CN104317321A

CN104317321A - Coking furnace hearth pressure control method based on state-space predictive functional control optimization

Info

Publication number: CN104317321A
Application number: CN201410492271.3A
Authority: CN
Inventors: 薛安克; 邹琴; 张日东; 王建中; 刘俊
Original assignee: Hangzhou Dianzi University
Current assignee: Hangzhou Dianzi University
Priority date: 2014-09-23
Filing date: 2014-09-23
Publication date: 2015-01-28

Abstract

The invention discloses a coking furnace hearth pressure control method based on state-space predictive functional control optimization. In industrial control, traditional PID control cannot achieve a satisfactory control effect. In the invention, first, a state-space model of a coking furnace pressure object is established based on real-time input and output data of the coking furnace pressure object, and then, an extended non-minimized state-space model is established based on the state process and output error. On the basis of the model, the parameters of a PID controller are optimized by the method of predictive functional control, and PID control on a controlled object is realized. The coking furnace hearth pressure control method of the invention has both good control performance of ENMSSPFC and the simple form of PID control.

Description

Coking furnace hearth pressure control method based on state space prediction function control optimization

Technical Field

The invention belongs to the technical field of automation, and relates to a Proportional Integral Derivative (PID) control method for the hearth pressure of a coking furnace based on extended non-minimized state space prediction function control (ENMSSPFC) optimization.

Background

In practical industrial control, due to the limitation of factors such as cost and hardware, some advanced control methods are applied to a certain extent, but cannot replace the traditional PID control. The pressure control of the hearth of the coking furnace is a process with large time lag and nonlinearity, and the traditional PID control cannot achieve a satisfactory control effect. The control performance of the control based on the extended non-minimized state space prediction function in the coking furnace pressure control is better than that of PID control, and if the control performance of ENMSSPFC can be given to PID control, the simple form of the control structure can be ensured, and better control performance can be obtained.

Disclosure of Invention

The invention aims to provide a coking furnace hearth pressure PID control method based on ENMSSPFC optimization by means of data acquisition, model establishment, prediction mechanism, optimization and the like aiming at the defects of the existing PID control so as to obtain good control performance in the actual process. The method combines the ENMSSPFC and PID control to obtain the ENMSSPFC optimized PID control method. The method has the good control performance of ENMSSPFC, and simultaneously has a simple form of PID control.

The method comprises the following steps:

step 1, establishing an extended non-minimized state space model of a controlled object, which comprises the following specific steps:

1.1, establishing a model by using a least square method by acquiring real-time input and output data of a controlled object, wherein the form is as follows:

y_L(k)＝Ψ^Tθ,θ＝[S₁,-L₁,S₂,-L₂,...,S_n,-L_n]^T

Ψ＝[u(k-1),y(k-1),...,u(k-n),y(k-n)]^T

wherein, y_L(k) An output value representing a prediction model at time k, y (k) an output value representing an actual process at time k, u (k) a control quantity at time k, n is an order of input and output variables corresponding to the actual process, L₁,L₂,...,L_n,S₁,S₂,...,S_nT is the transposed symbol of the matrix for the coefficients that need to be identified.

Acquiring N groups of sample data by using the acquired real-time process data, wherein the form is as follows:

Y＝[y(1),y(2),...,y(j),...,y(N)]^T

therein, Ψ_jY (j) represents the input data and output values of the j-th group acquired, and N represents the total number of samples.

The identification result is:

1.2, converting the model obtained in the step 1.1 into a differential model form:

Δy(k+1)+L₁Δy(k)+L₂Δy(k-1)+...+L_nΔy(k-n+1)

＝S₁Δu(k)+S₂Δu(k-1)+...+S_nΔu(k-n+1)

where Δ is the difference operator.

1.3, selecting the non-minimized state space variables as shown in the following:

Δx_m(k)^T＝[Δy(k),Δy(k-1),...,Δy(k-n+1),Δu(k-1),Δu(k-2),Δu(k-n+1)]

and further converting the model in the step 1.2 into a state space model, wherein the form of the state space model is as follows:

Δx_m(k+1)＝A_mΔx_m(k)+B_mΔu(k)

Δy(k+1)＝C_mΔx_m(k+1)

wherein

A_{m} = [\begin{matrix} - L_{1} & - L_{2} & . . . & - L_{n - 1} & - L_{n} & S_{2} & . . . & S_{n - 1} & S_{n} \\ 1 & 0 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ 0 & 1 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ . & . & . & . & . & . & . \\ . & . & . . . & . & . & . & . . . & . & . \\ . & . & . & . & . & . & . \\ 0 & 0 & . . . & 1 & 0 & 0 & . . . & 0 & 0 \\ 0 & 0 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ 0 & 0 & . . . & 0 & 0 & 1 & . . . & 0 & 0 \\ . & . & . & . & . & . & . \\ . & . & . . . & . & . & . . . & . & . & . \\ . & . & . & . & . & . & . \\ 0 & 0 & . . . & 0 & 0 & 0 & . . . & 1 & 0 \end{matrix}],

B_{m} = {[\begin{matrix} S_{1} & 0 & . . . & 0 & 1 & 0 & . . . & 0 \end{matrix}]}^{T},

C_{m} = [\begin{matrix} 1 & 0 & 0 & . . . & 0 & 0 & 0 & 0 \end{matrix}],

Δx_m(k) The dimension m is 2 n-1.

