CN106371321A - PID control method for fuzzy network optimization of coking-furnace hearth pressure system - Google Patents

Abstract

The invention discloses a PID control method for fuzzy network optimization of a coking-furnace hearth pressure system. On the basis of step response data of a coking-furnace hearth pressure object, a model of the coking-furnace hearth pressure object is established, and basic features are extracted from the object; according to a model design controller, a fuzzy RBF network is used to set parameters of a corresponding PID controller; and PID control is implemented on the coking-furnace hearth pressure object. According to the invention, the performance of a traditional PID control method is improved, and application of fuzzy control and a neural network control method is prompted.

Description

Fuzzy network optimization PID control method for coking furnace pressure system

Technical Field

The invention belongs to the technical field of automation, and relates to a fuzzy RBF network optimization PID control method for a coking furnace pressure system.

Background

In an actual industrial process, the actual process object has many complex physical or chemical characteristics which are not known, and the system control process is interfered. With the increasing complexity of industrial processes, due to the problems of nonlinearity, hysteresis, coupling and the like of the controlled object, the traditional PID control can not meet the industrial requirements any more, and more advanced algorithms with better control effect still need to be researched. Coking furnace pressure system is the important device in the petrochemical production process, and wherein furnace pressure has very important influence to the cracking process, and too big furnace pressure can bring many potential safety hazards, and too low furnace pressure also can lead to the cracking efficiency step-down. Because the neural network has strong self-learning and association functions, and compared with the neural network, the fuzzy system has the advantages of easy understanding of reasoning process and good utilization of expert knowledge, the PID is optimized by combining the advantages of fuzzy control and the neural network, the transient response, the steady-state precision and the robustness of the system can be effectively improved, and the industrial utilization prospect is good.

Disclosure of Invention

The invention aims to provide a fuzzy RBF network optimization PID control method of a coking furnace hearth pressure system aiming at the application defects of the existing PID control method so as to obtain better actual control performance. The method combines fuzzy control and a neural network control method to obtain an optimized PID control method. The method inherits the excellent characteristics of fuzzy control and neural network, ensures simple form and meets the requirement of actual process.

Firstly, establishing a model of a hearth pressure object based on step response data of the hearth pressure object of the coking furnace, and extracting the characteristics of a basic object; then designing a controller according to the model, and setting corresponding PID controller parameters by using a fuzzy RBF network; and finally, PID control is carried out on the coke oven hearth pressure object.

The method comprises the following steps:

step 1, establishing a model of a controlled object through real-time step response data of a coking furnace hearth pressure object, wherein the specific method comprises the following steps:

1.1 the fuzzy cluster number c, the fuzzy weighting index m and the termination criterion >0 are first selected.

1.2 randomly generating a fuzzy partition matrix lambda, and enabling the fuzzy partition matrix lambda to meet the following condition:

${\mathrm{\&mu;}}_{ik}\&Element;\&lsqb;0,1\&rsqb;,\underset{i=1}{\overset{c}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}=1,0<\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}<N$

wherein, mu_ikAnd N is the membership degree of the kth data relative to the ith clustering center, and is the number of samples.

1.3 calculate the cluster center using the following formula:

$v_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m{z}_k}{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m}$

1.4 calculate the distance norm using the following formula:

$D_{ik}^2=\left|\right|z_k-v_i|{|}_{A_i}^2={(z_k-v_i)}^T{A}_i(z_k-v_i)$

wherein,

A_i＝(ρdet(F_i))^1/nF_i ^-1

ρ＝det(A_i)

$F_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m(z_k-v_i){(z_k-v_i)}^T}{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m}$

1.5 update the fuzzy partition matrix Λ using the following equation.

${\mathrm{\&mu;}}_{ik}=\frac{1}{\underset{j=1}{\overset{c}{\&Sigma;}}{(D_{ik}/D_{jk})}^{2/(m-1)}}$

1.6 when the condition is satisfied | | | Λ^l-Λ^l-1Stopping if the absolute value is less than or equal to the absolute value, otherwise, returning to the step 1.3.

