Nonlinear model predictive control method for strip steel temperature of continuous annealing furnace

Abstract

The invention discloses a nonlinear model predictive control method for the strip steel temperature of a continuous annealing furnace, and relates to the technical field of metallurgical industry automation control, and the method comprises the following steps: collecting historical data in the production process of the continuous annealing furnace; a nonlinear autoregression exogenous input model based on Sigmoid-ARX is established; the model parameters are optimized through a Levenberg-Marquardt algorithm, and the model parameters are optimized through the Levenberg-Marquardt algorithm; based on the optimized Sigmoid-ARX model, designing a nonlinear model prediction controller, performing local linearization near a given working point, and converting a nonlinear optimization problem into a quadratic programming problem; by constructing the Sigmoid-ARX nonlinear model and the predictive control capability and system-level constraint processing characteristics of the model predictive control algorithm, the strip steel temperature predictive precision is improved, stable control over strip steel of different specifications in the transition stage is achieved by optimizing the control strategy, the standard deviation of the strip steel temperature and speed is reduced, and the stability of the strip steel temperature and speed is improved. The average speed of a production line is improved, and the yield is increased.

Description

Technical Field

[0001] The present invention relates to the technical field of metallurgical industrial automation control, and particularly relates to a non-linear model predictive control method for strip temperature in a continuous annealing furnace. Background Art

[0002] The annealing process is a very important process in cold-rolled sheet production. It is a heat treatment process that heats the cold-rolled steel strip above the critical temperature, holds it for a period of time, and then cools it slowly. Its main purpose is to improve the mechanical properties of the material, eliminate processing stress, and adjust the organizational structure of the material. The main equipment for implementing this process in modern steel mills is the continuous annealing furnace (CAF), and its main structure is as Figure 1 shown. It consists of a preheating section (JPF), a reheating section (RTF), a soaking section (SF), a cooling section, an aging section, a final cooling section, and a water cooling section. The main heating process of the strip is completed in the reheating section (RTF). Therefore, the temperature setting of the reheating section (RTF) is the key to the annealing process.

[0003] Traditional control systems, such as proportional, integral, and derivative controllers (PID controllers), have many difficulties in meeting the control requirements of continuous annealing furnaces. This is mainly because the continuous annealing furnace system has characteristics such as time delay, non-linearity, large thermal inertia, load disturbance, and temperature drift. In addition, during the transition stage of strips of different specifications, due to changes in strip size, annealing temperature requirements, and speed requirements, the control process becomes more complex. Although rule-based expert systems and fuzzy logic control methods have higher consistency and accuracy than manual operation and shorter response times, due to the complexity of the annealing furnace and the diversity of operating conditions, the installation, commissioning, and adjustment costs of these control concepts are very high. Therefore, a control method that can accurately control the strip temperature in a continuous annealing furnace, optimize the production line speed, and reduce energy consumption is needed to solve the above problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a non-linear model predictive control method for strip temperature in a continuous annealing furnace to solve the problems existing in the prior art as mentioned in the above background art.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] A non-linear model predictive control method for strip temperature in a continuous annealing furnace, comprising the following steps:

[0007] S1: Collect historical data during the production process of the continuous annealing furnace;

[0008] S2: Establish a non-linear autoregressive exogenous input model based on Sigmoid-ARX;

[0009] S3: Optimize the model parameters through the Levenberg - Marquardt algorithm;

[0010] S4: Based on the optimized Sigmoid - ARX model, design a non - linear model predictive controller, perform local linearization near the given operating point, and transform the non - linear optimization problem into a quadratic programming problem;

[0011] S5: Design the objective function, with controlling the strip temperature near the target temperature as the primary goal and maximizing the production line speed as the secondary goal under the condition of meeting the temperature requirements;

[0012] S6: Set the control constraint conditions, including strip temperature constraints, speed constraints, and actuator constraints;

[0013] S7: Solve the quadratic programming problem to obtain the optimal control sequence;

[0014] S8: Apply the first element of the optimal control sequence as the control input to the continuous annealing furnace system;

[0015] S9: At the next sampling moment, repeat steps S4 to S8 to achieve rolling optimization control.