1.4, converting the state space model obtained in the step 1.3 into an extended non-minimized state space model containing state variables and output errors, wherein the form is as follows:

z(k+1)＝Az(k)+BΔu(k)+CΔr(k+1)

wherein

e(k)＝y(k)-r(k)

r (k) is the desired output value at time k, e (k) is the difference between the actual output value and the desired output value at time k, and 0 is a zero matrix of dimension m.

Step 2, designing a PID controller of a controlled object, and the specific steps are as follows:

2.1, calculating a predicted output value of the k time to the k + P time, wherein the form is as follows:

z(k+P)＝A^Pz(k)+ψΔu(k)+θΔR

wherein,

r(k+i)＝αⁱy(k)+(1-αⁱ)c(k),i＝1,2,...,P，

p is the prediction time domain, A^PDenotes the multiplication of P matrices a, α is the softening factor of the reference trajectory, and c (k) is the set value at time k.

2.2, selecting an objective function J (k) of the controlled object, wherein the form is as follows:

minJ(k)＝z(k+P)^ΤQz(k+P)

where Q is a (2n-1) × (2n-1) weight matrix and min represents the minimum.

2.3, solving the parameters of the PID controller according to the objective function in the step 2.2, wherein the specific method comprises the following steps: firstly, the controlled quantity u (k) is transformed:

u(k)＝u(k-1)+K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)+K_d(k)(e₁(k)-2e₁(k-1)+e₁(k-2))

e₁(k)＝c(k)-y(k)

wherein, K_p(k)、K_i(k)、K_d(k) Proportional, differential and integral parameters of the PID controller at the time k, respectively, e₁(k) Is the error between the set value and the actual output value at time k.

The control quantity u (k) can then be reduced to the form of a matrix:

u(k)＝u(k-1)+w(k)^ΤE(k)

w(k)＝[w₁(k),w₂(k),w₃(k)]^Τ

E(k)＝[e₁(k),e₁(k-1),e₁(k-2)]^Τ

w₁(k)＝K_p(k)+K_i(k)+K_d(k)

w₂(k)＝-K_p(k)-2K_d(k)

w₃(k)＝K_d(k)

by combining the matrix form of the controlled variable u (k) and the objective function in step 2.2, it is possible to obtain:

further, it is possible to obtain:

K_p(k)＝-w₂(k)-2K_d(k)

K_i(k)＝w₁(k)-K_P(k)-K_d(k)

K_d(k)＝w₃(k)

2.4obtaining the parameter K of the PID controller_p(k)、K_i(k)、K_d(k) Then, a control amount: u (K) ═ u (K-1) + K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)+K_d(k)(e₁(k)-2e₁(k-1)+e₁(k-2)), and then applied to the controlled object.

2.5, circularly solving the new parameter K of the PID controller according to the steps from 2.1 to 2.4 at the moment of K + l_p(k+l)、K_i(k+l)、K_d(k+l)，l＝1,2,3，...。

The method comprises the steps of firstly establishing a state space model of the coking furnace pressure object based on real-time input and output data of the coking furnace pressure object, and then establishing an expanded non-minimized state space model by combining a state process and an output error. On the basis of the model, parameters of the PID controller are optimized according to a predictive function control method, and finally PID control is realized on a controlled object, so that the defects of the traditional control method are effectively overcome, and the control performance of the system can be effectively improved.

Detailed Description

The invention is further explained below by taking the coking furnace pressure process control as an example, wherein the adjusting means is to adjust the opening of the flue damper in the coking furnace pressure control process.

The method for controlling the hearth pressure of the coking furnace by controlling and optimizing the state space prediction function comprises the following specific steps:

1.1, establishing a model by acquiring real-time input and output data of a controlled object by using a least square method, wherein the form is as follows:

y_L(k)＝Ψ^Tθ,θ＝[S₁,-L₁,S₂,-L₂,...,S_n,-L_n]^T

Ψ＝[u(k-1),y(k-1),...,u(k-n),y(k-n)]^T

wherein, y_L(k) Representing the output value of the prediction model at the time k, y (k) representing the output value of the furnace pressure object in the pressure process at the time k, u (k) representing the control quantity at the time k, n being the order of the input and output variables of the corresponding pressure process, L₁,L₂,...,L_n,S₁,S₂,...,S_nT is the transposed symbol of the matrix for the coefficients that need to be identified.

