Data-driven thickness and tension control method for tandem cold rolling system

Abstract

The present invention discloses a data-driven thickness and tension control method for a tandem cold rolling system, which relates to the technical field of intelligent predictive control. The present invention uses a non-autonomous data-driven neural network model for prediction, and realizes dynamic mapping of tension and thickness parameters through a self-learning mechanism, so that high-precision prediction can be completed without relying on real-time measurement data. This method effectively overcomes the hysteresis and error accumulation problems of the traditional measurement link, and effectively suppresses the deviation transmission in the collaborative control of multiple racks while significantly improving the prediction efficiency. The Laguerre function is integrated, and the parameter dimensionality reduction of the network weight space is achieved through orthogonal projection, which reduces the amount of calculation and shortens the time to reach the target value. A multivariable coupling mathematical model of cold-rolled strip tension and thickness is constructed, and based on the distributed optimal control theory framework, the Nash equilibrium game optimization strategy is introduced to realize multi-objective collaborative optimization control of tension and thickness.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent prediction control, and in particular relates to a thickness and tension control method of a tandem cold rolling system based on data driving. Background Art

[0002] Cold rolling is a core process in sheet metal processing. The coordinated control of thickness and tension during the process directly determines the dimensional accuracy and mechanical properties of the final product. Under high-speed rolling conditions, deviations in strip thickness can lead to an increase in the finished product's shape defect rate by over 30%, while tension fluctuations exceeding ±5% can cause strip breakage. More critically, the strong coupling between thickness and tension can lead to oscillation failure of the thickness control system. This nonlinear, time-varying characteristic means that single-parameter control often leads to systemic quality risks.

[0003] At present, Chinese patent CN118635278A discloses a double-stand secondary cold rolling control system, method and device for tension roller group, such as Figure 1 As shown, the tension control method is as follows: determine a first tension corresponding to the inlet side of the tension roller group, and determine a second tension corresponding to the outlet side of the tension roller group; based on the first tension and the second tension, determine a third tension corresponding to the first tension roller and the second tension roller respectively; when the first parameter value corresponding to the first tension roller and the second parameter value corresponding to the second tension roller are the same, determine a fourth tension corresponding to the inlet side of the tension roller group and a fifth tension corresponding to the outlet side of the tension roller group based on the first tension, the second tension and the third tension; and based on the fourth tension and the fifth tension, respectively allocate tension to the first tension roller and the second tension roller in the tension roller group. Chinese patent CN118768394B discloses a dual-stand secondary cold rolling control system, method and device for speed distribution, such as Figure 2 As shown, the speed control method is as follows: based on the rolling relationship achieved by the first stand and the second stand, the dual-stand secondary cold rolling production line corresponding to the transmission mechanism is divided into multiple areas, wherein the rolling relationship is used to indicate the thickness relationship of the strip corresponding to each area; the speed distribution parameter is obtained, and the speed information of each area is determined according to the speed distribution parameter; and the speed is respectively distributed to each area according to the determined speed information.

[0004] The tension control method of patent CN118635278A has the following technical limitations: First, this method is based on multi-stage tension calculation (deriving the third tension from the first and second tensions, and then determining the fourth and fifth tensions), which requires reliance on complex mathematical modeling and dynamic parameter adjustment. However, changes in material properties (such as fluctuations in the elastic modulus and unstable friction coefficient) or abnormal equipment status (such as roller wear) in actual working conditions can cause model parameters to deviate from their actual values, triggering a cumulative deviation effect, thereby reducing control accuracy. Second, its core control logic has a strong dependence on the tension detection data on the inlet and outlet sides. However, in actual applications, sensor performance limitations (such as measurement delays or errors of weighing sensors under high-frequency disturbances) can directly contaminate the data source, causing cascading errors in subsequent multi-stage tension distribution links. Third, the above two types of problems may couple with each other during the dynamic control process, further amplifying the risk of system instability, and ultimately affecting product quality and production efficiency.

[0005] Although patent CN118768394B achieves thickness adjustment through speed control, its technical solution has two limitations: first, the patent adopts a static mathematical model based on the regional division of the rolling relationship, and does not fully consider the impact of dynamic disturbances in the rolling process (such as tension mutation, thermal deformation of the roll, etc.) on the model accuracy, resulting in insufficient control robustness under actual working conditions; second, the setting of its speed distribution parameters (such as rolling rate, forward slip rate) is highly dependent on high-precision sensor data. When parameter calibration deviations occur in actual production due to sensor errors, changes in roll gap lubrication effect or fluctuations in material hardness, the static distribution model lacks a dynamic compensation mechanism and cannot achieve adaptive adjustment of parameters, thereby affecting the stability of thickness control.

[0006] The common disadvantage of the above two patents is that the control object is single, and both of the above two patents are only dual-stand control, while five-stand series cold rolling is usually used in engineering. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the present invention provides a data-driven thickness and tension control method for a tandem cold rolling system. This method utilizes a data-driven network discretization model to generate training data, trains the data, and constructs a deep residual network based on Laguerre function dimensionality reduction. This method then integrates a distributed optimal controller framework and introduces a Nash equilibrium distributed optimization strategy to achieve multi-objective dynamic coordinated control of tension and thickness. This method addresses the complex multi-level computational challenges inherent in existing control methods and reduces their strong reliance on real-time measurement data.