[0016] Preferably, in the said S1, the historical data includes strip width, thickness, steel grade, speed, set temperature of the heating section, inlet temperature of the heating section, and outlet temperature of the heating section.

[0017] Preferably, in the said S2, the mathematical expression of the non - linear autoregressive exogenous input model of Sigmoid - ARX is:

[0018] y t = f(Y,U)+e t = f(y t-1 ,y t-2 ,…,y t-n ,u t-1 ,u t-2 ,…,u t-m )+e t

[0019] where, y t is the system target output, i.e., the outlet temperature of the heating section; u t is the exogenous input variable affecting the target output, including strip width, thickness, speed, steel grade, and inlet temperature of the heating section, n and m are the lag orders of the target variable and the exogenous input variable respectively, f is a non - linear function using the Sigmoid function as the activation function, and e t is the error term of the model.

[0020] Preferably, in the step S4, the local linearization is performed by performing a first-order Taylor expansion around a given operating point (y0, u0) to obtain a local linear model:

[0021]

[0022] Preferably, in the step S4, the expression of the quadratic programming problem is:

[0023]

[0024] where u is the optimization variable, H is the Hessian matrix, f is the linear term coefficient vector, P is the constraint matrix, b is the constraint vector, and f0 is the constant term.

[0025] Preferably, in the step S5, the expression of the objective function is:

[0026]

[0027] where T strip is the actual temperature of the strip, T target is the target temperature of the strip, v is the strip speed, setT is the set temperature value, Δv is the speed change, ΔsetT is the set temperature change, W T and W v 、W setT 、W Δv 、W ΔsetT are weight matrices, W T is the weight of the temperature error, W v and W setT are the speed and temperature weights respectively, W Δv and W ΔsetT are the weights of the temperature and speed control increments respectively, and n is the prediction horizon length.

[0028] Preferably, in the step S6, the constraint conditions include:

[0029] Strip temperature constraint: y min ≤y(t + i|t)≤y max , i = 1, 2…, N

[0030] Speed constraint: v min ≤v(t + i - 1)≤v max , i = 1, 2…, N

[0031] Actuator constraint: Δu min ≤Δu(t + i - 1)≤Δu max , i = 1, 2…, N.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] The present invention improves the prediction accuracy of strip temperature by constructing the prediction control ability of the Sigmoid-ARX nonlinear model and the model predictive control algorithm and the system-level constraint handling characteristics, realizes the smooth control in the transition stage of strips with different specifications by optimizing the control strategy, reduces the standard deviations of strip temperature and speed, increases the average speed of the production line, and increases the output. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of the main structure of the continuous annealing furnace.

[0035] Figure 2 It is a comparison diagram of the prediction results of the Sigmoid-ARX model of the present invention and the real data.

[0036] Figure 3 It is a structure diagram of the Sigmoid-ARX model predictive control system of the present invention.

[0037] Figure 4 It is a comparison diagram of the temperature error distribution under traditional control and MPC control.

[0038] Figure 5 It is an effect diagram of speed and temperature control when the thick strip of the present invention transitions to the thin strip.

[0039] Figure 6 It is an effect diagram of speed and temperature control when the thin strip of the present invention transitions to the thick strip.

[0040] Figure 7 It is a comparison diagram of the present invention's MPC control and traditional control in terms of temperature and speed standard deviations.

[0041] Figure 8 It is a comparison diagram of the average speed of the present invention's MPC control and traditional control.

[0042] Figure 9 It is a schematic diagram of the HMI operation interface of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0043] In order to make the technical means, creative features, achieved purposes and functions of the present invention easy to understand, the present invention will be further described below in conjunction with specific embodiments.

[0044] Please refer to Figures 1-9 , the present invention provides the following technical solutions:

[0045] A nonlinear model predictive control method for strip temperature of a continuous annealing furnace, comprising the following steps:

[0046] S1: Collect historical data during the production process of the continuous annealing furnace; the historical data includes strip width, thickness, steel grade, speed, set temperature in the heating section, inlet temperature in the heating section, and outlet temperature in the heating section, etc.