1.7 calculate membership function variance using the following formula

${\mathrm{\&sigma;}}_{ij}^2=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}{(x_{jk}-v_{jk})}^2}{\underset{k=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}}$

1.8 calculate model back-part parameters using the following formula

θ_i＝[X^TW_iX]^-1X^TW_iy

Wherein the input variables, the output variables and the weighting matrix are

X＝[x₁,x₂,…,x_N],

y＝[y₁,y₂,…,y_N],

W_i＝diag(μ_i1,μ_i2,…,μ_iN)

1.9 obtaining the T-S model as

R_i:If x₁(k)is A_i1and x₂(k)is A_i2and…and x_n(k)is A_in

$Then{\hat{y}}_i\left(k\right)={\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)$

Wherein: r_iDenotes the ith fuzzy rule, x_jRepresenting an input variable, A_ijThe representation defines a membership function in the input theory domain.

Step 2, designing a PID controller of the process object, wherein the specific method comprises the following steps:

2.1, carrying out weighted average on the T-S fuzzy rule model, wherein the model output is as follows:

$y(k+1)=\frac{\underset{i=1}{\overset{n}{\&Sigma;}}{B}_i\left(x\right)\&lsqb;{\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)\&rsqb;}{\underset{i=1}{\overset{n}{\&Sigma;}}{B}_i\left(x\right)}$

wherein,n represents a fuzzy operator and represents a fuzzy operator,and representing a membership function of the fuzzy antecedent variable.

Note the bookShould satisfyAnd 0 is not less than omega_i(x)<1。

The above formula can be expressed as

$y(k+1)=\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&omega;}}_i\left(x\right)\&lsqb;{\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)\&rsqb;$

2.2 fuzzy RBF network tuning PID control, the network will be input byA layer, a fuzzy inference layer and an output layer, the network output is K_p,K_i,K_d。

2.3 the nodes of the input layer are directly connected to the components of the input quantity, which is passed to the next layer. The input and output to each node i of the layer is represented as:

f₁(i)＝X＝[x₁,x₂,…,x_n]

2.4 use of Gauss-type functions as membership functions, c_ijAnd b_ijThe mean and standard deviation of the membership functions of the ith input variable, the jth fuzzy set, respectively.

$f_2(i,j)=\exp \&lsqb;\frac{{\left(f_1\right(i)-c_{ij})}^2}{{\left(b_{ij}\right)}^2}\&rsqb;$

Wherein i is 1,2, …, n; j is 1,2, …, n.

2.5 the fuzzy inference layer completes the matching of the fuzzy rules through the connection with the fuzzy layer, and realizes the fuzzy operation among all nodes, namely obtains the corresponding activation strength through the combination of all fuzzy nodes. The output of each node j is the product of all the input signals of the node, namely:

$f_3\left(j\right)=\underset{j=1}{\overset{N}{\&Pi;}}{f}_2(i,j)$

in the formula,

2.6 output layer output f₄Is K_p,K_i,K_dAs a result of the setting, the layer is composed of three nodes, namely:

$f_4\left(i\right)=w\&CenterDot;f_3=\underset{j=1}{\overset{N}{\&Sigma;}}w(i,j)\&CenterDot;f_3\left(j\right)$

in the formula, w_ijAnd the connection weight matrix i of the output node and each node of the third layer is 1,2 and 3.

2.7 from step 2.3 to step 2.6, the control quantity can be found as:

△u(k)＝f₄·xc＝K_pxc(1)+K_ixc(2)+K_dxc(3)

wherein,

K_p＝f₄(1),K_i＝f₄(2),K_d＝f₄(3)

xc(1)＝e(k)

xc(2)＝e(k)-e(k-1)

xc(3)＝e(k)-2e(k-1)+e(k-2)

an incremental PID control algorithm is adopted:

u(k)＝u(k-1)+△u(k)

2.8 correcting the adjustable parameters by adopting a Delta learning rule, and defining an objective function as follows:

$E=\frac{1}{2}{\left(rin\right(k)-yout(k\left)\right)}^2$

wherein rin (k) and yout (k) represent the actual output and the ideal output of the network, respectively, and the control error of each iteration step k is rin (k) -yout (k). The learning algorithm of the network weight is as follows:

