JPH0433102A - Model prediction controller - Google Patents

Abstract

PURPOSE:To start a controller in a short time by providing an evaluation function parameter control means which calculates a stable allowance from the frequency response of a open-loop transfer function in a control system and which decides a stable allowance condition so that it is satisfied. CONSTITUTION:In the control system 11, a manipulated variable (u) for making the controlled variable (y) of a plant 13 to follow a target value is calculated by a model prediction controller 17. A test signal generation means 25 generates a test signal and inputs it to the plant 13. The manipulated variable (u) and the controlled variable (y) are inputted to a dynamice characteristic model estimation means 23 and a dynamice characteirstic model is estimated. The evaluation function parameter control means 2 decides the parameter of an appropriate function from the stable allowance condition which a stable allowance setting means 19 sets and the control constant of the model prediction controller 17 is adjuted. The control system always hold sufficient stability with such constitution and model prediction control persistent to a model difference can be executed.

Description

[Detailed Description of the Invention] [Objective of the Invention] (Industrial Application Field) The present invention predicts the future movement of a control response based on a dynamic characteristic model of a controlled object, and adjusts the manipulated variable while taking this prediction into consideration. The present invention relates to a model predictive control device that calculates and controls a controlled object.

(Prior Art) In recent years, model predictive control devices have often been used in the field of process control. The following characteristics have been pointed out in this model control.

■Achieves stable control response for processes with long dead time.

■Followability can be improved by feedforward control using future target values.

■It can also be applied to multivariable control systems.

■Control systems can be easily designed from step responses, for example, without requiring an accurate dynamic characteristic model of the controlled object.

■By including the physical laws and nonlinear characteristics of the controlled object (plant) in the prediction model, fine-grained control can be expected.

■Constraint conditions related to the operation of the controlled object (for example, upper and lower limiters, rate of change limiters, etc.) can be directly included in the control law.

Many predictive control methods have been proposed so far.

These are for example ■Nishitani: Application of Model Predictive Control, Measurement and Control Vol.

28, NO, pl), 99B-1004 (1989) I
ID, V, CIarke & C, Mohtadl: P
properties of generalized
Predietlve Control, Autosa
25-8pp, 859 (1989), etc. In particular, in the above document ■, generalized predictive control (Generic predictive control) that includes various model predictive control methods
ralized Predlctive Contro
1: GPC) has been proposed.

This predicts the control response future value y based on the model of the controlled object (process) when the future target value y1 is given, and calculates the evaluation function J=Σ(D (z-') (
y (k+ i)-y'''(k-!-1)))"10λ
Method for determining the manipulated variable increment Δu (k) that minimizes Σ(Δu (k+i−1>)” (Problems to be Solved by the Invention) Problems of the conventional model predictive control device will be described below.

First, in order to obtain the control parameters of the model predictive control device, a dynamic characteristic model of the controlled object is required. In particular, in certain types of model predictive control methods (see Material ①), it is necessary to measure the step response as a dynamic characteristic model of the controlled object.

However, in an actual plant, the control response is disturbed by disturbances, and it is dangerous to leave the plant in an open loop state for a long time. Therefore, in order to estimate the step response of the controlled object to an accurate model, It is difficult to measure over a long period of time until it has sufficiently stabilized. Furthermore, in plants whose dynamic characteristics change depending on operating conditions and time, there is a problem in that the characteristics change during long-term measurement of control response data.

Secondly, in model predictive control, it is an evaluation function parameter included in the above-mentioned evaluation function. Prediction start length, prediction length N
p, control length Nu, weighting coefficient λ, closed loop pole placement polynomial D
Since the characteristics and stability of the control system vary greatly depending on how (z-') is selected, it is necessary to appropriately adjust (tune) them when starting the control device.

However, in the conventional model predictive control device 3 that controls the control system 1 as shown in FIG. The evaluation function parameters were given to 4.

However, the relationship between parameters and control characteristics is not clear, and it takes time to adjust the control system so that it is sufficiently stable, and as a result, it takes time to start up the control device.

