CN110794676A - CSTR process nonlinear control method based on Hammerstein-Wiener model - Google Patents

CSTR process nonlinear control method based on Hammerstein-Wiener model Download PDF

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CN110794676A
CN110794676A CN201911065612.8A CN201911065612A CN110794676A CN 110794676 A CN110794676 A CN 110794676A CN 201911065612 A CN201911065612 A CN 201911065612A CN 110794676 A CN110794676 A CN 110794676A
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李峰
姚克明
薛波
陶为戈
陈连玉
崔渊
沈明霞
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Jiangsu University of Technology
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Abstract

The invention provides a CSTR process nonlinear control method based on a Hammerstein-Wiener model, which comprises the following steps: s1, constructing a CSTR nonlinear dynamics model by utilizing a Hammerstein-Wiener model, wherein the Hammerstein-Wiener model comprises an input static nonlinear module, a dynamic linear module and an output static nonlinear module which are connected in series; s2, estimating parameters of each series module and noise model parameters in the Hammerstein-Wiener model by using a sampling signal source; and S3, controlling the CSTR by using a linear controller by using the reversible principle of an input static nonlinear module and an output static nonlinear module in the Hammerstein-Wiener model. The invention can convert the nonlinear system control problem of the CSTR process into the linear system control problem, thereby simplifying the design of the controller, and the constructed model has simple calculation, high precision and more stable control process.

Description

CSTR process nonlinear control method based on Hammerstein-Wiener model
Technical Field
The invention relates to the technical field of process control, in particular to a CSTR process nonlinear control method based on a Hammerstein-Wiener model.
Background
CSTRs (Continuous Stirred Tank reactors) are typical, highly non-linear chemical reaction systems in the process industry. Since the reactor in which the reaction takes place plays a very important role, and its operation directly affects the efficiency and quality standards of the production, in order to ensure the normal operation of the reaction, it is necessary to control some key process parameters in the reactor, such as concentration, pressure, temperature, etc., to ensure the stability of the system.
The most common control method in the CSTR process control method is PID (Proportional-Integral-Derivative) control, which is linear control based on a process object with an accurate mathematical model, and the CSTR system has strong nonlinearity, so it is difficult to achieve ideal control accuracy using this control. In recent years, with the development of modern control theory and intelligent control, many advanced and effective control modes, such as fuzzy control, robust control, neural network control, predictive control and the like, are developed in the research of CSTR. These control methods can obtain good control effect, but still have the defects of large calculation amount and complex control rule.
Disclosure of Invention
The invention aims to solve at least one of the technical problems in the technology to a certain extent, and therefore the invention aims to provide a CSTR process nonlinear control method based on a Hammerstein-Wiener model, which can convert the nonlinear system control problem of the CSTR process into the linear system control problem, thereby simplifying the design of a controller, and the constructed model is simple and easy to calculate, high in precision and relatively stable in control process.
In order to achieve the above object, an embodiment of the present invention provides a CSTR process nonlinear control method based on a Hammerstein-Wiener model, including the following steps: s1, constructing a CSTR nonlinear dynamics model by utilizing a Hammerstein-Wiener model, wherein the Hammerstein-Wiener model comprises an input static nonlinear module, a dynamic linear module and an output static nonlinear module which are connected in series; s2, estimating parameters and noise model parameters of each series module in the Hammerstein-Wiener model by using a sampling signal source; and S3, controlling the CSTR by adopting a linear controller by utilizing the reversible principle of an input static nonlinear module and an output static nonlinear module in the Hammerstein-Wiener model.
According to the CSTR process nonlinear control method based on the Hammerstein-Wiener model, the CSTR nonlinear dynamics model is built by utilizing the Hammerstein-Wiener model, parameters and noise model parameters of all series modules in the Hammerstein-Wiener model are estimated by utilizing a sampling signal source, reversible principles of an input static nonlinear module and an output static nonlinear module in the Hammerstein-Wiener model are utilized, and a linear controller is adopted to control the CSTR, so that the nonlinear system control problem of the CSTR process can be converted into a linear system control problem, the design of the controller is simplified, the built model is simple and easy to calculate, the accuracy is high, and the control process is stable.
