CN113050710B - Modeling of Hammerstein nonlinear dynamic system and continuous stirred reactor concentration control - Google Patents
Modeling of Hammerstein nonlinear dynamic system and continuous stirred reactor concentration control Download PDFInfo
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Abstract
The invention provides modeling of a Hammerstein nonlinear dynamic system and concentration control of a continuous stirring reactor thereof, wherein the Hammerstein nonlinear dynamic system is utilized to establish a continuous stirring reactor model, a three-layer BP neural network is utilized to approach a static nonlinear module, and a transfer function model is utilized to establish a linear dynamic module model; secondly, estimating parameters of a static nonlinear module in the model through a random gradient descent optimizing algorithm containing momentum factors based on input and output data of random signals; finally, the special structure of the Hammerstein nonlinear system is utilized to convert the reactant concentration control problem of the continuous stirring reactor system into the linear system control problem, so that the design of a control system is simplified, and a better control effect is obtained.
Description
Technical Field
The invention belongs to the field of process industry, and relates to modeling of a Hammerstein nonlinear dynamic system and concentration control of a continuous stirring reactor thereof.
Background
Currently, in the field of modeling and control research of nonlinear dynamic systems, a novel nonlinear dynamic system with a block structure becomes a hot spot of current research. In the nonlinear dynamic system with a block structure, the Hammerstein nonlinear dynamic system is a typical nonlinear system with a specific structure, and combines a static nonlinear module and a linear dynamic module, so that the system can better describe industrial equipment and processes, such as a fermentation bioreactor system, a continuous stirring reaction kettle, a neutralization process, a distillation tower and other nonlinear processes.
Modeling research of a Hammerstein nonlinear dynamic system is mainly divided into modeling of a static nonlinear module and modeling of a linear dynamic module, and focuses on research on a modeling method of the nonlinear module with high precision and ductility, such as: basic functions, polynomials, spline functions, piecewise linear functions, support vector machines, neural networks, fuzzy systems, and the like. These methods can be classified into two types: (1) Given that nonlinearity is a linear combination of some known nonlinear bases, such as polynomials, spline functions, piecewise linear functions, and support vector machines, this approach requires a large number of parameters and very high order when studying a multivariate system; (2) The method can better approximate the nonlinear system based on the nonlinear model of the data, such as a neural network and a fuzzy system, and is suitable for the condition that the nonlinear model is difficult to parameterize.
After the model of each series module of the Hammerstein system is established, a series of parameter estimation methods are used for estimating unknown parameters in the model. After a specific model is obtained, the Hammerstein nonlinear dynamic system control problem is converted into a linear system control problem by utilizing the reversible principle of a static nonlinear module, and the Hammerstein nonlinear dynamic system control method has important theoretical and practical significance for the design of a nonlinear control system in the process industry. At present, a plurality of important achievements are obtained in the modeling of a nonlinear system and the research of a control method thereof, and various characteristic theoretical methods are formed, but the following problems still exist:
1. the complex industrial process has the characteristics of strong nonlinearity, uncertainty and the like, so that the problem of difficult modeling is caused, and how to establish a mathematical model of a Hammerstein nonlinear system meeting the process characteristics is the basis for solving the optimization problem and implementing effective control;
in the aspect of parameter estimation of a Hammerstein nonlinear system, the existing parameter estimation method often contains product terms of system parameters, and separation of the parameters is realized by adopting a decomposition technology, so that the complexity of calculation and the difficulty of parameter estimation are increased. How to utilize an effective parameter estimation method to reduce the calculation complexity and improve the accuracy and the robustness of system parameter estimation;
3. in the aspect of control of a nonlinear system, the existing composite control strategy can obtain a good control effect, but the defects of large calculated amount and complex control rule still exist. How to apply a more effective control method to reduce the calculated amount and the complexity of the control law and realize the efficient control of the nonlinear system.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides modeling of a Hammerstein nonlinear dynamic system and concentration control of a continuous stirring reactor thereof.
The Hammerstein nonlinear system is formed by connecting a static nonlinear module and a linear dynamic module in series, the static nonlinear module of the Hammerstein nonlinear system is approximated by using a three-layer BP neural network, a linear dynamic module model is established by using a transfer function model, on the basis, parameters of the static nonlinear module and the linear dynamic module are estimated by using binary-random composite signals, and a control system is further designed by using the obtained model and is applied to reactant concentration control of a continuous stirring reactor system. In the method, firstly, according to input and output data of binary signals, a least square method is adopted to estimate parameters of a dynamic linear module in a model; secondly, estimating parameters of a static nonlinear module in the model through a random gradient descent optimizing algorithm containing momentum factors based on input and output data of random signals; finally, the special structure of the Hammerstein nonlinear system is utilized to convert the reactant concentration control problem of the continuous stirring reactor system into the linear system control problem, so that the design of a control system is simplified, and a better control effect is obtained.