[0008] A first aspect of the present invention provides a data-driven method for controlling thickness and tension of a tandem cold rolling system, comprising the following steps:

[0009] Generate training dataset;

[0010] A residual network is constructed to approximate the nonlinear state transfer function of the series cold rolling system;

[0011] Use the training data set to train the residual network to obtain a trained residual network;

[0012] Based on the trained residual network, a distributed control model Data-DMPC based on Nash equilibrium is constructed, and the distributed control model Data-DMPC based on Nash equilibrium is used to control the tension and thickness of the series cold rolling system.

[0013] Furthermore, the generating of the training data set is specifically as follows:

[0014] A1: Construct a discrete state space model of cold rolling for tandem cold rolling system;

[0015] (1);

[0016] in, Tandem cold rolling system The increment of the state variable at time , For the A moment, is the time sequence number, is the state transition matrix, To control the input increment, including the adjustment amount of the roll gap and the adjustment amount of the roll linear speed, is the system uncertainty parameter, is the adjustment amount of the roller gap, is the adjustment amount of the roller linear speed, is the perturbation input matrix, Tandem cold rolling system External disturbances at any moment, Tandem cold rolling system The output variable at time, is the output observation matrix, is the control input matrix, is transposed;

[0017] A2: Increment the control input in the cold rolling discrete state space model of the tandem cold rolling system parameterized over a local time period;

[0018] For a local time period , the length of this local time period is ,in, For the a moment;

[0019] Select the quadratic polynomial as the basis function and set the control input increment The parameterization in the local time period is as follows:

[0020] (2);

[0021] in, is the local control input, is a local time variable, is a local parameter set, is the initial reference value of the control input increment, is the linear rate of change of the control input increment, is the quadratic rate of change of the control input increment;

[0022] A3: Based on the parameterization results of the control input increment in the local time period, obtain data samples for each local time period;

[0023] The method for obtaining data samples for each local time period is as follows: , first, from the state space I x The current state variable increment is obtained by uniform sampling , then, randomly generate a local parameter set , and construct local control input ,in is the value range constraint of the local parameter set. Then, a high-precision numerical method is used to solve the cold rolling discrete state space model of the tandem cold rolling system to obtain the state variable increment at the next moment: , finally, save the data sample ( );

[0024] A4: Aggregate the data samples from all local time periods into a training dataset;

[0025] The training dataset is represented as:

[0026] (3);

[0027] in, is the training data set, is the number of the data sample, is the total number of samples, For the The current state variable increment in data samples, For the The increment of the state variable at the next moment in the data sample, For the The local parameter set in the data sample, For the The length of the local time period in a data sample.

[0028] Furthermore, the residual network is used to approximate the nonlinear state transfer function of the series cold rolling system , The nonlinear state transfer function is used to describe the dynamic characteristics of the tandem cold rolling system. The residual network input is the current state variable increment. , local parameter set and the length of the local time period , the output is the state variable increment at the next moment .

[0029] Furthermore, the dimension of the input layer in the residual network is , the hidden layer is a multi-layer fully connected layer, each layer uses an activation function, and the dimension of the output layer is , directly predict the state variable increment at the next moment, where is the dimension of the state variable increment, The number of coefficients of the quadratic polynomial used when inputting increments for parametric control.

[0030] Furthermore, the mapping form of the residual network is:

[0031] (7);

[0032] in, is the next moment state variable increment predicted by the residual network, is the residual network, are the parameters of the residual network.

[0033] Furthermore, the distributed control model Data-DMPC based on Nash equilibrium includes Z control models Data-MPC and 1 communication system. The first control model Data-MPC is used to adjust the roll gap opening of the first frame, the second to Z-1 control models Data-MPC are used to adjust the roll gap opening of the corresponding frame and the roll linear speed of the previous frame, and the Zth control model Data-MPC is used to adjust the roll linear speed of the Z-1th frame, thereby realizing the coordinated control of thickness and tension. At the same time, each control model Data-MPC communicates with other control models Data-MPC except itself through the communication system. A residual network is used in each control model Data-MPC to predict the state variable increment at the next moment, thereby obtaining the state prediction value.

[0034] Furthermore, the method for controlling the tension and thickness of the tandem cold rolling system using the distributed control model Data-DMPC based on Nash equilibrium is specifically as follows:

[0035] B1: Treat each stand in the series cold rolling system as a subsystem and construct the state equation of each subsystem;

[0036] The state equation of each subsystem is:

[0037] (10);

[0038] in, For the subsystem, For subsystem exist The coupling state at the moment, For subsystem exist The state of the moment, is the state dimension, For subsystem exist The control input at the moment, To control the input dimension, is the nonlinear state transfer function, Representation and Subsystem Coupled neighbor sets, For subsystem subsystems in a coupled set of neighbors, To describe the subsystem Subsystem The coupling effect, For subsystem exist The state of the moment, For subsystem exist Control input at each moment;