[0047] S2: Establish a nonlinear autoregressive exogenous input model based on Sigmoid-ARX; the mathematical expression of the nonlinear autoregressive exogenous input model of Sigmoid-ARX is:

[0048] y t = f(Y,U) + e t = f(y t-1 ,y t-2 ,…,y t-n ,u t-1 ,u t-2 ,…,u t-m ) + e t

[0049] where, y t is the system target output, i.e., the outlet temperature in the heating section; u t is the exogenous input variable affecting the target output, including strip width, thickness, speed, steel grade, and inlet temperature in the heating section. n and m are the lag orders of the target variable and the exogenous input variable respectively. f is a nonlinear function using the Sigmoid function as the activation function, and e t is the error term of the model.

[0050] S3: Optimize the model parameters through the Levenberg-Marquardt algorithm, and evaluate the model performance through the AIC value and RMSE.

[0051] S4: Based on the optimized Sigmoid-ARX model, design a nonlinear model predictive controller. The controller structure is as Figure 3 shown, including a model predictive controller, an actuator, and a state estimator, etc.;

[0052] Perform local linearization near the given operating point. The local linearization is to perform a first-order Taylor expansion near the given operating point (y0,u0) to obtain a local linear model:

[0053]

[0054] Convert the nonlinear optimization problem into a quadratic programming problem. The expression of the quadratic programming problem is:

[0055]

[0056] Among them, \(u\) is the optimization variable, \(H\) is the Hessian matrix, \(f\) is the linear term coefficient vector, \(P\) is the constraint matrix, \(b\) is the constraint vector, and \(f_0\) is the constant term. \(f_0\) does not affect the optimization result but only affects the optimal value.

[0057] S5: Design the objective function, with controlling the strip temperature near the target temperature as the primary objective and maximizing the production line speed as the secondary objective under the condition of meeting the temperature requirements; the expression of the objective function is:

[0058]

[0059] Among them, \(T\) strip is the actual strip temperature, \(T\) target is the target strip temperature, \(v\) is the strip speed, \(setT\) is the set temperature value, \(\Delta v\) is the speed change, \(\Delta setT\) is the set temperature change, \(W\) T and \(W\) v 、\(W\) setT 、\(W\) Δv 、\(W\) ΔsetT are weight matrices, \(W\) T is the weight of the temperature error, \(W\) v and \(W\) setT are the speed and temperature weights respectively, \(W\) Δv and \(W\) ΔsetT are the weights of the temperature and speed control increments respectively, and \(n\) is the prediction horizon length.

[0060] S6: Set the control constraint conditions, including strip temperature constraints, speed constraints, and actuator constraints; the constraint conditions are as follows:

[0061] Strip temperature constraint: \(y\) min ≤y(t + i|t)≤y max , i = 1, 2…, N

[0062] Speed constraint: \(v\) min ≤v(t + i - 1)≤v max , i = 1, 2…, N

[0063] Actuator constraint: \(\Delta u\) min ≤\(\Delta u\)(t + i - 1)≤\(\Delta u\) max , i = 1, 2…, N.

[0064] S7: Solve the quadratic programming problem to obtain the optimal control sequence.

[0065] S8: Apply the first element of the optimal control sequence as the control input to the continuous annealing furnace system.

[0066] S9: At the next sampling moment, repeat steps S4 to S8 to implement rolling optimization control.

[0067] Compare the prediction results of the model with the actual production data. As Figure 2 shown, verify the accuracy of the model. The prediction accuracy of the Sigmoid-ARX model of the present invention is as high as 85.26%.

[0068] Experiment with the Sigmoid-ARX model of the present invention and traditional control methods to obtain the following conclusions:

[0069] (1) Temperature control accuracy: As Figure 4 shown, compared with the traditional control method, the MPC control of the present invention increases the proportion of the strip temperature error within the range of ±5°C from 50% to 77%;

[0070] (2) Transition control of strips of the same specification: As Figure 5 and Figure 6 shown, when transitioning from thick strips to thin strips and from thin strips to thick strips, the MPC controller of the present invention can achieve good coordinated control of speed and temperature;

[0071] (3) Improvement of production stability and output: As Figure 7 and Figure 8 shown, compared with the traditional control method, the MPC control of the present invention reduces the standard deviation of the strip temperature and speed, increases the average speed of the production line, and increases the output;

[0072] As Figure 9 shown, a switch for starting and stopping the control model of the present invention and the display of related parameters are added to the HMI operation interface, facilitating the setting and operation of the control model.