The technical terms appearing in the present invention will be described below first:
hammerstein nonlinear dynamic system: the nonlinear system is a typical nonlinear system with a specific structure, is formed by connecting static nonlinear modules and linear dynamic modules in series, and can effectively describe a large nonlinear industrial process.
Static nonlinear module: the finger module has static characteristics, namely, when the input signal is a signal which does not change with time, the nonlinear relation between the output quantity and the input quantity is provided.
Linear dynamic module: the finger module has dynamic characteristics, namely, when the input is a signal changing along with time, the output quantity and the input quantity have linear relation.
Binary-random complex signal: is formed by combining a binary signal and a random signal.
Random gradient descent optimization algorithm with momentum factor: based on the input and output data of random signals, the weights from the input layer to the hidden layer and the weights from the hidden layer to the output layer of the neural network are learned by utilizing an error back propagation algorithm, and momentum factors are added into the learning algorithm in order to prevent oscillation from occurring in the learning process and accelerate convergence.
Continuous stirred reactor system: is an anaerobic treatment technology for making fermentation raw material and microbe be in complete mixing state, and the reaction process includes physical and chemical change of material, and the parameters for characterizing its characteristics include temperature, concentration and flow rate, etc.. In the system, F represents the flow rate, which is the input to the system, C B The concentration of reactant B is indicated and is the output of the system. The purpose of this reaction is to control the concentration C by the flow rate F B 。
The invention adopts the following technical scheme:
step 1: control equations for a continuous stirred reactor system are determined, as are characteristic parameters related to reactant concentrations.
A continuous stirred reactor system is a typical nonlinear dynamic system consisting of nonlinear differential equations and linear differential equations, whose characteristics can be represented by the following mathematical expressions:
wherein C is A Represents the concentration of reactant A in the reactor, C B Represents the concentration of reactant B in the reactor, F represents the flow rate, k 1 、k 2 And k 3 As a kinetic parameter, C Af Representing the feed concentration of reactant a, V is the volume of the reactor. Reactant a to reactant B are a dynamic reaction.
In the above equation, the concentration C of reactant A is calculated by simplification A Is eliminated to obtain the concentration C of the flow rate F and the reactant B B Relationship between them. Therefore, only the flow rate F and the concentration C need to be considered in modeling the system B The relation between them is just enough.
Step 2: and (3) establishing a continuous stirring reactor system model by utilizing a Hammerstein nonlinear dynamic system according to the control equation and the characteristic parameters in the step (1).
In order to effectively control the continuous stirring reactor system, a Hammerstein nonlinear dynamic system is utilized to establish a continuous stirring reactor model, namely, a static nonlinear module of the Hammerstein system is utilized to fit a nonlinear differential equation of the continuous stirring reactor system, and a linear dynamic module of the Hammerstein system is utilized to approach a linear differential equation of the continuous stirring reactor system. In the Hammerstein nonlinear dynamic system, the invention approximates a static nonlinear module of the Hammerstein nonlinear system by using a three-layer BP neural network, and approximates a linear dynamic module model by using a transfer function model. Thus, the mathematical expression for a Hammerstein nonlinear dynamic system is expressed as:
v(k)＝f(F(k))
wherein k represents the sampling time; c (C) B (k) For system output, i.e., concentration, F (k) is system input, i.e., flow rate; v (k) =f (F (k)) is an expression of a static nonlinear block,
is an expression of a linear dynamic module, wherein,
z -1 the unit shift-back operator is represented,
and->
Representing parameters of the linear dynamic module.
Modeling of linear dynamic and static nonlinear modules, respectively, is described below:
a) Modeling of linear dynamic modules
The modeling method of the linear dynamic module mainly comprises the following steps: impulse response, transfer function, state space and other methods, which can effectively describe the dynamic characteristics of the system and the mutual influence relationship among variables, are widely used.
B) Modeling of static nonlinear modules
Modeling of the Hammerstein system focuses on researching a modeling method of a static nonlinear module with high precision and ductility, and the common modeling method mainly comprises the following steps:
(1) Linear combinations of basis functions such as basis functions, polynomials, spline functions, support vector machines, etc. Such methods are linear combinations of some known nonlinear bases, requiring a large number of parameters and very high orders in modeling complex systems.