[0039] B2: Establish local objective optimization function for each subsystem;

[0040] The Laguerre orthogonal basis function is used to expand the control input increment and map the high-dimensional control input to the low-dimensional parameter space:

[0041] (11);

[0042] in, For the future moment Subsystem The control input increment, To predict discrete time steps in the time domain, is the oth-order Laguerre orthogonal basis function at the future time The value of For subsystem The expansion coefficient of the control input increment on the oth order Laguerre orthogonal basis function, is the order of the Laguerre orthogonal basis function, and o is the order index of the Laguerre orthogonal basis function;

[0043] Subsystem The local objective optimization function is:

[0044] (12);

[0045] in, For subsystem The target optimization function value is To predict the number of time domain steps, For subsystem The state in the future The predicted value of is the reference state vector, is the weight matrix of the state tracking error, is the coefficient vector of the Laguerre orthogonal basis function, which includes the subsystem The expansion coefficient of the control input increment on all order Laguerre orthogonal basis functions, Regularize the weight matrix for control input;

[0046] B3: Construct the optimization problem of each subsystem based on its local objective optimization function;

[0047] Each subsystem solves the following optimization problem:

[0048] (13);

[0049] in, For the The coefficient vector of the Laguerre orthogonal basis function after iterative rounds of optimization, is the iteration round;

[0050] B4: Iteratively solve the optimization problem of each subsystem to obtain the coefficient vector of the optimized Laguerre orthogonal basis function;

[0051] B5: Calculate the control input increment at the current moment based on the coefficient vector of the optimized Laguerre orthogonal basis function;

[0052] The Laguerre orthogonal basis function coefficients obtained after optimization are set to , then the control input increment at the current moment is calculated as:

[0053] (20);

[0054] in, The subsystem at the current moment The control input increment, is the initial value of the oth-order Laguerre orthogonal basis function;

[0055] B6: Obtain the absolute control input at the current moment based on the control increment at the current moment;

[0056] (twenty one);

[0057] in, For subsystem At the moment The absolute control input, For subsystem Absolute control input at the previous moment;

[0058] The absolute values ​​of the roll gap and the roll linear speed are:

[0059] (twenty two);

[0060] (twenty three);

[0061] B7: The tandem cold rolling system implements absolute control input to achieve coordinated control of tension and thickness.

[0062] Furthermore, the optimization problem of each subsystem is iteratively solved to obtain the coefficient vector of the optimized Laguerre orthogonal basis function, specifically:

[0063] B4.1: Set the current iteration round to 1 and initialize the coefficient vector of the Laguerre orthogonal basis function;

[0064] B4.2: Based on the current state variable increment, local parameter set, and local time segment length of each subsystem, use the trained residual network to predict the next state variable increment.

[0065] B4.3: Add the next-moment increment of each subsystem's state variable to the measured state of the subsystem at the current moment to obtain the predicted state value of the subsystem.

[0066] (14);

[0067] in, For the Iteration round subsystem The state prediction value, 、 、 and Respectively Iteration round subsystem The thickness prediction value, tension prediction value, roll gap prediction value and roll linear speed prediction value;

[0068] B4.4: Solve the optimization problem for each subsystem and obtain the coefficient vector of the updated Laguerre orthogonal basis function;

[0069] (15);

[0070] in, It is Subsystem updated after iterations The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function;

[0071] B4.5: Use the communication system to broadcast the updated coefficient vector of the Laguerre orthogonal basis function and the state prediction value of each subsystem;

[0072] B4.6: Each subsystem updates its coupling state based on the broadcasted updated state prediction value of each subsystem to obtain the coupling state of each subsystem;

[0073] (16);

[0074] in, For the Iteration round subsystem exist The coupling state at the moment;

[0075] B4.7: Calculate the maximum relative change in the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems;

[0076] (17);

[0077] in, For the The maximum relative change of the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems in the iteration round is: For the The coefficient vector of the Laguerre orthogonal basis function for the iteration round;

[0078] (18);

[0079] in, It is Subsystem updated after iterations The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function;

[0080] B4.8: Nash equilibrium convergence is determined based on the maximum relative change in the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems, and the threshold is set to ,like , output the coefficient vector of the Laguerre orthogonal basis function of the current iteration as the coefficient vector of the optimal Laguerre orthogonal basis function, otherwise add 1 to the current iteration and return to B4.2;

[0081] (19);

[0082] in, is the coefficient vector of the optimal Laguerre orthogonal basis function, The coefficient vector of the optimal Laguerre orthogonal basis function is the subsystem The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function.

[0083] The second aspect of the present invention provides an electronic device, comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the data-driven tandem cold rolling system thickness and tension control method are performed.

[0084] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored therein. When the computer program is executed by a processor, the steps of the data-driven tandem cold rolling system thickness and tension control method are executed.

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] 1. Utilizing a non-autonomous data-driven neural network model for prediction, a self-learning mechanism enables dynamic mapping of tension and thickness parameters, enabling high-precision prediction without relying on real-time measurement data. This approach effectively overcomes the hysteresis and error accumulation inherent in traditional measurement processes, significantly improving prediction efficiency while effectively suppressing bias propagation in multi-rack collaborative control.