$\begin{array}{c}{\mathrm{\&Delta;w}}_j\left(k\right)=-\mathrm{\&eta;}\&CenterDot;\frac{\&part;E}{\&part;w_j}=\mathrm{\&eta;}\&CenterDot;\left(rin\right(k)-yout(k))\&CenterDot;\frac{\&part;yout}{\&part;\mathrm{\&Delta;}u}\frac{\&part;\mathrm{\&Delta;}u}{\&part;f_4}\frac{\&part;f_4}{\&part;w_j}\\ =\mathrm{\&eta;}\&CenterDot;\left(rin\right(k)-yout(k\left)\right)\&CenterDot;\frac{\&part;yout}{\&part;\mathrm{\&Delta;}u}xc\left(j\right)f_3\left(j\right)\end{array}$

in the formula, w_jFor the connection weight of the network output node and the nodes in the previous layer, j is 1,2, …, and N, η is the learning rateThen, the weight of the output layer is:

w_j(k)＝w_j(k-1)+△w_j(k)+α(w_j(k-1)-w_j(k-2))

in the formula, k is an iteration step of the network, and alpha is a learning momentum factor.

Designing a fuzzy control-based RBF network through the model in the step 2, obtaining PID control parameters through continuous learning optimization of the network, and adjusting the control performance on line.

The invention provides a fuzzy RBF network optimization PID control method of a coking furnace hearth pressure system, which effectively improves the performance of the traditional PID control method and simultaneously promotes the application of fuzzy control and neural network control methods.

Drawings

FIG. 1 is a fuzzy RBF network tuning PID control chart;

fig. 2 is a fuzzy RBF neural network structure.

Detailed Description

Taking the control of the hearth pressure process of the coking furnace as an example:

the hearth pressure of the coking furnace is an important parameter in the cracking process of the coking furnace, and the opening degree of the flue baffle is adopted as an adjusting means.

The method comprises the following steps:

step 1, establishing a model of a controlled object through real-time step response data of a coking furnace hearth pressure object, wherein the specific method comprises the following steps:

1.1 the fuzzy cluster number c, the fuzzy weighting index m and the termination criterion >0 are first selected.

1.2 randomly generating a fuzzy partition matrix lambda, and enabling the fuzzy partition matrix lambda to meet the following condition:

${\mathrm{\&mu;}}_{ik}\&Element;\&lsqb;0,1\&rsqb;,\underset{i=1}{\overset{c}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}=1,0<\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}<N$

wherein, mu_ikAnd N is the membership degree of the kth data relative to the ith clustering center, and is the number of samples.

1.3 calculate the cluster center using the following formula:

$v_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m{z}_k}{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m}$

1.4 calculate the distance norm using the following formula:

$D_{ik}^2=\left|\right|z_k-v_i|{|}_{A_i}^2={(z_k-v_i)}^T{A}_i(z_k-v_i)$

wherein,

A_i＝(ρdet(F_i))^1/nF_i ^-1

ρ＝det(A_i)

$F_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m(z_k-v_i){(z_k-v_i)}^T}{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m}$

1.5 update the fuzzy partition matrix Λ using the following equation.

${\mathrm{\&mu;}}_{ik}=\frac{1}{\underset{j=1}{\overset{c}{\&Sigma;}}{(D_{ik}/D_{jk})}^{2/(m-1)}}$

1.6 when the condition is satisfied | | | Λ^l-Λ^l-1Stopping if the absolute value is less than or equal to the absolute value, otherwise, repeating the step 1.3.

1.7 calculate membership function variance using the following formula

${\mathrm{\&sigma;}}_{ij}^2=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}{(x_{jk}-v_{jk})}^2}{\underset{k=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}}$

1.8 calculate model back-part parameters using the following formula

θ_i＝[X^TW_iX]^-1X^TW_iy

Wherein the input variables, the output variables and the weighting matrix are

X＝[x₁,x₂,…,x_N],

y＝[y₁,y₂,…,y_N],

W_i＝diag(μ_i1,μ_i2,…,μ_iN)

1.9 obtaining the T-S model as

R_i:If x₁(k)is A_i1and x₂(k)is A_i2and…and x_n(k)is A_in

$Then{\hat{y}}_i\left(k\right)={\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)$

Wherein: r_iDenotes the ith fuzzy rule, x_jRepresenting an input variable, A_ijThe representation defines a membership function in the input theory domain.

