CN108388111B - Batch process two-dimensional prediction function control method - Google Patents

Abstract

The invention discloses a two-dimensional prediction function control method for a batch process. According to the method, a novel structural model is expanded according to a state control model, state prediction is obtained through the novel model and is corrected, then a novel error compensation method is provided to improve the control performance, finally, a prediction function control law and a corresponding cost function are selected, and the optimal control law is obtained through minimization of the cost function. The present invention improves control performance through an improved state model. The independent weighting of the tracking error in the performance indicator in turn provides more degrees of freedom for the controller design. So that the method has good control characteristics for batch processes.

Description

Batch process two-dimensional prediction function control method

Technical Field

The invention belongs to the technical field of automation, and relates to a novel iterative learning control method for a batch industrial process.

Background

With rapid development of economy and continuous growth of demand, the control requirements are more and more strict, and the control of the mass production process is also challenging. Repeatability is a typical problem during batch processing. And various uncertain factors inevitably exist really in the practical production process. The existing related control strategies still need to be improved, and the expected control performance cannot be guaranteed under the uncertain conditions. Therefore, it is necessary to develop an advanced control method of a batch process to deal with the problems of model uncertainty and repeatability to improve the control performance.

Disclosure of Invention

The invention aims to provide a batch process two-dimensional prediction function control method for improving the control performance of the control method in a batch industrial process.

According to the method, a novel structural model is expanded according to a state control model, state prediction is obtained through the novel model and is corrected, then a novel error compensation method is provided to improve the control performance, finally, a prediction function control law and a corresponding cost function are selected, and the optimal control law is obtained through minimization of the cost function.

The technical scheme of the invention is to establish a two-dimensional prediction function control method to design the controller by means of model establishment, prediction mechanism, optimization compensation and the like. Control performance is improved by an improved state model. The independent weighting of the tracking error in the performance indicator in turn provides more degrees of freedom for the controller design. So that the method has good control characteristics for batch processes.

The method comprises the following steps:

step 1, establishing a state control model of a controlled object in a batch process, specifically:

1.1 for a typical batch process with repeatability, introducing a state control model and processing, the following form can be obtained:

Δ_tx_m(t+1,k)＝AΔ_tx_m(t,k)+BΔ_tu(t,k)

Δ_ty_m(t+1,k)＝CΔ_tx_m(t+1,k)

wherein Δ_tIs a time backward difference operator; x is the number of_m(t +1, k) is the model state at time t +1 of the kth cycle; x is the number of_m(t, k) is the model state at time t of the kth cycle; u (t, k) is the model input at time t of the kth cycle; y is_m(t +1, k) is the model output at time t +1 of the kth cycle; a, B, C are the corresponding coefficient matrices.

1.2 define the reference trajectory form as follows:

y_r(t+i,k)＝wⁱy(t,k)+(1-wⁱ)c(t+i)

wherein, y_r(t + i, k) is the reference trajectory at the instant t + i of the kth cycle; i-0, …, P-1; p is the prediction time domain; y (t, k) is the time output at time t of the kth cycle; c (t + i) is a set value at time t + i; w is a smoothing factor.

1.3 the uncorrected tracking error from step 1.2 is:

e_t(t,k)＝y_m(t,k)-y_r(t,k)

wherein e is_t(t, k) is the uncorrected tracking error at time t of the kth cycle; y is_m(t, k) is the kthOutputting a model at the moment of the period t; y is_r(t, k) is the reference trajectory at the instant of time t of the kth cycle.

1.4 from step 1.1 to step 1.3:

e_t(t+1,k)＝e_t(t,k)+Δ_ty_m(t+1,k)-Δ_ty_r(t+1,k)

＝e_t(t,k)+CAΔ_tx_m(t,k)+CBΔ_tu(t,k)-Δ_ty_r(t+1,k)

wherein e is_t(t +1, k) is the uncorrected tracking error at time t +1 of the kth cycle; y is_r(t +1, k) is the reference trajectory at the instant of the kth cycle t + 1.