[0087] 2. The Laguerre function is integrated into the neural network model, and the parameter dimension reduction of the network weight space is achieved through orthogonal projection, which reduces the amount of calculation and shortens the time to reach the target value.

[0088] 3. By constructing a multivariable coupled mathematical model for cold-rolled strip tension and thickness and introducing a Nash equilibrium game optimization strategy based on the framework of distributed optimal control theory, we achieved multi-objective coordinated optimization control of tension and thickness. This approach effectively overcomes the strong coupling interference between mill stands and ultimately successfully established a high-precision dynamic coordinated control system for the tandem cold rolling system. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a flow chart of the tension control method in the prior art;

[0090] Figure 2 It is a flow chart of the speed control method in the prior art;

[0091] Figure 3 Schematic diagram of the equipment layout of a five-stand tandem cold rolling mill according to an embodiment of the present invention;

[0092] Figure 4 Generate a point cloud image of a training data set in an embodiment of the present invention;

[0093] Figure 5 This is a data-driven neural network logic diagram in an embodiment of the present invention;

[0094] Figure 6 A closed-loop MPC system in an embodiment of the present invention;

[0095] Figure 7 Schematic diagram of the control system structure of a tandem cold rolling mill in an embodiment of the present invention;

[0096] Figure 8 This is a five-rack control simulation diagram based on Data-MPC in an embodiment of the present invention. DETAILED DESCRIPTION

[0097] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0098] In this embodiment, a five-stand series cold rolling system is taken as an example, and its equipment layout is as follows: Figure 3 shown.

[0099] A data-driven method for controlling thickness and tension of a tandem cold rolling system comprises the following steps:

[0100] Step 1: Generate training dataset;

[0101] Step 1.1: Construct a cold rolling discrete state space model of the tandem cold rolling system;

[0102] (1);

[0103] in, Tandem cold rolling system The increment of the state variable at time , For the A moment, is the time sequence number, is the state transfer matrix (coefficient matrix describing the dynamic characteristics of the tandem cold rolling system), To control the input increment, including the adjustment amount of the roll gap and the adjustment amount of the roll linear speed, is the system uncertainty parameter, is the adjustment amount of the roller gap, is the adjustment amount of the roller linear speed, is the perturbation input matrix, Tandem cold rolling system External disturbances at any moment, Tandem cold rolling system The output variable at time, is the output observation matrix, is the control input matrix (the influence coefficient of the control input on the state), is transposed;

[0104] Step 1.2: Increment the control input in the cold rolling discrete state space model of the tandem cold rolling system parameterized over a local time period;

[0105] For a local time period , the length of this local time period is ,in, For the a moment;

[0106] Select the quadratic polynomial as the basis function and set the control input increment The parameterization in the local time period is as follows:

[0107] (2);

[0108] in, is the local control input, is a local time variable, is a local parameter set, is the initial reference value of the control input increment, is the linear rate of change of the control input increment, is the quadratic rate of change of the control input increment;

[0109] Step 1.3: Based on the parameterization result of the control input increment in the local time period, obtain the data sample of each local time period;

[0110] The method for obtaining data samples for each local time period is as follows: , first, from the state space I x The current state variable increment is obtained by uniform sampling , then, randomly generate a local parameter set , and construct local control input ,in is the value range constraint of the local parameter set. Then, a high-precision numerical method (such as the fourth-order Runge-Kutta) is used to solve the cold rolling discrete state space model of the tandem cold rolling system to obtain the state variable increment at the next moment: , finally, save the data sample ( );

[0111] Step 1.4: Aggregate the data samples of all local time periods into a training data set;

[0112] The training dataset is represented as:

[0113] (3);

[0114] in, is the training data set, is the number of the data sample, is the total number of samples, For the The current state variable increment in data samples, For the The increment of the state variable at the next moment in the data sample, For the The local parameter set in the data sample, For the The length of the local time period in the data sample; the five-rack training data set generated in this embodiment is as follows Figure 4 As shown;

[0115] After completing the above steps, we need to verify whether the local control input can accurately generate the dynamic evolution process of the state variable increment from the initial moment to the final moment. The derivation method is as follows:

[0116] a. Local control input within a local time period:

[0117] (4);

[0118] b. Cold rolling discrete state space model integration:

[0119] (5);

[0120] in, is the external disturbance of the tandem cold rolling system;

[0121] The integral term is:

[0122] (6);

[0123] c. Consistency with numerical solutions: Use numerical methods such as Runge-Kutta to verify whether the integration results of the cold rolling discrete state space model are consistent with the state variable increments directly calculated by substituting the local control input into the analytical integration formula (i.e., formula (5) and formula (6));

[0124] Step 2: Construct a residual network (ResNet); the residual network approximates the nonlinear state transfer function of the series cold rolling system , The nonlinear state transfer function is used to describe the dynamic characteristics of the tandem cold rolling system. The residual network input is the current state variable increment. , local parameter set and the length of the local time period , the output is the state variable increment at the next moment ;