Step 2, designing a PID controller of the process object, wherein the specific method comprises the following steps:

2.1, carrying out weighted average on the T-S fuzzy rule model, wherein the model output is as follows:

$y(k+1)=\frac{\underset{i=1}{\overset{n}{\&Sigma;}}{B}_i\left(x\right)\&lsqb;{\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)\&rsqb;}{\underset{i=1}{\overset{n}{\&Sigma;}}{B}_i\left(x\right)}$

wherein,n represents a fuzzy operator and represents a fuzzy operator,and representing a membership function of the fuzzy antecedent variable.

Note the bookShould satisfyAnd 0 is not less than omega_i(x)<1。

The above formula can be expressed as

$y(k+1)=\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&omega;}}_i\left(x\right)\&lsqb;{\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)\&rsqb;$

2.2 fuzzy RBF network tuning PID control, the network will be input byA layer, a fuzzy inference layer and an output layer, the network output is K_p,K_i,K_dSee fig. 1 and 2.

2.3 the nodes of the input layer are directly connected to the components of the input quantity, which is passed to the next layer. The input and output to each node i of the layer is represented as:

f₁(i)＝X＝[x₁,x₂,…,x_n]

2.4 use of Gauss-type functions as membership functions, c_ijAnd b_ijThe mean and standard deviation of the membership functions of the ith input variable, the jth fuzzy set, respectively.

$f_2(i,j)=\exp \&lsqb;\frac{{\left(f_1\right(i)-c_{ij})}^2}{{\left(b_{ij}\right)}^2}\&rsqb;$

Wherein i is 1,2, …, n; j is 1,2, …, n.

2.5 the fuzzy inference layer completes the matching of the fuzzy rules through the connection with the fuzzy layer, and realizes the fuzzy operation among all nodes, namely obtains the corresponding activation strength through the combination of all fuzzy nodes. The output of each node j is the product of all the input signals of the node, namely:

$f_3\left(j\right)=\underset{j=1}{\overset{N}{\&Pi;}}{f}_2(i,j)$

in the formula,

2.6 output layer output f₄Is K_p,K_i,K_dAs a result of the setting, the layer is composed of three nodes, namely:

$f_4\left(i\right)=w\&CenterDot;f_3=\underset{j=1}{\overset{N}{\&Sigma;}}w(i,j)\&CenterDot;f_3\left(j\right)$

in the formula, w_ijAnd the connection weight matrix i of the output node and each node of the third layer is 1,2 and 3.

2.7 having steps 2.3 to 2.6, the control quantity can be found as:

△u(k)＝f₄·xc＝K_pxc(1)+K_ixc(2)+K_dxc(3)

wherein,

K_p＝f₄(1),K_i＝f₄(2),K_d＝f₄(3)

xc(1)＝e(k)

xc(2)＝e(k)-e(k-1)

xc(3)＝e(k)-2e(k-1)+e(k-2)

an incremental PID control algorithm is adopted:

u(k)＝u(k-1)+△u(k)

2.8 correcting the adjustable parameters by adopting a Delta learning rule, and defining an objective function as follows:

$E=\frac{1}{2}{(\mathrm{rin}\left(k\right)-\mathrm{yout}\left(k\right))}^2$

wherein rin (k) and yout (k) represent the actual output and the ideal output of the network, respectively, and the control error of each iteration step k is rin (k) -yout (k). The learning algorithm of the network weight is as follows:

$\begin{array}{c}{\mathrm{\&Delta;w}}_j\left(k\right)=-\mathrm{\&eta;}\&CenterDot;\frac{\&part;E}{\&part;w_j}=\mathrm{\&eta;}\&CenterDot;\left(rin\right(k)-yout(k\left)\right)\&CenterDot;\frac{\&part;yout}{\&part;\mathrm{\&Delta;}u}\frac{\&part;\mathrm{\&Delta;}u}{\&part;f_4}\frac{\&part;f_4}{\&part;w_j}\\ =\mathrm{\&eta;}\&CenterDot;\left(rin\right(k)-yout(k\left)\right)\&CenterDot;\frac{\&part;yout}{\&part;\mathrm{\&Delta;}u}xc\left(j\right)f_3\left(j\right)\end{array}$

in the formula, w_jFor the connection weight of the network output node and the nodes in the previous layer, j is 1,2, …, N, η is the learning rateAnd measuring the factor, wherein the weight of the output layer is as follows:

w_j(k)＝w_j(k-1)+△w_j(k)+α(w_j(k-1)-w_j(k-2))

in the formula, k is an iteration step of the network, and alpha is a learning momentum factor.

Designing a fuzzy control-based RBF network through the model in the step 2, obtaining PID control parameters through continuous learning optimization of the network, and adjusting the control performance on line.

Claims (1)

1. A fuzzy network optimization PID control method for a coking furnace pressure system is characterized by comprising the following steps:

step 1, establishing a model of a controlled object through real-time step response data of a coking furnace hearth pressure object, specifically:

1.1 firstly selecting fuzzy clustering number c, fuzzy weighting index m and termination standard > 0;

1.2 randomly generating a fuzzy partition matrix lambda, and enabling the fuzzy partition matrix lambda to meet the following condition:

${\mathrm{\&mu;}}_{ik}\&Element;\&lsqb;0,1\&rsqb;,\underset{i=1}{\overset{c}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}=1,0<\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}<N$

wherein, mu_ikThe membership degree of the kth data relative to the ith clustering center is shown, and N is the number of samples;

1.3 calculating the clustering center:

$v_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m{z}_k}{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m}$

1.4 calculating the distance norm:

$D_{ik}^2=\left|\right|z_k-v_i|{|}_{A_i}^2={(z_k-v_i)}^T{A}_i(z_k-v_i)$

wherein,

A_i＝(ρdet(F_i))^1/nF_i ^-1

ρ＝det(A_i)

$F_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m(z_k-v_i){(z_k-v_i)}^T}{\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\mathrm{\&mu;}}_{ik}\right)}^m}$

1.5 updating the fuzzy partition matrix Lambda;

${\mathrm{\&mu;}}_{ik}=\frac{1}{\underset{j=1}{\overset{c}{\&Sigma;}}{(D_{ik}/D_{jk})}^{2/(m-1)}}$

1.6 when the condition is satisfied | | | Λ^l-Λ^l-1Stopping if the absolute value is less than or equal to the absolute value, otherwise, returning to the step 1.3;

1.7 calculate membership function variance using the following formula

${\mathrm{\&sigma;}}_{ij}^2=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}{(x_{jk}-v_{jk})}^2}{\underset{k=1}{\overset{N}{\&Sigma;}}{\mathrm{\&mu;}}_{ik}}$

1.8 calculate model back-part parameters using the following formula

θ_i＝[X^TW_iX]^-1X^TW_iy

Wherein the input variables, the output variables and the weighting matrix are

X＝[x₁,x₂,…,x_N],

y＝[y₁,y₂,…,y_N],

W_i＝diag(μ_i1,μ_i2,…,μ_iN)

1.9 obtaining the T-S model as

R_i:If x₁(k)is A_i1and x₂(k)is A_i2and…and x_n(k)is A_in

$Then{\hat{y}}_i\left(k\right)={\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)$

Wherein: r_iDenotes the ith fuzzy rule, x_jRepresenting an input variable, A_ijRepresenting a membership function defined in an input theoretic domain;

step 2, designing a PID controller of the process object, specifically:

2.1, carrying out weighted average on the T-S fuzzy rule model, wherein the model output is as follows:

$y(k+1)=\frac{\underset{i=1}{\overset{n}{\&Sigma;}}{B}_i\left(x\right)\&lsqb;{\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)\&rsqb;}{\underset{i=1}{\overset{n}{\&Sigma;}}{B}_i\left(x\right)}$

wherein,n represents a fuzzy operator and represents a fuzzy operator,representing a membership function of the fuzzy front-part variable;

note the bookShould satisfyAnd 0 is not less than omega_i(x)<1；

The above formula can be expressed as

$y(k+1)=\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&omega;}}_i\left(x\right)\&lsqb;{\mathrm{\&theta;}}_{i1}{x}_1\left(k\right)+{\mathrm{\&theta;}}_{i2}{x}_2\left(k\right)+...+{\mathrm{\&theta;}}_{in}{x}_n\left(k\right)\&rsqb;$