1.5 choosing an extended state vector

The relevant structural extension model was obtained as follows:

z(t+1,k)＝A_ez(t,k)+B_eΔ_tu(t,k)+C_eΔ_ty_r(t+1,k)

wherein z (t +1, k) is a structure expansion model at the time of t +1 of the kth period;

matrix A_eAnd C_e0 in (2) represents a zero matrix having a certain dimension.

1.6 correction of tracking error prediction:

e_tc(t+i,k)＝e_t(t+i,k)+e(t,k)

e(t,k)＝y(t,k)-y_m(t,k)

wherein e is_tc(t + i, k) is the corrected tracking error prediction at time t + i of the kth cycle; e.g. of the type_t(t + i, k) is the uncorrected tracking error at time t + i of the kth cycle; e (t, k) is between the actual process output and the model output at the time of the kth cycle tAnd (4) error.

1.7 the available state prediction form of the structural extended model according to step 1.5 is as follows:

Z(k)＝θz(t,k)+ψΔ_tU(k)+ξΔ_tY_r(k)

wherein the content of the first and second substances,

z (t +1, k), z (t +2, k).. z (t + P, k) is the structure expansion model at the t +1 moment, t +2 moment … t + P moment of the kth cycle respectively; u (t, k), u (t +1, k).. u (t + P-1, k) is the model input at time t, t +1 time … t + P-1 of the kth cycle; y is_r(t+1,k),y_r(t+2,k)…y_r(t + P, k) is the reference trajectory at time t +1, t +2 and … t + P of the kth cycle.

1.8 correct the state prediction to the form:

Z_c(k)＝Z(k)+E(k)

wherein the content of the first and second substances,

e_v0 in (t, k) represents a zero vector having a certain dimension; z is a radical of_c(t+1,k),z_c(t+2,k)...z_c(t + P, k) are corrected state predictions at times t +1, t +2, …, t + P, respectively, of the kth cycle.

1.9 to improve control performance, tracking errors are further considered and error compensation is introduced:

Z_c(k)＝Z(k)+E(k)+τE_c(k-1)

wherein the content of the first and second substances,

e_r(t+i,j)＝y(t+i,j)-y_r(t+i,j)；

e_c0 in (t + i, k-1) means having a certain valueA zero vector of dimensions. τ is a weighting coefficient of the accumulated tracking error; e.g. of the type_c(t+1,k-1),e_c(t+2,k-1)…e_cAnd (t + P, k-1) is the error of the k-1 th cycle at the time t +1, the time t +2 and the time t + P after correction.

Step 2, designing a batch process controller of a controlled object, which comprises the following specific steps:

2.1 the structural form of the control law of the selected prediction function is as follows:

u(t+i,k)＝μ₁+μ₂i+μ₃i²+μ₄i³+…μ_Ni^N-1

wherein, 1, i²,…,i^N-1Is a basis function; mu.s₁,μ₂…μ_NIs a linear coefficient; n is an integer greater than 1.

2.2 combining step 1.7 and step 2.1, the state prediction can be further modified as:

Z(k)＝θz(t,k)+χW(k)+ξΔ_tY_r(k)-θ_uu(t-1,k)

wherein the content of the first and second substances,

2.3 the selected performance index form is as follows

Where minJ is the minimization of the cost function, γ (i), λ (i), β (i) are the corresponding weighting matrices or coefficients, and Δ k is the backward difference operator over the period.

2.4 in connection with step 2.1 to step 2.3, the cost function can be further written in the form:

minJ＝γZ_c(k)²+λ(GW(k))²+β(HW(k)-U(k-1))²

wherein the content of the first and second substances,

2.5 the optimal linear coefficients of the basis functions are obtained by minimizing the cost function in step 2.4:

W(k)＝-(χ^Tγχ+G^TλG+H^TβH)^-1(χ^Tγ(θz(t,k)+ξΔ_tY_r(k)

-θ_uu(t-1,k)+E(k)+τE_c(k))-H^TβU(k-1))

2.6 the optimal control law u (t, k) ═ μ from step 2.5₁Acts on the controlled object.

The invention has the following beneficial effects:

the invention provides a two-dimensional prediction function control method for a batch process. The method establishes a structural expansion model, designs a batch process controller of a controlled object, uses the structural expansion model, and ensures that the controller design adjustment has more freedom through the independent adjustment of state variables and tracking errors, thereby ensuring that the system has good control performance.