[0125] The dimension of the input layer in the residual network is , the hidden layer is a multi-layer fully connected layer, each layer uses an activation function (such as tanh), and the dimension of the output layer is , directly predict the state variable increment at the next moment, where is the dimension of the state variable increment (such as tension and roller gap, etc.), The number of coefficients of the quadratic polynomial used for parameterized control input increments. = 3;

[0126] The mapping form of the residual network is:

[0127] (7);

[0128] in, is the next moment state variable increment predicted by the residual network, is the residual network, are the parameters of the residual network;

[0129] Step 3: Use the training data set to train the residual network to obtain the trained residual network;

[0130] By minimizing the mean square error between the predicted state variable increment at the next moment and the actual state variable increment at the next moment, the residual network prediction is forced to be close to the actual state variable increment at the next moment. The loss function of the training process is as follows:

[0131] (8);

[0132] in, is the loss function, is the residual network prediction The next moment state variable increment of a data sample;

[0133] Use an optimization algorithm (such as Adam) to update the parameters of the residual network , until convergence, the update rule is:

[0134] (9);

[0135] in, are the parameters of the residual network before updating, are the parameters of the updated residual network, is the learning rate, and are the bias-corrected first-order and second-order moment estimates of the gradient, is a numerical stability constant, and the data-driven neural network logic is as follows Figure 5 As shown;

[0136] Step 4: Based on the trained residual network, a distributed control model Data-DMPC based on Nash equilibrium is constructed, and the distributed control model Data-DMPC based on Nash equilibrium is used to control the tension and thickness of the tandem cold rolling system;

[0137] For the tandem cold rolling system, the distributed model predictive control stage can not only ensure the global performance, but also effectively improve the flexibility of the control system and reduce the amount of calculation. The distributed control model Data-DMPC based on Nash equilibrium includes 6 control models Data-MPC and 1 communication system. The first control model Data-MPC is used to adjust the roll gap opening of the first stand, the second to fifth control models Data-MPC are used to adjust the roll gap opening of the corresponding stand and the roll linear speed of the previous stand, and the sixth control model Data-MPC is used to adjust the roll linear speed of the fifth stand, thereby realizing the coordinated control of thickness and tension. At the same time, each control model Data-MPC communicates with other control models Data-MPC except itself through the communication system, such as Figure 6 and Figure 7 As shown in the figure, HGC is the roll gap control of the roll by Data-MPC, and Drv is the speed control of the roll by Data-MPC. The method of using the distributed control model Data-DMPC based on Nash equilibrium to control the tension and thickness of the tandem cold rolling system is as follows:

[0138] Step 4.1: Treat each stand in the tandem cold rolling system as a subsystem and construct the state equation of each subsystem;

[0139] The state equation of each subsystem is:

[0140] (10);

[0141] in, For the subsystem, For subsystem exist The coupling state at the moment, For subsystem exist The state at the moment (including the current tension value, current thickness value, actual roll gap value and actual roll linear speed value), is the state dimension, For subsystem exist The control input at each moment (including the roll gap and the roll linear speed), To control the input dimension, is the nonlinear state transfer function, Representation and Subsystem Coupled neighbor sets, For subsystem subsystems in a coupled set of neighbors, To describe the subsystem Subsystem The coupling effect, For subsystem exist The state of the moment, For subsystem exist Control input at each moment;

[0142] Step 4.2: Establish the local objective optimization function for each subsystem;

[0143] Traditional MPC requires full-dimensional optimization of control inputs at multiple future moments, and the computational complexity increases exponentially with the control time domain. This paper uses Laguerre orthogonal basis functions to expand the control input increments and map the high-dimensional control inputs to a low-dimensional parameter space:

[0144] (11);

[0145] in, For the future moment Subsystem The control input increment, To predict discrete time steps in the time domain, is the oth-order Laguerre orthogonal basis function at the future time The value of For subsystem The expansion coefficient of the control input increment on the oth-order Laguerre orthogonal basis function (parameter to be optimized), is the order of the Laguerre orthogonal basis function, o is the order index (sum index) of the Laguerre orthogonal basis function;

[0146] Therefore, the subsystem The local objective optimization function is:

[0147] (12);

[0148] in, For subsystem The target optimization function value is To predict the number of time domain steps, For subsystem The state in the future The predicted value of is the reference state vector, is the weight matrix of the state tracking error, is the coefficient vector of the Laguerre orthogonal basis function, which includes the subsystem The expansion coefficient of the control input increment on all order Laguerre orthogonal basis functions, Regularize the weight matrix for control input;

[0149] Step 4.3: Construct the optimization problem for each subsystem based on its local objective optimization function;

[0150] Each subsystem solves the following optimization problem:

[0151] (13);

[0152] in, For the The coefficient vector of the Laguerre orthogonal basis function after iterative rounds of optimization, is the iteration round;

[0153] Step 4.4: Iteratively solve the optimization problem of each subsystem to obtain the coefficient vector of the optimized Laguerre orthogonal basis function;

[0154] Step 4.4.1: Set the current iteration round to 1 and initialize the coefficient vector of the Laguerre orthogonal basis function;

[0155] Step 4.4.2: Use a data-driven residual network to replace the state transition equation in the traditional MPC method. Based on the current state variable increment, local parameter set, and local time segment length of each subsystem, use the trained residual network to predict the next state variable increment.