On the other hand, in order to ensure the most important stability for control system 1, a method has been proposed in which the evaluation function parameters are adjusted while examining the pole arrangement of control system 1 (for example, ■Fujiwara: Stabilization of adaptive control Methods, Systems and Control Vol.
32. No. 3, pp. 189-198 (1988)).

However, in order to accurately determine the poles of a control system, an accurate dynamic characteristic model of the controlled object is required. For the first reason mentioned above, the poles could not be determined accurately, making this method impractical.

In consideration of the above facts, the present invention eliminates the need to measure control response data such as step response over a long period of time, and enables a safe control device to be activated easily and quickly without the need for thought-and-error adjustment of parameters8. The purpose is to provide a model predictive control device.

[Structure of the invention] (Means for solving the problem) In order to achieve the above object, the invention described in claim (1) provides the following:
Evaluation function parameter adjustment means that calculates a stability margin from the frequency response of a open loop transfer function of a control system for controlling a controlled object, and determines parameters included in the evaluation function so that a preset stability margin condition is satisfied. It is characterized by having the following.

Furthermore, the invention as set forth in claim (2) is characterized in that a dynamic characteristic model estimation means is provided using a minimum realization method based on a singular value decomposition method from data on the rise of a step response of a controlled object.

(Function) According to the invention set forth in claim (1), the evaluation function parameter adjusting means calculates gain margin, phase margin, etc. from the frequency response of the open loop transfer function of the control system in order to ensure the stability of the control system. While examining conditions related to a stability margin specified in advance, evaluation function parameters that satisfy these conditions are automatically determined, and control constants of the model predictive control device are determined based on the evaluation function parameters.

Specifically, among the above-mentioned evaluation function parameters, the prediction length Np, the prediction start length, and the control length N u s are determined based on the order n of the controlled object. Since the other weighting coefficients λ and the closed-loop pole placement polynomial greatly affect the stability of the control system, the open-loop transfer function of the model predictive control system is determined, and its frequency response is determined by the specified stability margins (gain margin GM, phase margin PM, According to the invention of claim (2), wherein the weighting coefficient and the closed-loop pole placement polynomial are characterized in that the stability margin threshold ε, 1) is obtained, the dynamic characteristic model estimating means calculates the After finding the impulse and estimating the discrete-time state space model using the minimum realization method using the singular value decomposition method, the dynamic characteristic model (discrete-time transfer function) is estimated.

By using the singular value decomposition method, the appropriate order of the controlled object can be automatically determined, and a dynamic characteristic model that accurately expresses the frequency characteristics of the intermediate frequency band (cutoff frequency band) of the controlled object can be created from short data. can be estimated.

Therefore, since the dynamic characteristic model is estimated using the minimum realization method using the singular value decomposition method, the dynamic characteristic model of the controlled object can be estimated even from a short step response, and when it is not possible to measure the step response until the settling time. can also be applied.

Further, although the dynamic characteristic model estimated from short data of only the rising portion of the step response is not completely accurate, it accurately represents the intermediate frequency (cutoff frequency) characteristics of the process.

This model is used to check the frequency response of the control system's open-loop transfer function while adjusting the evaluation function parameters to satisfy the safety margin. Stability can be evaluated with high accuracy. This makes it possible to realize a model predictive control system that is robust to model errors and sufficiently stable.

(Example) Next, an example of the model predictive control device according to the present invention will be described using FIGS. 1 to 5.

FIG. 1 is a block diagram showing the configuration of a control system 11 to which a model predictive control device 115 is applied.

As shown in FIG. 1, the model predictive control device 15:
It is composed of a model predictive controller 17, a stability margin setting means 19, an evaluation function parameter adjusting means 21, a dynamic characteristic model estimating means 23, and a test signal generating means 25.

In the control system 11 configured in this manner, the manipulated variable U for causing the controlled variable y of the plant 13 to follow the target value y1 is calculated by the model predictive controller 17. The test signal generating means 25 generates a test signal and inputs it to the plant 13.