2.2 fuzzy RBF network setting PID control, the network will be composed of input layer, fuzzy inference layer and output layer, the network output is K_p,K_i,K_d；

2.3 each node of the input layer is directly connected with each component of the input quantity, and the input quantity is transmitted to the next layer; the input and output to each node i of the layer is represented as:

f₁(i)＝X＝[x₁,x₂,…,x_n]

2.4 use of Gauss-type functions as membership functions, c_ijAnd b_ijRespectively the mean value and the standard deviation of the membership function of the jth fuzzy set of the ith input variable;

$f_2(i,j)=\exp \&lsqb;\frac{{\left(f_1\right(i)-c_{ij})}^2}{{\left(b_{ij}\right)}^2}\&rsqb;$

wherein i is 1,2, …, n; j is 1,2, …, n;

2.5 the fuzzy inference layer completes the matching of fuzzy rules through the connection with the fuzzy layer, and realizes fuzzy operation among all nodes, namely obtains corresponding activation strength through the combination of all fuzzy nodes; the output of each node j is the product of all the input signals of the node, namely:

$f_3\left(j\right)=\underset{j=1}{\overset{N}{\&Pi;}}{f}_2(i,j)$

in the formula,

2.6 output layer output f₄Is K_p,K_i,K_dAs a result of the setting, the layer is composed of three nodes, namely:

$f_4\left(i\right)=w\&CenterDot;f_3=\underset{j=1}{\overset{N}{\&Sigma;}}w(i,j)\&CenterDot;f_3\left(j\right)$

in the formula, w_ijA connection weight matrix i of the output node and each node of the third layer is 1,2 and 3;

2.7 from step 2.3 to step 2.6, the control quantity is determined as:

△u(k)＝f₄·xc＝K_pxc(1)+K_ixc(2)+K_dxc(3)

wherein,

K_p＝f₄(1),K_i＝f₄(2),K_d＝f₄(3)

xc(1)＝e(k)

xc(2)＝e(k)-e(k-1)

xc(3)＝e(k)-2e(k-1)+e(k-2)

an incremental PID control algorithm is adopted:

u(k)＝u(k-1)+△u(k)

2.8 correcting the adjustable parameters by adopting a Delta learning rule, and defining an objective function as follows:

$E=\frac{1}{2}{\left(rin\right(k)-yout(k\left)\right)}^2$

wherein rin (k) and yout (k) respectively represent the actual output and the ideal output of the network, and the control error of each iteration step k is rin (k) -yout (k); the learning algorithm of the network weight is as follows:

$\begin{array}{c}{\mathrm{\&Delta;w}}_j\left(k\right)=-\mathrm{\&eta;}\&CenterDot;\frac{\&part;E}{\&part;w_j}=\mathrm{\&eta;}\&CenterDot;\left(rin\right(k)-yout(k\left)\right)\&CenterDot;\frac{\&part;yout}{\&part;\mathrm{\&Delta;}u}\frac{\&part;\mathrm{\&Delta;}u}{\&part;f_4}\frac{\&part;f_4}{\&part;w_j}\\ =\mathrm{\&eta;}\&CenterDot;\left(rin\right(k)-yout(k\left)\right)\&CenterDot;\frac{\&part;yout}{\&part;\mathrm{\&Delta;}u}xc\left(j\right)f_3\left(j\right)\end{array}$

in the formula, w_jIf the momentum factor is considered, the weight of the output layer is:

w_j(k)＝w_j(k-1)+△w_j(k)+α(w_j(k-1)-w_j(k-2))

in the formula, k is an iteration step of the network, and alpha is a learning momentum factor;

designing a fuzzy control-based RBF network through the model in the step 2, obtaining PID control parameters through continuous learning optimization of the network, and adjusting the control performance on line.