[0156] Step 4.4.3: Add the next-moment increment of the state variable of each subsystem to the measured state of the subsystem at the current moment to obtain the predicted state value of the subsystem;

[0157] (14);

[0158] in, For the Iteration round subsystem The state prediction value, 、 、 and Respectively Iteration round subsystem The thickness prediction value, tension prediction value, roll gap prediction value and roll linear speed prediction value;

[0159] Step 4.4.4: Solve the optimization problem of each subsystem by using QP (quadratic programming) or gradient descent to obtain the coefficient vector of the updated Laguerre orthogonal basis function;

[0160] (15);

[0161] in, It is Subsystem updated after iterations The control input increment is the expansion coefficient on the o-th order Laguerre orthogonal basis function, which is solved by QP (quadratic programming) or gradient descent;

[0162] Step 4.4.5: Use the communication system to broadcast the updated coefficient vector of the Laguerre orthogonal basis function and the state prediction value of each subsystem to ensure the consistency of the dynamics of each subsystem;

[0163] Step 4.4.6: Each subsystem updates its coupling state according to the broadcasted updated state prediction value of each subsystem to obtain the coupling state of each subsystem;

[0164] (16);

[0165] in, For the Iteration round subsystem exist The coupling state at the moment is dynamically modified by transmitting the base coefficient and the predicted state through communication;

[0166] Step 4.4.7: Calculate the maximum relative change in the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems;

[0167] (17);

[0168] in, For the The maximum relative change of the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems in the iteration round is: For the The coefficient vector of the Laguerre orthogonal basis function for the iteration round;

[0169] The norm selection uses the two-norm to measure the relative change of the coefficient vector, that is:

[0170] (18);

[0171] in, It is Subsystem updated after iterations The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function;

[0172] Step 4.4.8: Based on the maximum relative change of the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems, the Nash equilibrium convergence is determined, and the threshold is set to ,like , output the coefficient vector of the Laguerre orthogonal basis function of the current iteration as the coefficient vector of the optimal Laguerre orthogonal basis function, otherwise add 1 to the current iteration and return to step 4.4.2;

[0173] (19);

[0174] in, is the coefficient vector of the optimal Laguerre orthogonal basis function, The coefficient vector of the optimal Laguerre orthogonal basis function is the subsystem The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function;

[0175] Step 4.5: Based on the coefficient vector of the optimized Laguerre orthogonal basis function, solve the control input increment at the current moment;

[0176] Assume that the Laguerre orthogonal basis function coefficients obtained after optimization are , then the control input increment at the current moment is calculated as:

[0177] (20);

[0178] in, The subsystem at the current moment The control input increment (such as roll gap adjustment and roll linear speed adjustment), is the initial value of the oth-order Laguerre orthogonal basis function, and the value of the Laguerre orthogonal basis function at the initial value is , the low-dimensional coefficients Converted into instantaneous control increment at the current moment;

[0179] Step 4.6: Obtain the absolute control input at the current moment based on the control increment at the current moment;

[0180] Accumulate control increments as absolute values:

[0181] (twenty one);

[0182] in, For subsystem At the moment Absolute control input (such as the absolute value of the roll gap and the set value of the roll linear speed), For subsystem Absolute control input at the previous moment;

[0183] Then, the absolute values ​​of the roll gap and the roll linear speed are:

[0184] (twenty two);

[0185] (twenty three);

[0186] Through the integral operation, the control quantity is ensured to be continuous and smooth, avoiding the impact of step jumps on the actuator.

[0187] Step 4.7: The tandem cold rolling system performs absolute control input to achieve coordinated control of tension and thickness;

[0188] Finally, the five stands adjust and control the calculated control quantities, roll gap opening and roll linear speed, through hydraulic cylinders and frequency converters, to further control the thickness and tension of the strip, thus realizing coordinated control of tension and thickness of the five stands in series.

[0189] This embodiment also provides an electronic device, comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the data-driven tandem cold rolling system thickness and tension control method are performed.

[0190] This embodiment also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the data-driven tandem cold rolling system thickness and tension control method are executed.

[0191] In this embodiment, a data-driven thickness and tension control method for a tandem cold rolling system proposed in the present invention is simulated:

[0192] The initial target tension setting for rack one is 15.0kN and the thickness is 2.00mm; the initial target tension setting for rack two is 12.0kN and the thickness is 1.27mm; the initial target tension setting for rack three is 10.0kN and the thickness is 0.76mm; the initial target tension setting for rack four is 8.0kN and the thickness is 0.46mm; the initial target tension setting for rack five is 5.0kN and the thickness is 0.30mm.

[0193] At 15 seconds, the targets for each rack are changed. The secondary target settings for rack one are 30.0 kN tension and 5.00 mm thickness; rack two is 25.0 kN tension and 4 mm thickness; rack three is 20.0 kN tension and 3 mm thickness; rack four is 15 kN tension and 2 mm thickness; and rack five is 10 kN tension and 1 mm thickness.