[0073] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A non - linear model predictive control method for the strip temperature of a continuous annealing furnace, characterized in that, It includes the following steps: S1: Collect historical data during the production process of the continuous annealing furnace; S2: Establish a non - linear autoregressive exogenous input model based on Sigmoid - ARX; S3: Optimize the model parameters through the Levenberg - Marquardt algorithm; S4: Based on the optimized Sigmoid - ARX model, design a non - linear model predictive controller, perform local linearization near the given operating point, and transform the non - linear optimization problem into a quadratic programming problem; S5: Design the objective function, taking controlling the strip temperature near the target temperature as the primary goal and maximizing the production line speed as the secondary goal under the condition of meeting the temperature requirements; S6: Set control constraint conditions, including strip temperature constraints, speed constraints, and actuator constraints; S7: Solve the quadratic programming problem to obtain the optimal control sequence; S8: Apply the first element of the optimal control sequence as the control input to the continuous annealing furnace system; S9: At the next sampling moment, repeat steps S4 to S8 to achieve rolling optimization control.

2. The nonlinear model predictive control method for the strip temperature of a continuous annealing furnace according to claim 1, characterized in that: In the above - mentioned S1, the historical data includes strip width, thickness, steel grade, speed, set temperature in the heating section, inlet temperature in the heating section, and outlet temperature in the heating section.

3. The nonlinear model predictive control method for strip temperature of a continuous annealing furnace according to claim 1, characterized in that In the above - mentioned S2, the mathematical expression of the non - linear autoregressive exogenous input model of Sigmoid - ARX is: y t = f(Y, U) + e t = f(y t-1 , y t-2 , …, y t-n , u t-1 , u t-2 , …, u t-m ) + e t Among them, y t is the system target output, i.e., the temperature at the outlet of the heating section; u t is the exogenous input variable affecting the target output, including strip width, thickness, speed, steel grade, and the temperature at the inlet of the heating section. n and m are the lag orders of the target variable and the exogenous input variable respectively, f is a non-linear function using the Sigmoid function as the activation function, and e t is the error term of the model.

4. The non-linear model predictive control method for strip temperature of a continuous annealing furnace according to claim 3, characterized in that In the above - mentioned S4, the local linearization is to perform a first - order Taylor expansion near the given operating point (y0, u0) to obtain the local linear model:

5. The nonlinear model predictive control method for strip temperature of a continuous annealing furnace according to claim 3, characterized in that, In the above - mentioned S4, the expression of the quadratic programming problem is: Among them, u is the optimization variable, H is the Hessian matrix, f is the coefficient vector of the linear term, P is the constraint matrix, b is the constraint vector, and f0 is the constant term.

6. The nonlinear model predictive control method for the strip temperature of a continuous annealing furnace according to claim 5, characterized in that: In the above - mentioned S5, the expression of the objective function is: Among them, T strip is the actual temperature of the strip steel, T target is the target temperature of the strip steel, v is the strip steel speed, setT is the set temperature value, Δv is the speed change amount, ΔsetT is the set temperature change amount, W T and W v 、W setT 、W Δv 、W ΔsetT are weight matrices, W T is the weight of the temperature error, W v and W setT are the speed and temperature weights respectively, W Δv and W ΔsetT are the weights of the temperature and speed control increments respectively, and n is the prediction time domain length.

7. The nonlinear model predictive control method for the strip temperature of a continuous annealing furnace according to claim 1, characterized in that, In the above - mentioned S6, the constraint conditions include: Strip temperature constraint: y min ≤y(t+i|t)≤y max , i = 1, 2…, N Velocity constraint: v min ≤ v(t + i - 1) ≤ v max , i = 1, 2…, N Actuator constraint: Δu min ≤Δu(t + i - 1)≤Δu max , i = 1, 2…, N.

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