JPH03235101A - Model norm type adaptive control method - Google Patents

Abstract

PURPOSE:To easily adjust the controller by allowing a characteristic of a control system to conform with a characteristic of a norm model even in the case a control led system has a non-linear characteristic by constituting a reverse system model of the control led system and the controller, of a neural network. CONSTITUTION:This system is constituted of a controller 4 for controlling a controlled system 1, a reverse system model identification system 5 for identifying a reverse system model of the controlled system 1, a controller adjustment system 6 for adjusting the controller 4 by using the identified reverse system, and a norm model 3 having a desirable response characteristic. In such a state, a time series signal of an input variable of the norm model 3 is used as learning input data, and a time series signal of an input variable of the controlled system 1 corresponding to a time series signal of an output variable of the norm model 3 is used as learning teacher data, and allowed to learn a neural network for a controller model. In such a way, even if the controlled system 1 has a non- linear characteristic, the controller can be adjusted easily so that a characteristic of a control system conforms with a characteristic of the norm model 3.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a model-based adaptive control method, and in particular, to adapting the characteristics of a control system to the characteristics of a reference model even when a controlled object has nonlinear characteristics. The present invention relates to a model-based adaptive control method suitable for adjusting a controller.

[Conventional technology]

When controlling a controlled object with a controller, it is necessary to adjust the control parameters of the controller according to the characteristics of the controlled object. One of the methods is "Theory and Practice of Adaptive Control Systems" (1, D.

There is an adjustment method described in the book (co-authored by David Landau and Masayoshi Tomizuka, published by Ohmsha, December 10, 1981). below,
An overview of this conventional adjustment method will be explained.

FIG. 4 shows the configuration of a conventional adjustment method. This method is
This is a method of adjusting the controller 2 so that the characteristics of the control system, that is, the system that combines the controller 2 and the controlled object, match the characteristics of the reference model 1 that has desirable response characteristics, and is called a model-based adaptive control method. It is. In this method, a controller adjustment algorithm is formulated when the controlled object is a linear system, that is, has linear characteristics. However, formulation was difficult when the controlled object had nonlinear characteristics.

[Problem to be solved by the invention]

The above conventional technology has a problem in that when the controlled object has nonlinear characteristics, it is difficult to adjust the controller so that the characteristics of the control system match the characteristics of the reference model.

An object of the present invention is to provide a model-based adaptive control method that can adjust a controller so that the characteristics of a control system match the characteristics of a reference model even when a controlled object has nonlinear characteristics.

[Means to solve the problem]

In order to achieve the above objective, the inverse system of the controlled object is identified using a neural network, and the time-series signal of the input variable of the controlled object is obtained from the time-series signal of the output variable of the reference model by the inverse system of the controlled object. The controller is adjusted so that the time-series signal of the input variable and the time-series signal of the controller's output variable match.

In addition, the controller is configured with a neural network, and the time-series signal of the input variable of the controlled object is obtained from the time-series signal of the output variable of the reference model by the inverse system of the controlled object, and the time-series signal of this input variable and the output of the controller are calculated. The controller is adjusted through learning so that the time series signals of variables match.

[Effect]

The time-series signal of the output variable of the controlled object is used as the input data for learning, and the time-series data of the input variable of the controlled object is used as the training data, and the neural network for identifying the inverse system model is trained. Inverse system models of controlled objects with nonlinear characteristics can be easily identified.

In addition, the time-series signal of the output variable of the reference model is input to the inverse system model of the controlled object, and the time-series signal of the input variable of the controlled object at this time is obtained as the output of the inverse system model, so the output of the reference model is The time-series signal of the input variable of the controlled object corresponding to the time-series signal of the variable can be easily obtained.

Furthermore, the time-series signal of the input variable of the reference model is used as the input data for learning, and the time-series signal of the input variable of the controlled object corresponding to the time-series signal of the output variable of the reference model is used as the training data for the controller. Since the neural network for the model is trained, even if the controlled object has nonlinear characteristics, the controller can be easily adjusted so that the characteristics of the control system match the characteristics of the reference model.

〔Example〕

FIG. 1 shows a block diagram of an embodiment of the present invention.

This embodiment includes a controller 4 that controls a controlled object 1, an inverse system model that identifies an inverse system model of the controlled object 1, and an inverse system model that identifies an inverse system model of the controlled object 1.
a model identification system 5; a controller adjustment system 6 for adjusting the controller 4 using the identified inverse system;
It consists of a reference model 3 with desirable response characteristics.

C' = F'(8')...
(11) Here, C': Time-series signal of input variables of controlled object 1 Z': Time-series signal of output variables of controlled object 1 F': Inverse system model function Time-series signal of input variables of controlled object 1 C' is expressed by the following formula.

C' = [x(t)x(t-1)-x(t-L')]
”...(12) Here, x (t-flood): (t-Q) manipulated variable L' of controlled object 1 at the time of sampling Quadratic number T: symbol representing transposition Also, the output variable of controlled object 1 The time series signal 2' is given by the following equation.