Y＝[y(1),y(2),...,y(j),...,y(N)]^T

The identification result is:

1.2, converting the model of the coking furnace pressure control process obtained in the step 1.1 into a differential model form:

Δy(k+1)+L₁Δy(k)+L₂Δy(k-1)+...+L_nΔy(k-n+1)

＝S₁Δu(k)+S₂Δu(k-1)+...+S_nΔu(k-n+1)

where Δ is the difference operator.

Δx_m(k)^T＝[Δy(k),Δy(k-1),...,Δy(k-n+1),Δu(k-1),Δu(k-2),Δu(k-n+1)]，

Δx_m(k+1)＝A_mΔx_m(k)+B_mΔu(k)

Δy(k+1)＝C_mΔx_m(k+1)

wherein,

B_{m} = {[\begin{matrix} S_{1} & 0 & . . . & 0 & 1 & 0 & . . . & 0 \end{matrix}]}^{T}

C_{m} = [\begin{matrix} 1 & 0 & 0 & . . . & 0 & 0 & 0 & 0 \end{matrix}]

A_{m} = [\begin{matrix} - L_{1} & - L_{2} & . . . & - L_{n - 1} & - L_{n} & S_{2} & . . . & S_{n - 1} & S_{n} \\ 1 & 0 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ 0 & 1 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ . & . & . & . & . & . & . \\ . & . & . . . & . & . & . & . . . & . & . \\ . & . & . & . & . & . & . \\ 0 & 0 & . . . & 1 & 0 & 0 & . . . & 0 & 0 \\ 0 & 0 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ 0 & 0 & . . . & 0 & 0 & 1 & . . . & 0 & 0 \\ . & . & . & . & . & . & . \\ . & . & . . . & . & . & . . . & . & . & . \\ . & . & . & . & . & . & . \\ 0 & 0 & . . . & 0 & 0 & 0 & . . . & 1 & 0 \end{matrix}]

Δx_m(k) the dimension m is 2 n-1.

z(k+1)＝Az(k)+BΔu(k)+CΔr(k+1)

wherein,

e(k)＝y(k)-r(k)

r (k) is the desired pressure at time k, e (k) is the difference between the actual and desired pressures for the furnace at time k, and 0 is a zero matrix with dimension m.

And 2, designing a PID controller of the coking furnace pressure process, and specifically comprising the following steps:

2.1, calculating the predicted output value of the hearth pressure of the coking furnace at the k moment and the k + P moment, wherein the form is as follows:

z(k+P)＝A^Pz(k)+ψΔu(k)+θΔR

wherein,

r(k+i)＝αⁱy(k)+(1-αⁱ)c(k),i＝1,2,...,P

p is the prediction time domain, A^PDenotes the multiplication of the P matrices a, α being the softening factor of the reference trajectory, c (k) being the set value of the pressure course at time k.

minJ(k)＝z(k+P)^ΤQz(k+P)

where Q is a (2n-1) × (2n-1) weight matrix and min represents the minimum.

2.3, solving the parameters of the PID controller according to the objective function in the step 2.2, wherein the specific method comprises the following steps: firstly, converting the flue damper opening degree control quantity u (k) in the coking furnace pressure process:

e₁(k)＝c(k)-y(k)

wherein, K_p(k)、K_i(k)、K_d(k) Proportional, differential and integral parameters of the PID controller at the time k, respectively, e₁(k) Is the error between the set value and the actual output value of the furnace pressure control process at the moment k.

The control quantity u (k) can then be reduced to the form of a matrix:

u(k)＝u(k-1)+w(k)^ΤE(k)

w(k)＝[w₁(k),w₂(k),w₃(k)]^Τ

E(k)＝[e₁(k),e₁(k-1),e₁(k-2)]Τ

w₁(k)＝K_p(k)+K_i(k)+K_d(k)

w₂(k)＝-K_p(k)-2K_d(k)

w₃(k)＝K_d(k)

further, it is possible to obtain:

K_p(k)＝-w₂(k)-2K_d(k)

K_i(k)＝w₁(k)-K_P(k)-K_d(k)

K_d(k)＝w₃(k)

2.4 obtaining the parameter K of the PID controller_p(k)、K_i(k)、K_d(k) Then, the controlled variable u (K) is constituted by u (K-1) + K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)+K_d(k)(e₁(k)-2e₁(k-1)+e₁(k-2)), and then applied to a flue damper of the coke oven pressure process.