In addition, the CSTR process nonlinear control method based on the Hammerstein-Wiener model provided by the embodiment of the invention may also have the following additional technical features:
according to an embodiment of the present invention, the step S1 includes: taking initial values of flow and reactant concentration in the CSTR process as initial values of characteristic parameters; fitting an input static nonlinear module and an output static nonlinear module of the Hammerstein-Wiener model by using a neural fuzzy model; fitting a dynamic linear module of the Hammerstein-Wiener model by using a finite impulse response model; and carrying out normalization processing on the initial value of the characteristic parameter, and substituting the characteristic parameter after the normalization processing into the Hammerstein-Wiener model.
According to one embodiment of the invention, the neuro-fuzzy model is a four-layer neuro-fuzzy model consisting of a fuzzy system and a radial basis function neural network.
According to one embodiment of the invention, the cross-correlation function of the intermediate variable is replaced by the product of the autocorrelation function of the sampling signal source and a constant value, and the parameters of each series module in the Hammerstein-Wiener model and the noise model parameters are estimated.
According to an embodiment of the present invention, the sampling signal source includes a separable signal and a random signal, and the step S2 includes: estimating parameters of the output static nonlinear module by using a clustering algorithm and a least square method based on input and output data of two groups of separable signals with different amplitudes; estimating the order of the finite impulse response model according to the rank of a Hankel matrix based on input and output data of a group of separable signals, and further estimating the parameters of the dynamic linear module by using a correlation analysis method; and estimating parameters of the static nonlinear module and parameters of the noise model by using a clustering algorithm and a recursive augmented least square method based on the input and output data of the random signal.
According to one embodiment of the invention, a formula is used
Figure BDA0002259240110000031
And
Figure BDA0002259240110000032
and estimating the former parameters of the neural fuzzy model, and estimating the latter parameters of the neural fuzzy model by using a least square method, thereby obtaining the parameters of the output static nonlinear module.
According to one embodiment of the invention, a formula is used
Figure BDA0002259240110000033
Parameters of the dynamic linearity module are further estimated.
According to one embodiment of the invention, a formula is used
Figure BDA0002259240110000034
And
Figure BDA0002259240110000035
estimating antecedent parameters of the neuro-fuzzy model and using recursionAnd estimating a back-piece parameter and a noise model parameter of the neural fuzzy model by using an augmented least square method, thereby obtaining a parameter and a noise model parameter of the input static nonlinear module.
According to one embodiment of the invention, the separable signal is a binary signal, a sinusoidal signal or a gaussian signal.
According to one embodiment of the invention, the linear controller is a PI (Proportional Integral) controller.
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FIG. 1 is a flow chart of a CSTR process nonlinear control method based on a Hammerstein-Wiener model according to an embodiment of the present invention;
FIG. 2 is a flow chart of Hammerstein-Wiener model parameter estimation of a CSTR process nonlinear control method based on a Hammerstein-Wiener model according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of CSTR control by the Hammerstein-Wiener model obtained by the embodiment of the present invention;
FIG. 4 is a CSTR process reactant concentration control diagram of a CSTR process nonlinear control method based on a Hammerstein-Wiener model in accordance with one embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the CSTR process nonlinear control method based on the Hammerstein-Wiener model according to the embodiment of the present invention includes the following steps:
s1, constructing a CSTR nonlinear dynamics model by using a Hammerstein-Wiener model, wherein the Hammerstein-Wiener model comprises an input static nonlinear module, a dynamic linear module and an output static nonlinear module which are connected in series.
Specifically, initial values of flow and reactant concentration in the CSTR process can be used as initial values of characteristic parameters, a neural fuzzy model is used for fitting an input static nonlinear module and an output static nonlinear module of a Hammerstein-Wiener model, a finite impulse response model is used for fitting a dynamic linear module of the Hammerstein-Wiener model, then normalization processing is carried out on the initial values of the characteristic parameters, and the characteristic parameters after the normalization processing are substituted into the Hammerstein-Wiener model.
In one embodiment of the present invention, the dynamic behavior of the system during a given CSTR can be expressed as:
Figure BDA0002259240110000051
substituting the equation set of the dynamic characteristics into the equation set of the dynamic characteristics to obtain the concentration C of the reactant AAThe flow rate F and the concentration C of the reactant B can be obtained after the eliminationBThe relationship between them, therefore, only the flow rate F and the concentration C of the reactant B need to be considered in the modelingBThe relationship therebetween is sufficient. Initial value F of flow F0And concentration C of reactant BBInitial value of (C)B0The initial value of the characteristic parameter of the CSTR process is a known quantity, and it should be noted that the initial value of the characteristic parameter refers to a steady state value corresponding to a reaction in a steady state operating point thereof.