Detailed Description

Taking the control of the injection speed in the batch process as an example:

step 1, establishing a state control model of a batch process, specifically:

1.1 for a typical batch process with repeatability, introducing a state control model and processing, the following form can be obtained:

Δ_tx_m(t+1,k)＝AΔ_tx_m(t,k)+BΔ_tu(t,k)

Δ_ty_m(t+1,k)＝CΔ_tx_m(t+1,k)

wherein Δ_tIs a time backward difference operator; x is the number of_m(t +1, k) is the model state at time t +1 of the kth cycle; x is the number of_m(t, k) is the model state at time t of the kth cycle; u (t, k) is the model input at time t of the kth cycle; y is_m(t +1, k) is the model output at time t +1 of the kth cycle; a, B, C are the corresponding coefficient matrices.

1.2 define the reference trajectory form as follows:

y_r(t+i,k)＝wⁱy(t,k)+(1-wⁱ)c(t+i)

wherein, y_r(t + i, k) is the reference trajectory at the instant t + i of the kth cycle; i-0, …, P-1; p is the prediction time domain; y (t, k) is the time output at time t of the kth cycle; c (t + i) is a set value at time t + i; w is a smoothing factor.

1.3 the uncorrected tracking error from step 1.2 is:

e_t(t,k)＝y_m(t,k)-y_r(t,k)

wherein e is_t(t, k) is the uncorrected tracking error at time t of the kth cycle; y is_m(t, k) is the model output at time t of the kth cycle; y is_r(t, k) is the reference trajectory at the instant of time t of the kth cycle.

1.4 from step 1.1 to step 1.3:

e_t(t+1,k)＝e_t(t,k)+Δ_ty_m(t+1,k)-Δ_ty_r(t+1,k)

＝e_t(t,k)+CAΔ_tx_m(t,k)+CBΔ_tu(t,k)-Δ_ty_r(t+1,k)

wherein e is_t(t +1, k) is the uncorrected tracking error at time t +1 of the kth cycle; y is_r(t +1, k) is the reference trajectory at the instant of the kth cycle t + 1.

1.5 choosing an extended state vector

The relevant structural extension model was obtained as follows:

z(t+1,k)＝A_ez(t,k)+B_eΔ_tu(t,k)+C_eΔ_ty_r(t+1,k)

wherein z (t +1, k) is a structure expansion model at the time of t +1 of the kth period;

matrix A_eAnd C_e0 in (2) represents a zero matrix having a certain dimension.

1.6 correction of tracking error prediction:

e_tc(t+i,k)＝e_t(t+i,k)+e(t,k)

e(t,k)＝y(t,k)-y_m(t,k)

wherein e is_tc(t + i, k) is the corrected tracking error prediction at time t + i of the kth cycle; e.g. of the type_t(t + i, k) is the uncorrected tracking error at time t + i of the kth cycle; e (t, k) is the error between the actual process output and the model output at time t of the kth cycle.

1.7 the available state prediction form of the structural extended model according to step 1.5 is as follows:

Z(k)＝θz(t,k)+ψΔ_tU(k)+ξΔ_tY_r(k)

wherein the content of the first and second substances,

z (t +1, k), z (t +2, k).. z (t + P, k) is the structure expansion model at the t +1 moment, t +2 moment … t + P moment of the kth cycle respectively; u (t, k), u (t +1, k).. u (t + P-1, k) is the model input at time t, t +1 time … t + P-1 of the kth cycle; y is_r(t+1,k),y_r(t+2,k)…y_r(t + P, k) is the reference trajectory at time t +1, t +2 and … t + P of the kth cycle.

1.8 correct the state prediction to the form:

Z_c(k)＝Z(k)+E(k)

wherein the content of the first and second substances,

e_v0 in (t, k) represents a zero vector having a certain dimension; z is a radical of_c(t+1,k),z_c(t+2,k)...z_c(t + P, k) are corrected state predictions at times t +1, t +2, …, t + P, respectively, of the kth cycle.