(2) Based on data driven models such as neural networks, neural fuzzy systems, etc. The method can better approximate to a nonlinear system, and is suitable for the situation that a nonlinear model is difficult to parameterize. It should be noted that, in the patent application of CN201910450381.6, a neural fuzzy system is used to build a static nonlinear module model, when solving the model parameters, the calculation amount is relatively complex, and the BP neural network can easily solve the model parameters by using a reverse error propagation method. Therefore, in the invention, a BP neural network is adopted to build a static nonlinear module model.
Step 3: when the input F (k) of the continuous stirring reactor system is a binary signal, the characteristic that the binary signal does not excite the nonlinear system is utilized, namely, after the binary input signal passes through the nonlinear system, the output signal v (k) and the input keep the binary signals with the same frequency and different amplitudes, so that the separation of the parameter identification of each serial module in the Hammerstein system is realized under the action of the binary signal, the problem that the information of the intermediate variable of the system is not measurable is solved, and the identification process is simplified; compared with the correlation function relation of the separable signal in the patent application of CN201910450381.6 under the nonlinear system, the characteristic that the binary signal does not excite the nonlinear system has the advantages of simple module separation, less calculation amount of model parameters and easy identification;
step 4: at the step ofBased on steps 1 and 2, the binary input F (k) and the corresponding output C of the continuous stirred reactor system B (k) Determining the order of a transfer function model, i.e., n, using Lipschitz quotient criteria a And n b And then adopting a standard least squares method to identify the parameters of linear dynamic module in the Hammerstein system, namely a i (i＝1,2,…,n a ) And b j (j＝1,2,…,n b )；
Step 5: continuously stirred reactor system based on input F (k) and corresponding output C of continuously stirred reactor system under random signal B (k) The parameters of a static nonlinear module in a Hammerstein system, namely the weights from an input layer to an implicit layer and the weights from the implicit layer to an output layer of a BP neural network are solved by adopting a random gradient descent optimizing algorithm containing a momentum factor, and the momentum factor can effectively change the convergence of the parameters, and has the advantages of overlarge value, slower convergence speed, overlarge value and high convergence speed, but is difficult to converge to a true value, so that the momentum factor needs to select a proper parameter;
step 6: the parameter estimation of each series module of the Hammerstein nonlinear dynamic system can be obtained by utilizing the steps, namely, a continuous stirring reactor system is established, and on the basis, the control problem of the Hammerstein nonlinear dynamic system is converted into the control problem of a linear system by utilizing the reversible principle of a static nonlinear module in the Hammerstein system, namely, the control problem of the reactant concentration of the continuous stirring reactor system is converted into the control problem of the linear system, and then, the concentration is controlled by adopting a linear controller, so that the problems of large calculated amount, incapability of guaranteeing convergence and stability and the like of the traditional nonlinear control method are avoided.
Applying the Hammerstein nonlinear dynamic system control method to a continuous stirred reactor system, wherein the input F (k) of the continuous stirred reactor system is represented by the input u (k) and represents the flow rate F; output C of continuous stirred reactor system B (k) Expressed as output y (k), represents the concentration of reactant B; initial value F of flow velocity F 0 Reactant B concentration C B Initial value C of B0 To a known amount F 0 And C B0 For the initial value of the characteristic parameter of the continuous stirred reactor system, the characteristic parameter initial value refers to the steady state value corresponding to the reaction at a steady state working point, and the initial value of the characteristic parameter is normalized, namely the flow rate F= (F-F) 0 )/F 0 Concentration C B ＝(C B -C B0 )/C B0 The method comprises the steps of carrying out a first treatment on the surface of the The goal of a continuous stirred reactor system is to control the concentration C of the system by the flow rate F of the system B 。
Further, in step 2, the three layers of BP neural network specifically function as: the first layer is an input layer whose neurons act to pass input signals directly to the next layer, the input of which is f= (F-F) 0 )/F 0 Wherein F represents a flow rate, F 0 An initial value representing a flow rate; the second layer is an implicit layer which receives signals from the input layer and calculates a sigmoid function, the input of the implicit layer being
Wherein m represents the number of hidden layer neurons, < ->
For the weight between the j-th neuron of the hidden layer and the input, k represents the sampling time, u (k) represents the concentration input, O 2 (k)＝f(net 2 (k) Output of hidden layer, wherein +.>
Is a sigmoid function; the third layer is an output layer composed of a neuron, and the output is +.>
Wherein (1)>
V (k) is an intermediate variable that is not measurable by the Hammerstein system, which is the weight between the jth neuron of the hidden layer and the output.