The manipulated variable U and the controlled variable y are input to the dynamic characteristic model estimating means 23, and a dynamic characteristic model is estimated. Further, based on the stability margin conditions set by the stability margin setting means 19, the evaluation function parameter adjustment means 21 determines appropriate evaluation function parameters and adjusts the control constants of the model predictive controller 17.

Model predictive controller 17 > Test signal generating means 25 when starting the model predictive controller 17
A step signal or other signal is generated from and added to the manipulated variable U. At this time, if the step signal is applied to the control system 11 in an open loop state, the step response (S+s2, 82N) of the plant 13 is measured.

Otherwise, the input/output response of the plant y (k)
Measure u (k).

<Dynamic characteristic model estimation means 23> (i) Impulse response h1 (i-1,
2,・2N), ms.

It is determined by h 1 =S + -81-+. Or, (i i) Impulse response model y (k) = hx u (k-1>+hz u (k
-2) +----1 b2Ilu (k-2N) at least 2
Estimate by multiplication.

(The least squares method is used, for example, in the academic book edited by the Society of Instrument and Control Engineers.
Estimate the impulse response of the process (see ``System Identification''). Next, the order n of the plant dynamic characteristic model is determined from the Wankel matrix from the impulse response and its characteristic value σ. Furthermore, the state space model X k+) = A X * + B, u k
yi w Cx* +Dum A-Σ-"2U"H2V" Σ-1/2B-4-
1”V [10--0]”C-[10・ ・ ・
・0]UΣI/2D-ho (generally O) However, Σcod old ag (σ1 ・medium・σ.) U is a matrix consisting of the first n columns of U V is a matrix consisting of the first n rows of V Find it, decompose it into singular values, and get H,=Lldjag (σ,...σ,...σ,)V
'NWN
IIIN, and the process model is B (z-')/A (z-') = C(z I-A)
−' Determined by B+D.

If the process has dead time, the dead time d is d-max (i; hi ≦ 1-
ε ) (threshold value ε is, for example, 0.1), and the first d impulse responses are ignored and the subsequent parts are used. In addition, the obtained process model B (
z-') includes dead time 2 as shown below.

B (z-') -B (z-') x zIn this way, the dynamic characteristics model of the plant A (z-')-10a
, z-'+-・-+a, z-'B (z-')-b.

+b, Z-'+-bm z are obtained. By sequentially substituting u (k)-1 (K-1, 2, 3.) from this model, the step response can be determined to be any longer than the observed length. Similarly, u(1)=1
, u (k)-0(k-2,3-), the impulse response can be obtained as long as desired.

Evaluation function parameter adjustment means 21> The evaluation function parameter adjustment means 21 calculates an evaluation function J=Σ(D(z−') (y(k+i) −y' (k
+iH1'+λΣ(Δu (k+1-1))" include the evaluation parameters, prediction length Np, prediction start length, control length Nu, weighting coefficient λ, closed loop pole placement polynomial D(
z'−') is determined as follows.

■Determination of predicted length NpNp-2n Or, NpmrRin (k; s, ≧ (step response final value x 90%) (Step response S, calculated from the dynamic characteristic model) Or, Np-k However, h , is the peak value of the impulse response (Impulse response is calculated from the dynamic characteristic model) ■Determination of the prediction start length -d Or, L=n Or, L-1 ■Determination of the control length Nu■n Or , N u -rankG This performs singular value decomposition of the matrix and G-U diag(cy, * (7t *
cr,,l V” rankG=mtn from its singular value σ (k: Σσ direct/Σσ−≧1−
ε) (threshold ε is, for example, 0.1).

■Determination of initial value of weighting coefficient λ λ-ε〉0, (e.g. ε-0,01) ■Determination of initial value of closed-loop pole placement polynomial D(z-') Fixed at D(z-'')-1 or, D(z-')-1-ρ 2 (for example, ρ "0.01") Here, ρ specifies the damping characteristics of the control system, and the closer ρ is to 1.0, the slower the damping of the control system. become.