Z' = [y(t)y(t-1)...y(t-L')
]”...(13) Here, y(t-Q): (t-Q) The controlled variable inverse system function F'(Z') at the sampling time is a multilayer (m' layer) shown in FIG. The neural network consists of a neural network of
−(14) ua(k)=Σw l J (k 1
, k )・V J (k 1 )...(15
) Here, u, +(k): sum of inputs to unit j of the th layer vJ(k): output of the th unit of the th layer wIJ(k-1, k): (k-1) Weighting coefficient f for the connection from the j-th unit of the layer to the J-th unit of the layer: a function giving the input-output relationship of each unit The first layer of the neural network is the input layer,
The output of the first layer units becomes the input signal to the neural network. In the embodiment of the present invention, the input signal to the neural network for inverse system model identification is the time-series signal Z' of the output variable of the controlled object 2, and its correspondence can be expressed as the following equation and the final layer of the neural network. The (m'th layer in the embodiment of the present invention) is the output layer, and the output of the units in this layer becomes the output signal of the neural network. In the embodiment of the present invention, the output signal of the neural network is the estimated value C' of the time-series signal of the input variable of the controlled object, and the correspondence thereof is shown in the following equation.

here,? (t-4): Estimated value of x(t-Q) (11)
The inverse system model function F'(Z') shown in Eq.
As the input/output relationship of the unit shown in equations (14) and (15) changes, it changes accordingly. That is, the number of layers of the neural network, the number of units in each layer,
When the weighting coefficient wi, i (k 1°k) of each unit and the function f giving the input-output relationship of each unit change, the inverse system model function Fl (Zl) changes. Therefore,
An inverse system model function F that fits the purpose is created by adjusting the number of layers, the number of units in each layer, the weighting coefficient w+J(k1.k) of each unit, and the function f that gives the input-output relationship of each unit 1 to 1. '(Z') can be constructed.

The inverse system model identification system 4 is constructed by inverse system model function F'(Z')& learning, and identifies an inverse system model to be controlled. Next, this learning algorithm will be explained.

First, when an input/output pair (Z'C') is given as learning data, the square of the error shown in the following equation is defined as the loss ratio R.

R=-Σ(va(m')(w,z/) CJ
' ) 2j ... (17) Here, W: The sum of all the weighting coefficients of the connections in the neural network vt (m' ) (W, Z' ) 8 Input Z' and the weighting coefficient W
The correction amount ΔW of the output W of the j-th unit of the m'-th layer (output layer), which is obtained comprehensively, is determined from the slope of the loss function R with respect to W, and is expressed by the following equation.

a wlj (k −1,, k) ... (18) Here, Δw+J (k 1.k): Weight of connection from the i-th unit of the (k-1)th layer to the j-th unit of the (k-1)th layer Modification amount of coefficient w = a (k 1 , k ) 8 = positive constant Right side (7) of equation (18) a R/ a w+a(k
1, k) It can be transformed as shown in the 11th degree equation.

aRaRauJ(k) aw+J(k-1,k) auJ(k) aw*J(
k1. k)...(19) When formula (15) is substituted into formula (19) and rearranged, the following formula is derived.

...(20) When Lc#m', a R/a on the right side of equation (20)
v J (k) is determined by the following equation.

(21) By substituting equation (14) and (t5) into equation (21) and rearranging, the following equation is obtained.

(22) Here, f': derivative aur(k) of the function f giving the input/output relationship of each unit. It is expressed by the following equation.

ΔwtJ(kLk)=E di(k)'vt
(k-1)=-εvt(k-1)・dJ(k) ...(23) dJ(k)=(Σda(k+1)-WJt(k, +1
))・f' (u, (k)) = (ΣwJt(k,+1)・dt(k+1)・f'
(uJ(k)))...(24) Also, when k=m', a R/ a ua(m'
) is obtained from equation (17) using the following equation.

=(vJ(m')-c-')f'(ua(m')
))...(25) Using equations (23), (24), and (25), the weighting coefficient w l J (k 1 s k ) of the connection can be modified from k=m' to =2. It is calculated recursively.

That is, using as input the error between the ideal output c, / and the actual output v, (m') (w+Z') in the output layer,
from the output layer to the input layer, in the opposite direction of signal propagation w
It propagates while taking the sum weighted by Jm (+1 to k).

This is the error backpropagation learning algorithm.

It is assumed that the function f giving the input/output relationship of each unit is common to all units and is expressed by the following equation.

From equation (26), the following equation is obtained.

f'(u)=f(u)(1-f(u))
=427) From equations (14) and (27), the following equation is derived.

f' (+, z(k)) = vJ(k) (1vJ(k))
-(28) Note that in order to converge learning smoothly and quickly, equation (23) can be modified as shown in the following equation.