In one embodiment of the present invention, the input static nonlinear module and the output static nonlinear module have a static characteristic, that is, when a time-invariant signal is input, a nonlinear relationship exists between an output quantity and an input quantity; the dynamic linear module has a dynamic characteristic, that is, when the input is a time-varying signal, the output quantity and the input quantity have a linear relationship. When the input static nonlinear module and the output static nonlinear module are modeled, the same modeling mode can be selected according to the actual situation, and different modeling modes can also be selected. The common modeling methods mainly include: linear combinations of basis functions and data-based models; the modeling mode of the dynamic linear module mainly comprises an impulse response mode, a transfer function mode, a state space mode and the like.
Firstly, an input static nonlinear module and an output static nonlinear module of a Hammerstein-Wiener model can be fitted through a neural fuzzy model according to the dynamic characteristics of the CSTR process.
Specifically, the neuro-fuzzy model may be a four-layer neuro-fuzzy model consisting of a fuzzy system and a radial basis function neural network. Wherein, the first layer is an input layer, the layer of neurons is used for directly transmitting the input signal to the next layer, and the input of the layer is: f ═ F-F0)/F0(ii) a The second layer is a membership function layer which receives the signal from the input layer and calculates a membership function of the input variable, the membership function of each neuron being
Figure BDA0002259240110000053
Wherein L represents the number of fuzzy rules,
Figure BDA0002259240110000054
clbeing the centre of the membership function, σlIs the width of the membership function; the third layer is a fuzzy rule layer, each neuron node of the layer represents a fuzzy rule, namely the node number is equal to the fuzzy rule number L; the fourth layer is an output layer consisting of a neuron with an output of
Figure BDA0002259240110000061
Then, a dynamic linear model of the Hammerstein-Wiener model can be fitted through a finite impulse response model according to the dynamic characteristics of the CSTR process.
Then, the initial value of the characteristic parameter may be normalized, i.e., the flow rate F ═ F-F0)/F0Concentration CB＝(CB-CB0)/CB0Substituting the characteristic parameters after the normalization treatment into a Hammerstein-Wiener model to obtain a table of the Hammerstein-Wiener modelThe mode is as follows:
v(k)＝f(F(k))
x(k)＝B(q)v(k)
w(k)＝D(q)e(k)
z(k)＝x(k)+w(k)
CB(k)＝g(z(k))
wherein k represents a sampling time; cB(k) Is the model output, representing the concentration of reactant B; f (k) is a model input representing flow F; f (F) (k) is the expression of the input static nonlinear module, g (z (k)) is the expression of the output static nonlinear module, v (k), w (k), z (k) are intermediate variables of the model,
Figure BDA0002259240110000062
as an expression for a dynamic linear module, q-1A unit back-shift operator is represented.
And S2, estimating parameters of each series module in the Hammerstein-Wiener model and noise model parameters by using the sampling signal source.
In one embodiment of the present invention, the sampling signal source may include a separable signal and a random signal, wherein the separable signal may be a binary signal, a sinusoidal signal, or a gaussian signal. The separation of the parameter identification of the input static nonlinear module, the dynamic linear module and the output static nonlinear module of the Hammerstein-Wiener model can be realized by utilizing the correlation function relation of the nonlinear system under the action of a sampling signal source.
In particular, the cross-correlation function of the intermediate variables, i.e. R, is replaced by the product of the autocorrelation function of the sampled signal source and a constant value constantvF(τ)＝b0RF(τ) wherein, b0E (v) (k) f (k))/E (f (k)) is a constant, τ is a time constant, and the cross-correlation function R is constantvF(τ) ═ E (v (k) F (k- τ)), autocorrelation function RF(τ) ═ E (F (k) F (k- τ)), in this way, parameters of each series module in the Hammerstein-Wiener model and noise model parameters are estimated, separation of parameter estimation of the input static nonlinear module, dynamic linear module, output static nonlinear module and noise model can be achieved, thereby not only simplifying the process of parameter estimation, but also reducing the modelThe method can effectively simplify the identification process of the Hammerstein-Wiener model.
First, the parameters of the static nonlinear module can be estimated and output by using a clustering algorithm and a least square method based on the input and output data of two sets of separable signals with different amplitudes.