In step 3 the binary input signal passes through a non-lineAfter sexual system, the output signal and the input keep the same frequency and different amplitude binary signals, i.e. v (k) =b 0 u (k), wherein b 0 V (k) is an unmeasurable intermediate variable of the Hammerstein system, and the characteristic can be used for realizing the separation of parameter estimation of a static nonlinear module and a linear dynamic module.
The parameters of the linear dynamic module are identified in step 4 by using the standard least squares method, namely a i (i＝1,2,…,n a ) And b j (j＝1,2,…,n b ) The method is specifically expressed as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
P L is the dimension of the binary signal.
The random gradient descent optimizing algorithm with momentum factor in step 5, the estimation of the system output is expressed as
Defining criterion function->
Wherein (1)>
Representing the error between the desired output and the neural network output, deriving the partial derivative to get +.>
And->
The weight learning algorithm from the hidden layer to the output layer is further obtained as +.>
And the weight learning algorithm from the input layer to the hidden layer is as follows
Wherein (1)>
Wherein η represents a learning rate; adding momentum factors into the algorithm to obtain +.>
Where α represents a momentum factor.
In step 6, the reversible principle of the static nonlinear module is used to convert the Hammerstein nonlinear dynamic system control problem into a linear system control problem, which is specifically expressed as follows: on the basis of obtaining the BP neural network model, the back f is inverted through the BP neural network model -1 The effect of (-) approximates the Hammerstein nonlinear system to a linear system L (-), thereby simplifying the complex nonlinear system control problem to a mature linear system control problem.
The Hammerstein nonlinear dynamic system control method is applied to a continuous stirring reactor system, a PI controller is adopted to control the concentration of reactants, and the parameter of the PI controller is set to K c ＝2.8，τ I =2, the target value of the system reactant concentration was set to 0.1.
Compared with the prior art, the invention has the following characteristics and beneficial effects:
(1) The three-layer BP neural network is utilized to approximate a static nonlinear module of the Hammerstein system, a transfer function model is utilized to fit a linear dynamic module of the Hammerstein system, and the obtained Hammerstein nonlinear dynamic system model has high-precision characteristics.
(2) The binary-random composite signal is utilized to realize the separation of the parameter estimation of the static nonlinear module and the linear dynamic module of the Hammerstein system, thereby simplifying the parameter estimation process and reducing the calculation complexity of the model.
(3) The special structure of the Hammerstein nonlinear system is used for converting the control problem of the nonlinear system into the control problem of the linear system, so that the design of the control system is simplified, and the problems that the traditional nonlinear control method is large in calculated amount, and the convergence and stability cannot be guaranteed are avoided.
Drawings
The invention is further described below with reference to the drawings and examples.
FIG. 1 is a schematic diagram of a Hammerstein nonlinear dynamic system modeling and control method thereof according to the present invention.
FIG. 2 is a flow chart of the Hammerstein nonlinear system parameter estimation of the present invention.
FIG. 3 is a graph of reactant concentration control for a continuously stirred reactor system in accordance with the present invention, wherein (a) is a graph of concentration change from an original steady state operating point 0 to a new operating point 0.1, and (b) is a graph of flow rate change for the system.
Detailed Description
The present invention will now be described in detail with reference to the accompanying drawings. The figure is a simplified schematic diagram illustrating the basic structure of the invention only by way of illustration, and therefore it shows only the constitution related to the invention.
The present invention will now be described in detail with reference to the accompanying drawings. The figure is a simplified schematic diagram illustrating the basic structure of the invention only by way of illustration, and therefore it shows only the constitution related to the invention.
As shown in fig. 1, modeling of a Hammerstein nonlinear dynamic system and continuous stirring reactor concentration control thereof comprise the following steps:
first, in a continuously stirred reactor system, F 0 =34.3 (L/h) and C B0 =1.12 (mol/L) is the steady state value corresponding to the reaction at a steady state operating point, wherein F 0 Representing steady state value of flow rate, C B0 Indicating the steady state value of the concentration of reactant B. The invention is thatUsing binary-random composite signal as input of system, firstly making data normalization treatment: f= (F-34.3)/34.3, c B ＝(C B -1.12)/1.12, wherein F is the system input, C B Is output by the system. The composite signal source obtained after normalization processing comprises: (1) 200 sets of binary signals of amplitude 0 or 1; (2) Group 400 [ -1,1]A uniformly distributed random signal. And then fitting a static nonlinear module of the Hammerstein system by using a three-layer BP neural network, and fitting a linear dynamic module of the Hammerstein system by using a transfer function.
