to This makes it possible to redo the design by changing the sample control period or design parameters.

The control performance of the digital follow-up control system constructed according to the above embodiment will be described below.

The control target is a system with a direct component. In mechanical systems, systems with direct components are often controlled using gears and the like. In other words, if there is play in the gear, the gear will move without any load for the amount of play, and after the teeth make contact, it will be displaced with a time constant depending on the load.

The movement for the first backlash can be regarded as the direct movement. In plants, it can also be seen in the flow rate, for example. When the valve is opened, the downstream flow rate increases rapidly,
After overshooting, it gradually decreases to a constant value. Since there is a large difference between the initial increase speed and the subsequent decrease speed, this can also be treated as a system with a direct component. The above is about one elemental system, but in complex systems, systems with fast response and systems with slow response often overlap and appear in the control amount. The dynamic characteristics can be expressed as

The control target handled here is a model of a certain plant. The transfer function is Gp(8""1+48+2.48"+0.4488"
+0.128'"" It is given by Equation 39, and the direct result is 0.5.

When trying to design a system with such a direct component,
The conventional method has a gain of 0.5 for this direct result,
The system was approximated to a first-order or second-order system with an extremely small time constant and treated as an expanded system. This approach increases the number of dimensions, which increases the amount of computational processing required for design, and also degrades accuracy.

Moreover, for the control object of equation 39 for which it is impossible to design a digital follow-up control system, a digital follow-up control system is constructed according to an embodiment of the present invention. Set the sample control period to 0.5. The weighting coefficient matrix of the evaluation function is Q=I, R=0.1
Designed as. FIG. 5 shows a response waveform when the target value of the control system is changed in steps. FIG. 5a shows a case where the design is made without taking the direct result into consideration, and FIG. 5A shows a case where the design is made with the direct result in consideration, as in the embodiment of the present invention.

Here, the curve 21 is the response waveform of the control tt (output), and the curve 22 is the behavior of the manipulated variable.

Comparing Figures 5a and 5b, we can see that the output disturbance is suppressed by taking into account the direct output component.

It can also be seen that energy consumption can be realized.

With conventional design methods, it is possible to determine the control constants of a control system using an analog controller, but it is not possible to determine the control constants of a digital follow-up control system as shown in FIG. For this reason, there is no choice but to use a digital controller as an alternative to an analog controller by setting an extremely fine sample control period. According to the present invention, control constants for a digital controller can be optimally determined by explicitly considering the sample control period. The burden on the computer can be reduced compared to the conventional method.

Furthermore, according to the present invention, it is also possible to handle a controlled object expressed as a system with direct components.

In conventional design methods, direct results are approximated by a system with fast response and treated as an expanded system, which increases the computational processing required for design and degrades calculation accuracy. According to the present invention, it is possible to design by taking into account direct results. Therefore, there is no need to increase the dimension as described above. Moreover,
It is also possible to approximate a fast-responsive system to a direct component and treat it in a reduced-dimensional manner.

〔Effect of the invention〕

As described above, according to the control constant determination device for a digital follow-up control system of the present invention, it is possible to design a digital control device that takes into account the sample control period, which has not been possible in the past. Furthermore, since it is possible to handle systems with direct components, it is possible to construct a follow-up control system with excellent responsiveness while suppressing operation energy consumption.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of a control constant determining device according to an embodiment of the present invention, FIG. 2 is a flow chart showing the processing procedure of a one-control constant determining device, and FIG. 3 is a one-control constant determining device. It can be designed using the control constant determination device according to the invention. Figure 4 shows the configuration of a conventional tracking control system equipped with an analog controller. Figure 5 shows the target value of the digital tracking control system. FIG. 3 is a diagram showing the time response of the manipulated variable and the controlled variable when the variable is changed stepwise. l... Controlled object, 2... Analog controller, 3...
Digital controller, 5...Digital control calculation section. 11... Dynamic characteristic input section, 12... Dynamic characteristic expression conversion section. 13... Sample control period setting unit, 14... Discretization calculation unit, 15... Expanded deviation system configuration unit, 16... Design parameter setting unit, 17... Equation solving unit, 18...
- Control constant calculation section, 19... Time response calculation section, 20.
... Judgment department. Agent Patent Attorney Noriyuki Chika Yudo Kikuo Takehana TIME Figure 5

Claims (2)

[Claims] (1) A dynamic characteristics input section that inputs system data representing the dynamic characteristics of the controlled object, and a dynamic characteristics input section that receives the results input in the dynamic characteristics input section and converts them into a differential equation expression if the result is a transfer function expression. an expression conversion section, a sample control period setting section that inputs and sets the sample control period, and inputs the set sample control period and the differential equation expression of the dynamic characteristic that is the output of the dynamic characteristic conversion section, and sets the sample control period. a discretization calculation unit that calculates a differential equation representation of a controlled object by discretizing a differential equation representation based on a design parameter setting section for inputting and setting design parameters, and an equation solving method for solving Riccati type equations and finding the maximum solution based on the design parameters set here and the expanded deviation system configured by the expanded deviation system configuration section. a control constant calculation unit that calculates the control constants of the digital tracking control system based on the result obtained here and the difference equation expression that is the output of the discretization calculation unit; a time response calculation unit that configures a digital tracking control system using the dynamic characteristic differential equation expression of the controlled object which is the output of the dynamic characteristic expression conversion unit, calculates the time response of the control system, and displays the result; A digital tracking system comprising: a determination section capable of determining whether the designed control system has achieved the design target based on the results of the response calculation section, and inputting the determination result at that time. Control constant determination device for control systems. (2) A system in which the dynamic characteristics of the controlled object are such that the influence of the input (manipulated amount) appears immediately on the output (controlled amount) without any time delay (hereinafter this is referred to as a system with a direct component) )
2. A control constant determination device for a digital follow-up control system according to claim 1, characterized in that the control constant determination device for a digital follow-up control system is configured such that the control constant can be determined taking this into consideration even if