In particular, by clustering algorithms, using equations
Figure BDA0002259240110000071
And
Figure BDA0002259240110000072
estimating the precursor parameters of the neuro-fuzzy model, i.e. the centre of the Gaussian membership function
Figure BDA0002259240110000073
And width
Figure BDA0002259240110000074
Data F (1) was input as the first cluster, and its cluster center was set to c1F (1), for the kth data F (k), the similarity criterion is followed
Figure BDA0002259240110000075
(N represents the total number of input data, e represents an exponential function) calculating the similarity of the kth data and each cluster center, judging whether to add a new cluster, and according to the similarity
Figure BDA0002259240110000076
Adjusting the cluster center, and repeating the step until all input data are assigned to corresponding clusters, wherein lambda belongs to [0,1 ]]Represents an adjustable parameter, according to
Figure BDA0002259240110000077
Calculating the width of the membership function; estimation of the back-part parameters of the neuro-fuzzy model, i.e. the weights of the neuro-fuzzy, using least squares
Figure BDA0002259240110000078
The concrete expression is as follows:wherein the content of the first and second substances,
Figure BDA0002259240110000081
wherein P is a time constant (P ≧ n)b)。
Then, the order of the finite impulse response model can be estimated according to the rank of the Hankel matrix based on the input and output data of a set of separable signals, and the parameters of the dynamic linear module can be further estimated by using a correlation analysis method.
In particular, the order of the finite impulse response model, i.e. n, is estimated according to the rank of the Hankel matrixbItem, using correlation analysis, using formulaThe parameters of the dynamic linear model are further estimated, wherein,
Figure BDA0002259240110000084
Figure BDA0002259240110000085
then, parameters of the static nonlinear module and parameters of the noise model can be estimated by using a clustering algorithm and a recursive augmented least square method based on input and output data of the random signal.
Wherein, using a clustering algorithm, a formula is used
Figure BDA0002259240110000086
And
Figure BDA0002259240110000087
estimating a precursor parameter of the neuro-fuzzy model, i.e. the center of the Gaussian membership function
Figure BDA0002259240110000088
And width
Figure BDA0002259240110000089
And estimating parameters of a back part of the neural blur and parameters of a noise model by using a recursive augmented least square method, namely weight of the neural blurAnd dlAnd estimating parameters of a front part of the neural blur by using a clustering algorithm, wherein the parameters of the front part of the neural blur are similar to parameters of an estimation output static nonlinear module, estimating parameters of an input static nonlinear module and noise model parameters by using a recursive augmented least square method, replacing an unmeasurable noise item in an information vector by using an estimated value of the noise item, and further obtaining a weight value and noise model parameters of the neural blur by using the recursive augmented least square method.
In an embodiment of the present invention, as shown in fig. 2, the Hammerstein-Wiener model parameter estimation process is as follows:
s201, estimating and outputting the center of a neural fuzzy model in a static nonlinear module by using a clustering algorithm according to input and output data of two groups of separable signals with different amplitudes
Figure BDA0002259240110000091
And width
Figure BDA0002259240110000092
S202, estimating and outputting the weight of the static nonlinear module by using a least square method
Figure BDA0002259240110000093
S203, estimating a parameter theta of the dynamic linear module by using a correlation analysis method based on one group of binary signals1。
S204, initializing: k is 1.
And S205, normalizing the input and the output of the random signal.
S206, transportingEstimating the center of the neural fuzzy model in the input static nonlinear module by using clustering algorithm
Figure BDA0002259240110000094
And width
S207, estimating the weight of the neural fuzzy model input into the static nonlinear module by using a recursive augmented least square method
Figure BDA0002259240110000096
And noise model parameter dl。
S208, updating the model parameter theta2。
S209, judging whether k is equal to the data length N or not, ending the operation until the value of k is equal to the data length N, otherwise executing S210, and circulating the processes S205-S209 through increasing the value of k to update the model parameter theta2And the N input data are all correspondingly calculated.
S210，k＝k+1。
And S3, controlling the CSTR by using a linear controller by using the reversible principle of an input static nonlinear module and an output static nonlinear module in the Hammerstein-Wiener model.
In one embodiment of the present invention, the parameters of the input static nonlinear module and the output static nonlinear module are obtained through steps S1, S2, and then the nonlinear control problem can be converted into a linear control problem by using the inverse function of the input static nonlinear module and the output static nonlinear module, so that the CSTR can be controlled by using a simple linear controller.