1.9 to improve control performance, tracking errors are further considered and error compensation is introduced:

Z_c(k)＝Z(k)+E(k)+τE_c(k-1)

wherein the content of the first and second substances,

e_r(t+i,j)＝y(t+i,j)-y_r(t+i,j)；

e_c"0" in (t + i, k-1) represents a zero vector having a certain dimension. τ is a weighting coefficient of the accumulated tracking error; e.g. of the type_c(t+1,k-1),e_c(t+2,k-1)…e_cAnd (t + P, k-1) is the error of the k-1 th cycle at the time t +1, the time t +2 and the time t + P after correction.

Step 2, designing a batch process controller, which comprises the following specific steps:

2.1 the structural form of the control law of the selected prediction function is as follows:

u(t+i,k)＝μ₁+μ₂i+μ₃i²+μ₄i³+…μ_Ni^N-1

wherein, 1, i²,…,i^N-1Is a basis function; mu.s₁,μ₂…μ_NIs a linear coefficient; n is an integer greater than 1.

2.2 combining step 1.7 and step 2.1, the state prediction can be further modified as:

Z(k)＝θz(t,k)+χW(k)+ξΔ_tY_r(k)-θ_uu(t-1,k)

wherein the content of the first and second substances,

2.3 the selected performance index form is as follows

Where minJ is the minimization of the cost function, γ (i), λ (i), β (i) are the corresponding weighting matrices or coefficients, and Δ k is the backward difference operator over the period.

2.4 in connection with step 2.1 to step 2.3, the cost function can be further written in the form:

minJ＝γZ_c(k)²+λ(GW(k))²+β(HW(k)-U(k-1))²

wherein the content of the first and second substances,

2.5 the optimal linear coefficients of the basis functions are obtained by minimizing the cost function in step 2.4:

W(k)＝-(χ^Tγχ+G^TλG+H^TβH)-¹(χ^Tγ(θz(t,k)+ξΔ_tY_r(k)

-θ_uu(t-1,k)+E(k)+τE_c(k))-H^TβU(k-1))

2.6 the optimal control law u (t, k) ═ μ from step 2.5₁Acting on the control valve.

Claims (1)

1. A batch process two-dimensional prediction function control method is characterized by comprising the following steps:

step 1, establishing a state control model of a control valve in a batch process, specifically:

1.1 for a typical batch process with repeatability, a state control model of the control valves is introduced and processed, which can take the form:

Δ_tx_m(t+1,k)＝AΔ_tx_m(t,k)+BΔ_tu(t,k)

Δ_ty_m(t+1,k)＝CΔ_tx_m(t+1,k)

wherein Δ_tIs a time backward difference operator; x is the number of_m(t +1, k) is the model state at time t +1 of the kth cycle; x is the number of_m(t, k) is the model state at time t of the kth cycle; u (t, k) is the input injection velocity at time t of the kth cycle; y is_m(t +1, k) is the output injection velocity at the time of the kth cycle t + 1; a, B and C are corresponding coefficient matrixes;

1.2 define the reference trajectory form as follows:

y_r(t+i,k)＝wⁱy(t,k)+(1-wⁱ)c(t+i)

wherein, y_r(t + i, k) is the reference trajectory at the instant t + i of the kth cycle; i-0, …, P-1; p is the prediction time domain; y (t, k) is the time output at time t of the kth cycle; c (t + i) is a set value at time t + i; w is a smoothing factor;

1.3 the uncorrected tracking error from step 1.2 is:

e_t(t,k)＝y_m(t,k)-y_r(t,k)

wherein e is_t(t, k) is the uncorrected tracking error at time t of the kth cycle; y is_m(t, k) is the output injection velocity at time t of the kth cycle; y is_r(t, k) is the reference trajectory at time t of the kth cycle;

1.4 from step 1.1 to step 1.3:

e_t(t+1,k)＝e_t(t,k)+Δ_ty_m(t+1,k)-Δ_ty_r(t+1,k)

＝e_t(t,k)+CAΔ_tx_m(t,k)+CBΔ_tu(t,k)-Δ_ty_r(t+1,k)

wherein e is_t(t +1, k) is the uncorrected tracking error at time t +1 of the kth cycle; y is_r(t +1, k) is the reference trajectory at the instant of the kth cycle t + 1;