Secondly, the binary-random composite signal is utilized to realize the separation of the parameter estimation of the static nonlinear module and the linear dynamic module of the Hammerstein system. Based on binary input F (k) and corresponding output C of a continuously stirred reactor system B (k) Determining the order of a transfer function model, i.e., n, using Lipschitz quotient criteria a Has a value of 1, n b Has a value of 1; on the basis, the least square method is further adopted to estimate the parameters of the linear dynamic module as
Third, the continuously stirred reactor system is based on the input F (k) and the corresponding output C of the continuously stirred reactor system under the influence of a random signal B (k) And estimating the weight of the BP neural network by using a random gradient descent optimizing algorithm containing momentum factors, namely the weight from an input layer to an hidden layer and the weight from the hidden layer to an output layer. Setting the neuron number of the hidden layer as 12, and calculating to obtain the weight value from the input layer to the hidden layer as
The weight from the hidden layer to the output layer is
Fourth, hammerste can be obtained based on the above stepsParameter estimation of in nonlinear dynamic system, further adopting inverse f of BP neural network model -1 (. About.) the control problem of the nonlinear continuous stirred reactor system is converted into the control problem of a linear system, and the design of the control system is simplified due to the special structure of the model, so that a better control effect can be obtained by adopting a simple linear controller.
FIG. 2 is a flow chart of Hammerstein nonlinear dynamic system parameter estimation. The flow is as follows:
(1) Determining the order of a transfer function model, i.e., n, by utilizing Lipschitz quotient criterion based on input/output data of binary signals a And n b Then adopts standard least squares method to identify the parameter of linear dynamic module, namely a i (i＝1,2,…,n a ) And b j (j＝1,2,…,n b )。
(2) Based on the input and output data of random signals, a random gradient descent optimizing algorithm containing momentum factors is adopted to estimate the weight value from an input layer to an hidden layer
Implicit layer to output layer weight +.>
(3) Updating weights
And->
And ending the operation until the variable k value is equal to the data length N.
FIG. 3 is a reactant concentration control diagram of a continuous stirred reactor system.
In the invention, a PI controller is adopted to control the reactant concentration of a continuous stirring reactor system, and the parameter of the controller is set to K c ＝2.8，τ I =2, the target value of the system reactant concentration was set to 0.1. FIG. 3 (a) shows that the nonlinear PI controller designed by the invention has high response speed and overshootThe amount is small, a better control effect can be obtained, and the flow rate of the reactant gradually tends to be stable and keeps unchanged after the concentration of the reactant approaches to the set value in fig. 3 (b).
While the foregoing is directed to the preferred embodiment of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. The technical scope of the present invention is not limited to the description, but must be determined according to the scope of claims.
Claims (6)
1. A modeling and continuous stirring reactor concentration control method of a Hammerstein nonlinear dynamic system is characterized in that: the method comprises the following steps:
step 1: determining a control equation for the continuous stirred reactor system and a characteristic parameter related to the concentration of the reactant;
step 2: according to the control equation and the characteristic parameters in the step 1, a system model of the continuous stirring reactor is established by utilizing a Hammerstein nonlinear dynamic system;
step 3: converting the flow velocity into a binary signal F (k), and inputting the binary signal F (k) into the continuous stirring reactor system model in the step 2, so as to realize the separation of the parameter identification of each serial module in the Hammerstein nonlinear dynamic system;
step 4: based on step 2 and step 3, the binary signal F (k) and the corresponding concentration output C are input according to a continuous stirred reactor system B (k) Determining the order of a transfer function model by utilizing Lipschitz quotient criterion, and identifying parameters of a linear dynamic module in the Hammerstein nonlinear dynamic system by adopting a standard least squares method;
the method adopts the standard least square method to identify the parameters of the linear dynamic module, namely a i (i＝1,2,…,n a ) And b j (j＝1,2,…,n b ) The method is specifically expressed as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
P L is the dimension of the binary signal;
step 5: solving parameters of a static nonlinear module in the Hammerstein nonlinear dynamic system by adopting a random gradient descent optimizing algorithm containing momentum factors;
the random gradient descent optimizing algorithm containing momentum factors, and the estimation of the system output is expressed as
Defining criterion function->
Wherein (1)>
Representing the error between the desired output and the neural network output, deriving the partial derivative to get +.>
And->
The weight learning algorithm from the hidden layer to the output layer is further obtained as +.>
And the weight learning algorithm from the input layer to the hidden layer is as follows
Wherein (1)>
Wherein η represents a learning rate; adding momentum factors into the algorithm to obtain +.>
step 6: according to the parameter estimation of each series module of the Hammerstein nonlinear dynamic system obtained in the step 4 and the step 5, a continuous stirring reactor system is established, and on the basis, the reactant concentration control problem of the continuous stirring reactor system is converted into a linear system control problem by utilizing the reversible principle of a static nonlinear module in the Hammerstein nonlinear dynamic system, and then the concentration is controlled by adopting a linear controller.