In one embodiment of the invention, the linear controller is a PI controller, wherein the PI controller can form a control deviation according to a given value and an actual output value, and linearly combine the proportion and the integral of the deviation to form a control quantity to control the controlled object, so that the deviation can be reduced through proportion and integral adjustment, and the stability of the control can be improved.
In the inventionIn one embodiment of the invention, as shown in fig. 3, in the CSTR process nonlinear control method based on the Hammerstein-Wiener model, the Hammerstein-Wiener model includes an input static nonlinear module, a dynamic linear module and an output static nonlinear module connected in series, where the input static nonlinear module function is f (-) and the dynamic linear module function is L (-) and the output static nonlinear module function is g (-). Firstly, the CSTR is controlled by a Hammerstein-Wiener model, and then the reversible principle of an input static nonlinear module and an output static nonlinear module is utilized, and the inverse function f of the input static nonlinear module is utilized-1Inverse function g of (-) and output static nonlinear module-1And the linear controller converts the nonlinear system control problem of the CSTR process into the linear system control problem, thereby simplifying the design of a control system and adopting a simple linear controller to control the CSTR process.
In one embodiment of the present invention, as shown in FIG. 4, the reactant concentration of a CSTR system is controlled using a PI controller with the controller parameter set to Kc＝0.2,τIThe target value for the system reactant concentration was set to-0.5 ═ 10. Fig. 4 (a) shows that the nonlinear PI controller designed by the present invention can achieve better tracking performance, and as the concentration of the reactant tends to be stable, and (b) the flow rate of the reactant in the table also tends to be stable, so that the CSTR system can be effectively and stably controlled completely by using the simple linear controller through the model of the above embodiment, and a better control effect can be achieved.
In one embodiment of the present invention, the initial value of the state characteristic parameter of the CSTR system is F034.3(L/h) and CB01.12(mol/L), wherein F0Representing steady state values of flow, CB0Represents the steady-state value of the concentration of the reactant B.
Firstly, fitting an input static nonlinear module and an output static nonlinear module of a Hammerstein-Wiener model by utilizing a neural fuzzy model, and fitting a dynamic linear module of the Hammerstein-Wiener model by utilizing a finite impulse response model.
Then, the data is normalized：F＝(F-34.3)/34.3，CB＝(CB-1.12)/1.12, wherein F is the model input, CBAnd outputting the model. The multiple signal sources obtained after normalization processing comprise: (1) a binary signal having an amplitude of 0 or 1; (2) a binary signal having an amplitude of 0 or 0.5; (3) in the interval [ -1,1 [)]Uniformly distributed random signals. And the separation of the parameter estimation of the input static nonlinear module, the output static nonlinear module and the dynamic linear module of the Hammerstein-Wiener model is realized by utilizing multiple signal sources.
Then, the parameters of the static nonlinear module can be estimated and output according to the input and output data of two groups of binary signals with different amplitudes by a clustering algorithm and a least square method, and the parameters are specifically expressed by estimating the former parameters of the neural fuzzy model by using the clustering algorithm, namely the center of a Gaussian membership function
Figure BDA0002259240110000111
And width
Figure BDA0002259240110000112
Setting parametersρoutput＝1，λoutputGenerating 3 fuzzy rules to obtain the parameter theta of output static nonlinear module [ -1.2140,0.1672,0.0190 ═ 0](ii) a And the order of the finite impulse response model, namely n, can be estimated by utilizing the rank of the Hankel matrix according to the input and output data of one of two groups of separable signalsbFurther using correlation analysis to estimate the parameters of the dynamic linear model, i.e. θ1＝[0.0085，-0.0007](ii) a The parameters of the neural fuzzy model can also be estimated according to the input and output data of the random signal, wherein the clustering algorithm is used for estimating the precursor parameters of the neural fuzzy, namely the center of the Gaussian membership function
Figure BDA0002259240110000114
And width
Figure BDA0002259240110000115
Estimating parameters of a back part and a noise model of the neural blur by adopting a recursive augmented least square method, namely the weight of the neural blur
Figure BDA0002259240110000116
And dl. Parameters in the clustering algorithm are set as follows:
Figure BDA0002259240110000117
ρinput＝1，λinputgenerating 11 fuzzy rules to obtain the parameter theta of input static nonlinear module2＝[-1.0494，-0.6587，-0.8873，-0.6258，-0.7486，0.2298，-1.4976，0.8040，3.5973，1.2503]And noise model parameter dl。
Finally, the estimated Hammerstein-Wiener model can be obtained through the steps, the nonlinear system control problem of the CSTR process can be converted into the linear system control problem by applying the reversible principle of the input static nonlinear module and the output static nonlinear module, and the design of the control system is simplified by converting the problem into simple linear control.