Claims

1. The method for controlling the hearth pressure of the coking furnace by controlling and optimizing the state space prediction function is characterized by comprising the following steps of: the method comprises the following specific steps:

y_L(k)＝Ψ^Tθ,θ＝[S₁,-L₁,S₂,-L₂,...,S_n,-L_n]^T

Ψ＝[u(k-1),y(k-1),...,u(k-n),y(k-n)]^T

wherein, y_L(k) An output value representing a prediction model at time k, y (k) an output value representing an actual process at time k, u (k) a control quantity at time k, n is an order of input and output variables corresponding to the actual process, L₁,L₂,...,L_n,S₁,S₂,...,S_nFor the coefficients needing to be identified, T is a transposed symbol of the matrix;

Y＝[y(1),y(2),...,y(j),...,y(N)]^T

therein, Ψ_jY (j) represents the input data and output value of the j group collected, and N represents the total number of samples;

the identification result is:

Δy(k+1)+L₁Δy(k)+L₂Δy(k-1)+...+L_nΔy(k-n+1)

＝S₁Δu(k)+S₂Δu(k-1)+...+S_nΔu(k-n+1)

where Δ is the difference operator;

Δx_m(k)^T＝[Δy(k),Δy(k-1),...,Δy(k-n+1),Δu(k-1),Δu(k-2),Δu(k-n+1)]

Δx_m(k+1)＝A_mΔx_m(k)+B_mΔu(k)

Δy(k+1)＝C_mΔx_m(k+1)

wherein

A_{m} = [\begin{matrix} - L_{1} & - L_{2} & . . . & - L_{n - 1} & - L_{n} & S_{2} & . . . & S_{n - 1} & S_{n} \\ 1 & 0 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ 0 & 1 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ . & . & . & . & . & . & . \\ . & . & . . . & . & . & . & . . . & . & . \\ . & . & . & . & . & . & . \\ 0 & 0 & . . . & 1 & 0 & 0 & . . . & 0 & 0 \\ 0 & 0 & . . . & 0 & 0 & 0 & . . . & 0 & 0 \\ 0 & 0 & . . . & 0 & 0 & 1 & . . . & 0 & 0 \\ . & . & . & . & . & . & . \\ . & . & . . . & . & . & . . . & . & . & . \\ . & . & . & . & . & . & . \\ 0 & 0 & . . . & 0 & 0 & 0 & . . . & 1 & 0 \end{matrix}],

B_{m} = {[\begin{matrix} S_{1} & 0 & . . . & 0 & 1 & 0 & . . . & 0 \end{matrix}]}^{T},

C_{m} = [\begin{matrix} 1 & 0 & 0 & . . . & 0 & 0 & 0 & 0 \end{matrix}],

Δx_m(k) The dimension m is 2 n-1;

z(k+1)＝Az(k)+BΔu(k)+CΔr(k+1)

wherein

e(k)＝y(k)-r(k)

r (k) is the desired output value at time k, e (k) is the difference between the actual output value and the desired output value at time k, 0 is a zero matrix of dimension m;

z(k+P)＝A^Pz(k)+ψΔu(k)+θΔR

wherein,

r(k+i)＝αⁱy(k)+(1-αⁱ)c(k),i＝1,2,...,P，

p is the prediction time domain, A^PRepresents multiplication of P matrixes A, alpha is a softening factor of a reference track, and c (k) is a set value at the moment k;

minJ(k)＝z(k+P)^ΤQz(k+P)

wherein Q is a (2n-1) × (2n-1) weight matrix, and min represents the minimum value;

2.3, solving the parameters of the PID controller according to the objective function in the step 2.2, wherein the specific method comprises the following steps:

firstly, the controlled quantity u (k) is transformed:

e₁(k)＝c(k)-y(k)

wherein, K_p(k)、K_i(k)、K_d(k) Proportional, differential and integral parameters of the PID controller at the time k, respectively, e₁(k) Is the error between the set value at time k and the actual output value;

the control quantity u (k) can then be reduced to the form of a matrix:

u(k)＝u(k-1)+w(k)^ΤE(k)

w(k)＝[w₁(k),w₂(k),w₃(k)]^Τ

E(k)＝[e₁(k),e₁(k-1),e₁(k-2)]^Τ

w₁(k)＝K_p(k)+K_i(k)+K_d(k)

w₂(k)＝-K_p(k)-2K_d(k)

w₃(k)＝K_d(k)

further, it is possible to obtain:

K_p(k)＝-w₂(k)-2K_d(k)

K_i(k)＝w₁(k)-K_P(k)-K_d(k)

K_d(k)＝w₃(k)

2.4 obtaining the parameter K of the PID controller_p(k)、K_i(k)、K_d(k) Then, a control amount: u (K) ═ u (K-1) + K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)+K_d(k)(e₁(k)-2e₁(k-1)+e₁(k-2)), and then acting on the controlled object;