[0194] At 30 seconds, the targets of each rack are changed again. The three-time target setting of rack one is 46.0kN tension and 10.00mm thickness; the three-time target setting of rack two is 40.0kN tension and 9mm thickness; the three-time target setting of rack three is 33.0kN tension and 8mm thickness; the three-time target setting of rack four is 27kN tension and 7mm thickness; the three-time target setting of rack five is 19kN tension and 6mm thickness. The simulation results are as follows: Figure 8 shown.

[0195] Table 1. Comparison of Data-DMPC and traditional control methods in the control of five-stand tandem cold rolling mill;

[0196] Thickness standard deviation / µm Tension overshoot / kN PI controller 13 3.44 Traditional MPC 8.7 1.8 Data-DMPC 8.1 0.5

[0197] The comparison between the Data-DMPC proposed in this invention and the traditional control method in the control of a five-stand tandem cold rolling mill is shown in Table 1.

Claims

1. A data-driven thickness and tension control method for a tandem cold rolling system, characterized in that: The following steps are involved: Generate training dataset; A residual network is constructed to approximate the nonlinear state transfer function of the series cold rolling system; Use the training data set to train the residual network to obtain a trained residual network; Based on the trained residual network, a distributed control model based on Nash equilibrium, Data-DMPC, is constructed. The distributed control model based on Nash equilibrium, Data-DMPC, is used to control the tension and thickness of the tandem cold rolling system. The residual network is used to approximate the nonlinear state transfer function of the series cold rolling system , The nonlinear state transfer function is used to describe the dynamic characteristics of the tandem cold rolling system. The residual network input is the current state variable increment. , local parameter set and the length of the local time period , the output is the state variable increment at the next moment ; The dimension of the input layer in the residual network is , the hidden layer is a multi-layer fully connected layer, each layer uses an activation function, and the dimension of the output layer is , directly predict the state variable increment at the next moment, where is the dimension of the state variable increment, The number of coefficients of the quadratic polynomial used when inputting increments for parameterized control; The distributed control model Data-DMPC based on Nash equilibrium includes Z control models Data-MPC and 1 communication system. The first control model Data-MPC is used to adjust the roll gap opening of the first frame, the second to Z-1 control models Data-MPC are used to adjust the roll gap opening of the corresponding frame and the roll linear speed of the previous frame, and the Zth control model Data-MPC is used to adjust the roll linear speed of the Z-1th frame, thereby realizing the coordinated control of thickness and tension. At the same time, each control model Data-MPC communicates with other control models Data-MPC except itself through the communication system. A residual network is used in each control model Data-MPC to predict the state variable increment at the next moment, thereby obtaining the state prediction value.

2. The data-driven tandem cold rolling system thickness and tension control method according to claim 1, characterized in that: The generating of the training data set is specifically as follows: A1: Construct a discrete state space model of cold rolling for tandem cold rolling system; （1）； in, Tandem cold rolling system The increment of the state variable at time , For the A moment, is the time sequence number, is the state transition matrix, To control the input increment, including the adjustment amount of the roll gap and the adjustment amount of the roll linear speed, is the system uncertainty parameter, is the adjustment amount of the roller gap, is the adjustment amount of the roller linear speed, is the perturbation input matrix, Tandem cold rolling system External disturbances at any moment, Tandem cold rolling system The output variable at time, is the output observation matrix, is the control input matrix, is transposed; A2: Increment the control input in the cold rolling discrete state space model of the tandem cold rolling system parameterized over a local time period; For a local time period , the length of this local time period is ,in, For the a moment; Select the quadratic polynomial as the basis function and set the control input increment The parameterization in the local time period is as follows: （2）； in, is the local control input, is a local time variable, is a local parameter set, is the initial reference value of the control input increment, is the linear rate of change of the control input increment, is the quadratic rate of change of the control input increment; A3: Based on the parameterization results of the control input increment in the local time period, obtain data samples for each local time period; The method for obtaining data samples for each local time period is as follows: , first, from the state space I x The current state variable increment is obtained by uniform sampling , then, randomly generate a local parameter set , and construct local control input ,in is the value range constraint of the local parameter set. Then, a high-precision numerical method is used to solve the cold rolling discrete state space model of the tandem cold rolling system to obtain the state variable increment at the next moment: , finally, save the data sample ( ); A4: Aggregate the data samples from all local time periods into a training dataset; The training dataset is represented as: （3）； in, is the training data set, is the number of the data sample, is the total number of samples, For the The current state variable increment in data samples, For the The increment of the state variable at the next moment in the data sample, For the The local parameter set in the data sample, For the The length of the local time period in a data sample.

3. The data-driven thickness and tension control method for a tandem cold rolling system according to claim 1, characterized in that: The mapping form of the residual network is: （7）； in, is the next moment state variable increment predicted by the residual network, is the residual network, are the parameters of the residual network.