According to the CSTR process nonlinear control method based on the Hammerstein-Wiener model, the CSTR nonlinear dynamics model is built by utilizing the Hammerstein-Wiener model, parameters and noise model parameters of all series modules in the Hammerstein-Wiener model are estimated by utilizing a sampling signal source, reversible principles of an input static nonlinear module and an output static nonlinear module in the Hammerstein-Wiener model are utilized, and a linear controller is adopted to control the CSTR, so that the nonlinear system control problem of the CSTR process can be converted into a linear system control problem, the design of the controller is simplified, the built model is simple and easy to calculate, the accuracy is high, and the control process is stable.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (10)

1. A CSTR process nonlinear control method based on a Hammerstein-Wiener model is characterized by comprising the following steps:
s1, constructing a CSTR nonlinear dynamics model by utilizing a Hammerstein-Wiener model, wherein the Hammerstein-Wiener model comprises an input static nonlinear module, a dynamic linear module and an output static nonlinear module which are connected in series;
s2, estimating parameters and noise model parameters of each series module in the Hammerstein-Wiener model by using a sampling signal source;
and S3, controlling the CSTR by adopting a linear controller by utilizing the reversible principle of an input static nonlinear module and an output static nonlinear module in the Hammerstein-Wiener model.
2. The CSTR process nonlinear control method based on Hammerstein-Wiener model according to claim 1, wherein the step S1 comprises:
taking initial values of flow and reactant concentration in the CSTR process as initial values of characteristic parameters;
fitting an input static nonlinear module and an output static nonlinear module of the Hammerstein-Wiener model by using a neural fuzzy model;
fitting a dynamic linear module of the Hammerstein-Wiener model by using a finite impulse response model;
and carrying out normalization processing on the initial value of the characteristic parameter, and substituting the characteristic parameter after the normalization processing into the Hammerstein-Wiener model.
3. The CSTR process nonlinear control method based on the Hammerstein-Wiener model of claim 2, wherein the neuro-fuzzy model is a four-layer neuro-fuzzy model consisting of a fuzzy system and a radial basis function neural network.
4. The CSTR process nonlinear control method based on Hammerstein-Wiener model of claim 1, wherein the cross-correlation function of the intermediate variable is replaced by the product of the autocorrelation function of the sampled signal source and a constant value constant, and the parameters of each series module in the Hammerstein-Wiener model and the noise model parameters are estimated.
5. The CSTR process nonlinear control method based on Hammerstein-Wiener model of claim 4, wherein the sampling signal source comprises separable signal and random signal, and the step S2 comprises:
estimating parameters of the output static nonlinear module by using a clustering algorithm and a least square method based on input and output data of two groups of separable signals with different amplitudes;
estimating the order of the finite impulse response model according to the rank of a Hankel matrix based on input and output data of a group of separable signals, and further estimating the parameters of the dynamic linear module by using a correlation analysis method;
and estimating parameters of the static nonlinear module and parameters of the noise model by using a clustering algorithm and a recursive augmented least square method based on the input and output data of the random signal.
6. The Hammerstein-Wiener model-based CS of claim 5Method for nonlinear control of TR process, characterized in that formula is usedAndand estimating the former parameters of the neural fuzzy model, and estimating the latter parameters of the neural fuzzy model by using a least square method, thereby obtaining the parameters of the output static nonlinear module.
7. The CSTR process nonlinear control method based on the Hammerstein-Wiener model of claim 5, wherein a formula is used
Figure FDA0002259240100000023
Parameters of the dynamic linearity module are further estimated.
8. The CSTR process nonlinear control method based on the Hammerstein-Wiener model of claim 5, wherein a formula is used
Figure FDA0002259240100000024
And
Figure FDA0002259240100000025
estimating the former parameters of the neural fuzzy model, and estimating the latter parameters and the noise model parameters of the neural fuzzy model by using a recursive augmented least square method, thereby obtaining the parameters of the input static nonlinear module and the noise model parameters.
9. The CSTR process nonlinear control method based on the Hammerstein-Wiener model of claim 5, wherein the separable signal is a binary signal, a sinusoidal signal or a Gaussian signal.
10. The CSTR process nonlinear control method based on the Hammerstein-Wiener model of claim 1, wherein the linear controller is a PI controller.
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