2. The modeling of a Hammerstein nonlinear dynamic system and a continuous stirring reactor concentration control method thereof according to claim 1, wherein: the control equation of the continuous stirring reactor system consists of a nonlinear differential equation and a linear differential equation, and the characteristics of the control equation are represented by the following mathematical expression:
nonlinear differential equation:
linear differential equation:
wherein C is A Represents the concentration of reactant A in the reactor, C B Represents the concentration of reactant B in the reactor, F represents the flow rate, k 1 、k 2 And k 3 As a kinetic parameter, C Af Representing the feed concentration of reactant a, V is the volume of the reactor; reactant a to reactant B are a dynamic reaction;
in the above equation, the concentration C of reactant A is calculated by simplification A Is eliminated to obtain the concentration C of the flow rate F and the reactant B B Relationship between them.
3. The modeling of a Hammerstein nonlinear dynamic system and a continuous stirring reactor concentration control method thereof according to claim 2, wherein: the Hammerstein nonlinear dynamic system in the step 2 comprises a static nonlinear module and a linear dynamic module, the static nonlinear module of the Hammerstein nonlinear dynamic system is used for fitting a nonlinear differential equation of the continuous stirring reactor system, and the linear dynamic module of the Hammerstein nonlinear dynamic system is used for approaching the linear differential equation of the continuous stirring reactor system.
4. A method for modeling a Hammerstein nonlinear dynamic system and controlling the concentration of a continuous stirred reactor according to claim 3, wherein: in the step 2, in the Hammerstein nonlinear dynamic system, a static nonlinear module of the Hammerstein nonlinear dynamic system is approximated by using a three-layer BP neural network, and a linear dynamic module of the Hammerstein nonlinear dynamic system is approximated by using a transfer function model, so that the Hammerstein nonlinear dynamic system is expressed as:
v(k)＝f(F(k))
wherein k represents the sampling time; c (C) B (k) For the system output, i.e., the concentration of reactant B at k, F (k) is the system input, i.e., the flow rate at k; v (k) is a model intermediate variable, F (k)) is an expression of a static nonlinear module,
is an expression of a linear dynamic module, wherein +.>
z -1 Representing a unit shift operator +_>
And->
Representing parameters of the linear dynamic module.
5. The modeling of a Hammerstein nonlinear dynamic system and a continuous stirring reactor concentration control method thereof according to claim 4, wherein: the three layers of BP neural networks have the following specific functions: the first layer is an input layer whose neurons act to pass input signals directly to the next layer, the input of which is f= (F-F) 0 )/F 0 Wherein F represents a flow rate, F 0 An initial value representing a flow rate; the second layer is an implicit layer which receives signals from the input layer and calculates a sigmoid function, the input of the implicit layer being
Wherein m represents hiddenNumber of layer-containing neurons, +.>
For the weight between the jth neuron of the hidden layer and the input, k represents the sampling time, u (k) represents the input, O 2 (k)＝f(net 2 (k) Output of hidden layer, wherein +.>
Is a sigmoid function; the third layer is an output layer composed of a neuron, and the output is +.>
Wherein (1)>
V (k) is an intermediate variable that is not measurable by the Hammerstein system, which is the weight between the jth neuron of the hidden layer and the output.
6. The modeling of a Hammerstein nonlinear dynamic system and a continuous stirring reactor concentration control method thereof according to claim 1, wherein: in step 6, the reversible principle of the static nonlinear module is used to convert the Hammerstein nonlinear dynamic system control problem into a linear system control problem, which is specifically expressed as follows: on the basis of obtaining the BP neural network model, the back f is inverted through the BP neural network model -1 The effect of (-) approximates the Hammerstein nonlinear system to a linear system L (-), thereby simplifying the complex nonlinear system control problem to a mature linear system control problem.
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