■Weighting coefficient λ or closed loop pole placement polynomial % expression %) Evaluation function parameter predicted length N determined by above ■~■
Model prediction control parameters are designed based on p, prediction start length 1 control length Nu, weighting coefficient λ, and initial values of closed loop pole placement polynomial D(z-'). (The design method will be described later.) Next, calculate the open-loop transfer function L(z-') of the control system,
Its frequency response L (exp(-jωτ)) is determined.

In addition, in the stability margin setting means 19, the following parameters related to the stability margin are set in advance by the operator, and transmitted to the evaluation function parameter adjustment means 21.

Gain margin G,,* [dB] Phase margin PM* [degrees] Stability margin threshold ε1. (Usually 0.5 to 0.7) Next, check the following conditions for the frequency response L (exp(-jωτ)) (τ is the sampling period, and the angular frequency ω is in the range of [0, π/τ]). do.

(Jl) Gain margin GM --201oglL (ex
p(-jωr)≧GM* (b) Phase margin P+, l = L (exp(-jω
r )) + 180'≧PM (C) Sensitivity function peak value S ,,, -maxi/(L+L (exp('jc
+, + r ))≦ε1. .

In addition, the frequency response L (exp(-jωτ)) is shown in Fig. 4.
The relationship between the Nyquist diagram (vector locus), the gain margin Gλ, the phase margin PM, the stability margin threshold value, and In is shown. In particular, the stability margin threshold ε1o corresponds to the shortest allowable distance from the point (-1, 0) on the Nyquist trajectory. If the frequency response L (exp(-jωτ)) satisfies all of the above stability margin conditions (a), (b), (CG, then the weighting coefficient λ, the closed loop pole placement polynomial D(z-'
) is fixed as is. If the stability margin is not satisfied, process either λ-λ×1.01 or ρ-0,01+0.99Xρ, or both, and then repeat the process from the beginning.

As described above, the weighting coefficient λ, the closed loop pole placement polynomial D
(z') is repeatedly adjusted until the control system satisfies the specified stability margin.

Next, a method of calculating model predictive control parameters and a method of calculating a -cyclic transfer function processed in the evaluation function parameter adjusting means 21 will be explained.

Dynamic characteristic model of plant 13 ALZ'noA (z-')-1+a+ z-'+-allzB
(Z-')-b. + blz −' + b m z
is given, the evaluation function J=Σ(D(z-')(y(k+1)-3/"<k
11)))"+λΣ(Δu (k+1-1) )' and its increment Δu (k) are calculated by the following formula.

For the mass, j-1 to Np, the following equation (this can be expressed as Dl
D (referred to as the ophant ine equation) and D
-') =EJ (z-J (1-z-') A (
z−”) 10Z−’FJ (z−”) polynomial E j
(z-') (j-1st order monitor), F j (z
-') (nth order) B (z-') E j (z-') -Hj (Z-') 1Σh z z -' (a++j-1st order) is determined.

As a result, the control law is Au-g" tD (z-') y'"-F (z-')
y (k) −H(z−′) u (k−4) ). However, y" - [y'"(k+1)...y" (k+Np
)] Ding F (z-') = [F + (z-')
...FNp(z-')] TH(z-')
-[H+ (z') ”'HNp (z-')
] "g"-(G"G+λI)-1G" -th line,
However, S+ is the step response calculated from the dynamic characteristic model) (Actually, by singular value decomposition of G,
l yT (v" can be calculated using a matrix consisting of the first Nu rows of V.) Next, from the model predictive control parameters g" F (z-') and H (z-') obtained in this way - Calculate the circular transfer function. The model predictive control system can be expressed by the equivalent block diagram shown in FIG. Therefore, the round transfer function is as follows: B (Z-') z-'g' F (z-') Therefore, -
The frequency response of the circular transfer function is L (eu)(-jωτ))
becomes.

Next, the operation of this embodiment will be explained according to the flowchart shown in FIG.

In step 101, input/output response data of the plant 13 is observed. Here, the test signal generating means generates a test signal, which is added to the manipulated variable U, and this output response 3/ (k)
, u (k) are observed.

In step 103, the dynamic characteristic model estimating means 23 calculates an impulse response, and the step 105 estimates the dynamic characteristic model.