4. The data-driven thickness and tension control method for a tandem cold rolling system according to claim 1, characterized in that: The method for controlling the tension and thickness of a tandem cold rolling system using the distributed control model Data-DMPC based on Nash equilibrium is specifically as follows: B1: Treat each stand in the series cold rolling system as a subsystem and construct the state equation of each subsystem; The state equation of each subsystem is: （10）； in, For the subsystem, For subsystem exist The coupling state at the moment, For subsystem exist The state of the moment, is the state dimension, For subsystem exist The control input at the moment, To control the input dimension, is the nonlinear state transfer function, Representation and Subsystem Coupled neighbor sets, For subsystem subsystems in a coupled set of neighbors, To describe the subsystem Subsystem The coupling effect, For subsystem exist The state of the moment, For subsystem exist Control input at each moment; B2: Establish local objective optimization function for each subsystem; The Laguerre orthogonal basis function is used to expand the control input increment and map the high-dimensional control input to the low-dimensional parameter space: （11）； in, For the future moment Subsystem The control input increment, To predict discrete time steps in the time domain, is the oth-order Laguerre orthogonal basis function at the future time The value of For subsystem The expansion coefficient of the control input increment on the oth order Laguerre orthogonal basis function, is the order of the Laguerre orthogonal basis function, and o is the order index of the Laguerre orthogonal basis function; Subsystem The local objective optimization function is: （12）； in, For subsystem The target optimization function value is To predict the number of time domain steps, For subsystem The state in the future The predicted value of is the reference state vector, is the weight matrix of the state tracking error, is the coefficient vector of the Laguerre orthogonal basis function, which includes the subsystem The expansion coefficient of the control input increment on all order Laguerre orthogonal basis functions, Regularize the weight matrix for control input; B3: Construct the optimization problem of each subsystem based on its local objective optimization function; Each subsystem solves the following optimization problem: （13）； in, For the The coefficient vector of the Laguerre orthogonal basis function after iterative rounds of optimization, is the iteration round; B4: Iteratively solve the optimization problem of each subsystem to obtain the coefficient vector of the optimized Laguerre orthogonal basis function; B5: Calculate the control input increment at the current moment based on the coefficient vector of the optimized Laguerre orthogonal basis function; The Laguerre orthogonal basis function coefficients obtained after optimization are set to , then the control input increment at the current moment is calculated as: （20）； in, The subsystem at the current moment The control input increment, is the initial value of the oth-order Laguerre orthogonal basis function; B6: Obtain the absolute control input at the current moment based on the control increment at the current moment; （21）； in, For subsystem At the moment The absolute control input, For subsystem Absolute control input at the previous moment; The absolute values ​​of the roll gap and the roll linear speed are: （22）； （23）； B7: The tandem cold rolling system implements absolute control input to achieve coordinated control of tension and thickness.

5. The data-driven thickness and tension control method for a tandem cold rolling system according to claim 4, characterized in that: The optimization problem of each subsystem is iteratively solved to obtain the coefficient vector of the optimized Laguerre orthogonal basis function, specifically: B4.1: Set the current iteration round to 1 and initialize the coefficient vector of the Laguerre orthogonal basis function; B4.2: Based on the current state variable increment, local parameter set, and local time segment length of each subsystem, use the trained residual network to predict the next state variable increment. B4.3: Add the next-moment increment of each subsystem's state variable to the measured state of the subsystem at the current moment to obtain the predicted state value of the subsystem. （14）； in, For the Iteration round subsystem The state prediction value, 、 、 and Respectively Iteration round subsystem The thickness prediction value, tension prediction value, roll gap prediction value and roll linear speed prediction value; B4.4: Solve the optimization problem for each subsystem and obtain the coefficient vector of the updated Laguerre orthogonal basis function; （15）； in, is the updated subsystem after the lth iteration The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function; B4.5: Use the communication system to broadcast the updated coefficient vector of the Laguerre orthogonal basis function and the state prediction value of each subsystem; B4.6: Each subsystem updates its coupling state based on the broadcasted updated state prediction value of each subsystem to obtain the coupling state of each subsystem; （16）； in, For the Iteration round subsystem exist The coupling state at the moment; B4.7: Calculate the maximum relative change in the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems; （17）； in, For the The maximum relative change of the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems in the iteration round is: For the The coefficient vector of the Laguerre orthogonal basis function for the iteration round; （18）； in, It is Subsystem updated after iterations The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function; B4.8: Nash equilibrium convergence is determined based on the maximum relative change in the coefficient vectors of the Laguerre orthogonal basis functions of all subsystems, and the threshold is set to ,like , output the coefficient vector of the Laguerre orthogonal basis function of the current iteration as the coefficient vector of the optimal Laguerre orthogonal basis function, otherwise add 1 to the current iteration and return to B4.2; （19）； in, is the coefficient vector of the optimal Laguerre orthogonal basis function, The coefficient vector of the optimal Laguerre orthogonal basis function is the subsystem The expansion coefficient of the control input increment on the o-th order Laguerre orthogonal basis function.

6. An electronic device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus. When the machine-readable instructions are executed by the processor, the steps of the data-driven tandem cold rolling system thickness and tension control method according to any one of claims 1 to 5 are performed.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of the data-driven tandem cold rolling system thickness and tension control method according to any one of claims 1 to 5.

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