In the input/output set of learning data (z', c'), the input Z' is called the learning input data, and the output C' is called the learning teacher data. Next, the learning data in the embodiment of the first invention will be explained.

To identify the inverse system model, the operation data of the controlled object 1 is used as learning data. In this case, a time-series signal of the output variable (controlled amount) of the controlled object 1 is used as learning input data, and a time-series signal of the input variable (manipulated amount) of the controlled object 1 is used as the learning teacher data. As the input/output set (z', c') of these learning data, operating data that changes from moment to moment may be used. It is also possible to use operational data that has been recorded for a certain period of time. When the characteristics of the controlled object change rapidly, it is better to use operating data that changes from moment to moment.

Using the above training data input/output set (z', c'), the neural network for inverse system model identification is trained by the error backpropagation learning algorithm explained earlier, and the inverse system model function F '(Z')
Build.

The controller adjustment system 6 adjusts the controller 4 using the inverse system model identified by the inverse system model identification system 5. The controller 4 is constructed using a neural network, and is adjusted so that the response characteristics of a control system that combines the controller 4 and the controlled object 1 match the characteristics of a reference model having desirable response characteristics. next,
This will be explained.

The controller 4 is expressed by the following equation.

C'=F"(Z')...(29)
Here, C#: Current value t of input variable of controlled object 1 z': Time series signal of target value r of output variable of controlled object 1 F'': Controller model function Current value of input variable of controlled object 1 C″′ is expressed by the following formula.

C″= [x(t)]...(3
0) Here, x(t): Operation amount of the controlled object 1 at the current time t Also, the time series signal 2 of the target value P of the output variable of the controlled object 1
′ is given by the following equation.

Z'=[r(t)r(t, LL=r(t L
')]'...(31) Here, r(t -12): ('t -12) Target value at the sampling point ■, ': The order controller model function F'(Z') is the inverse system・Multilayer shown in Figure 2 used in the model (in this case m1 layer)
It consists of a neural network. The units that are the constituent elements of this neural network also use the units shown in FIG. 4 that were used in the inverse system model.

The input signal of the controller neural network is a time-series signal Z' of the target value r of the output variable of the controlled object 1, and its correspondence is shown in the following equation.

Further, the final layer of the neural network (the m'th layer in the embodiment of the present invention) is an output layer, and the output of the units in this layer becomes the output signal of the neural network. In an embodiment of the invention, a neural
The output signal of the network is the value C' of the input variable of the controlled object 1 at the current time t, and the correspondence thereof is shown in the following equation.

[vx(m)] = [x(t)] The controller adjustment system 6 constructs the controller ° model function F'(Z') by learning and provides the controller model to the controller 4.

To construct the controller model, the time-series signal of the input variable (target value of the controlled variable) of the reference model is used as the learning input data Z', and the output variable (control value) of the reference model corresponding to the time-series signal of this input variable is A time-series signal of the input variable (manipulated amount) of the controlled object 1 estimated thereby is inputted into the inverse system model and used as learning teacher data C'. Using these training data input/output pairs (Z', C'), the inverse system
The controller neural network is trained using the error backpropagation learning algorithm used in model identification, and controller model functions F' and (Z') are constructed.

〔Effect of the invention〕

According to the present invention, the time-series signal of the output variable of the controlled object is used as input data for learning, and the time-series data of the input variable of the controlled object is used as the teaching data for learning, and the neural Since the network is trained, it has the effect of easily identifying an inverse system model of a controlled object with nonlinear characteristics.

In addition, the time-series signal of the output variable of the reference model is input to the inverse system model of the controlled object, and the time-series signal of the input variable of the controlled object at this time is obtained as the output of the inverse system model, so the output of the reference model is This has the advantage that the time-series signal of the input variable to be controlled that corresponds to the time-series signal of the variable can be easily obtained. Furthermore, the time-series signal of the input variable of the reference model is used as the input data for learning, and the time-series signal of the input variable of the controlled object corresponding to the time-series signal of the output variable of the reference model is used as the training data for the controller. Since the neural network for the model is trained, even if the controlled object has nonlinear characteristics, the controller can be easily adjusted so that the characteristics of the control system match the characteristics of the reference model.

[Brief explanation of drawings]

FIG. 1 is a block diagram of one embodiment of the present invention, FIG.
The figure is an explanatory diagram of FIG. 1, and FIG. 4 is a block diagram of conventional model-based adaptive control. 1... Controlled object, 3... Normative model, 4... Control

Claims (1)

[Claims] 1. In a model-based adaptive control method that adjusts a controller to match the characteristics of a control system to the characteristics of a reference model,
A model-based adaptive control method characterized by configuring an inverse system model of a controlled object and a controller using a neural network. 2. The model-based adaptive control method according to claim 1, wherein the controller performs feedforward control. 3. The model-based adaptive control method according to claim 1, wherein the controller performs feedback control. 4. The model-based adaptive control method according to claim 1, wherein the controller performs feedforward control and feedback control.