In step 107, the evaluation function parameter adjusting means 21 determines the parameters according to the above-mentioned methods. After that, in step 10, the one-loop transfer function L(z-
J and its frequency response L (exp(-jωτ)
). In step 111, the stability margin is calculated,
In step 113, it is determined whether this stability margin satisfies a desired stability margin set in advance.

If the desired stability margin is not met, step 10
From 7 onwards, the following steps are repeated. Then, if the desired stability margin is satisfied, the process ends.

Next, the step response (sampling period: 0.1 sec) of the process shown by the following equation showing an actual numerical example of the model predictive control device 15 according to the present invention was measured, and the model predictive control device 15 according to the present embodiment , the dynamic characteristic model was estimated, and the evaluation function parameters were adjusted (tuned).

Stability margin conditions are Gx+-8dB or more, PM-50'
Above, ε. -0.6, the evaluation function parameter was adjusted to p-10 u-5 D(z-') λ -1,60. The control response of the control system before and after adjustment is shown in FIG. As shown in Figure 5, before adjustment (λ-0
, 1), the movement of the manipulated variable, which was excessive, became gentler due to the adjustment of λ, and the overshoot of the controlled variable was reduced. The stability margin is also the gain margin G1. is 5.03 to 9.09
In addition, the transfer margin PM increased from 89.2° to 51.4°. As a result, we have achieved a robust model predictive control system that maintains sufficient stability and is less susceptible to fluctuations in plant characteristics.

In this embodiment, the parameters are adjusted by the evaluation function parameter adjusting means based on the dynamic characteristics estimated by the dynamic characteristic model estimating means. However, the present invention is not limited to this, and if the dynamic characteristic model is known in advance, There is no need to use dynamic characteristic model estimation means.

Furthermore, the stability margin setting means and the evaluation function parameter adjustment means may be integrated.

Further, the test signal generation means and the dynamic characteristic model estimation means may be integrated.

[Effects of the Invention] As explained above, the model predictive control device according to the present invention can adjust the parameters of the evaluation function, which have been difficult to adjust appropriately.
Since the control system can be automatically adjusted to satisfy pre-specified stability margin conditions, the control system always maintains sufficient stability, is unaffected by fluctuations in plant characteristics, and model predictions are robust to model errors. The effect of enabling control can be obtained.

In addition, it has a function to estimate a dynamic characteristic model from short step responses of the plant, so there is no need to spend a long time measuring control response data such as step responses, and the control equipment can be started up easily in a short time. Excellent effects can be obtained.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing a control system to which the model predictive control device according to the present invention is applied, Fig. 2 is a flowchart showing the operation of model predictive control, and Fig. 3 is a model control equivalent to the control system predicted by the model. A block diagram showing the system, Fig. 4 is a Nyquist diagram showing the frequency response, Fig. 5 is a control response diagram showing before and after adjustment of the parameters of the evaluation function by the model predictive control device of the present invention, and Fig. 6 is a conventional model. FIG. 2 is a block diagram showing the configuration of a predictive control device. 11... Control system 13... Plant 15... Model predictive control device 17... Model predictive controller 19... Stability margin setting means 21... Evaluation function parameter adjusting means 23... Dynamic characteristic model Estimating means 25... test signal generating means

Claims (2)

[Claims] (1) Predict the future value of the controlled variable based on the dynamic characteristic model of the controlled object, form an evaluation function regarding the deviation signal and the manipulated variable increment between the predicted future value of the controlled variable and the future target value, and In a model predictive control device that calculates the manipulated variable that minimizes the evaluation function from the control amount and future target value, the stability margin is calculated from the frequency response of the open-loop transfer function of the control system, and the parameters included in the evaluation function are A model predictive control device, characterized in that it is provided with an evaluation function parameter adjusting means that determines so that a preset stability margin condition is satisfied. (2) The model predictive control device according to claim (1), further comprising a dynamic characteristic model estimating means using a minimum realization method based on a singular value decomposition method from data on the rise of a step response of a controlled object.