1.5 choosing an extended state vector

The relevant structural extension model was obtained as follows:

z(t+1,k)＝A_ez(t,k)+B_eΔ_tu(t,k)+C_eΔ_ty_r(t+1,k)

wherein z (t +1, k) is a structure expansion model at the time of t +1 of the kth period;

matrix A_eAnd C_e0 in (1) represents a zero matrix having a certain dimension;

1.6 correction of tracking error prediction:

e_tc(t+i,k)＝e_t(t+i,k)+e(t,k)

e(t,k)＝y(t,k)-y_m(t,k)

wherein e is_tc(t + i, k) is the corrected tracking error prediction at time t + i of the kth cycle; e.g. of the type_t(t + i, k) is the uncorrected tracking error at time t + i of the kth cycle; e (t, k) is the error between the actual injection velocity and the output injection velocity at the time of the kth cycle t;

1.7 the available state prediction form of the structural extended model according to step 1.5 is as follows:

Z(k)＝qz(t,k)+ψΔ_tU(k)+ξΔ_tY_r(k)

wherein the content of the first and second substances,

z (t +1, k), z (t +2, k).. z (t + P, k) is the structure expansion model at the t +1 moment, t +2 moment … t + P moment of the kth cycle respectively; u (t, k), u (t +1, k).. u (t + P-1, k) is the kth cycle time t, t +1 time … t + P-1 time input injection speed; y is_r(t+1,k),y_r(t+2,k)…y_r(t + P, k) is the reference trajectory at time t +1, t +2 and … t + P of the kth cycle;

1.8 correct the state prediction to the form:

Z_c(k)＝Z(k)+E(k)

wherein the content of the first and second substances,

e_v0 in (t, k) represents a zero vector having a certain dimension; z is a radical of_c(t+1,k),z_c(t+2,k)…z_c(t + P, k) are corrected state predictions at times t +1, t +2, …, t + P, respectively, of the kth cycle;

1.9 to improve control performance, tracking errors are further considered and error compensation is introduced:

Z_c(k)＝Z(k)+E(k)+τE_c(k-1)

wherein the content of the first and second substances,

e_r(t+i,j)＝y(t+i,j)-y_r(t+i,j)；

e_c0 in (t + i, k-1) represents a zero vector having a certain dimension; τ is a weighting coefficient of the accumulated tracking error; e.g. of the type_c(t+1,k-1),e_c(t+2,k-1)…e_c(t + P, k-1) is the corrected error of the k-1 th cycle at the time t +1, the time t +2 and the time t + P;

step 2, designing a batch process controller of the control valve, which specifically comprises the following steps:

2.1 the structural form of the control law of the selected prediction function is as follows:

u(t+i,k)＝μ₁+μ₂i+μ₃i²+μ₄i³+…μ_Ni^N-1

wherein, 1, i²,…,i^N-1Is a basis function; mu.s₁,μ₂…μ_NIs a linear coefficient; n is an integer greater than 1;

2.2 combining step 1.7 and step 2.1, the state prediction is further modified as:

Z(k)＝qz(t,k)+xW(k)+ξΔ_tY_r(k)-q_uu(t-1,k)

wherein the content of the first and second substances,

2.3 the selected performance index form is as follows

Where minJ is the minimization of the cost function, γ (i), λ (i), β (i) are the corresponding weighting matrices or coefficients, Δ k is the backward difference operator over the period;

2.4 in connection with step 2.1 to step 2.3, the cost function can be further written in the form:

minJ＝γZ_c(k)²+l(GW(k))²+β(HW(k)-U(k-1))²

wherein the content of the first and second substances,

2.5 the optimal linear coefficients of the basis functions are obtained by minimizing the cost function in step 2.4:

W(k)＝-(x^Tγx+G^TλG+H^TβH)^-1(x^Tγ(qz(t,k)+ξΔ_tY_r(k)-q_uu(t-1,k)+E(k)+τE_c(k))-H^TβU(k-1))

2.6 the optimal control law u (t, k) ═ μ from step 2.5₁Acting on the control valve.