Partition control method and system for temperature field of copper material heat treatment furnace

Abstract

The present application relates to the control field, specifically to a kind of copper material heat treatment furnace temperature field partition control method and system, the state space model of furnace temperature is established;In offline stage, by solving multi-parameter programming problem, a strategy library containing multiple efficient affine control law is calculated in advance, according to the coupling strength of each temperature zone in furnace, the furnace temperature state space is divided into multiple explicit control partitions, and a group of alternative control law is specified for each partition;When running online, according to the current furnace temperature, determine the partition to which it belongs, through short-time domain prediction, quickly select the performance cost minimum from the alternative control law of the partition as the current optimal law, when the predicted furnace temperature will enter the boundary of partition, the optimal control law of current partition and adjacent partition is weighted and mixed;Otherwise, directly adopt current optimal law to generate control instruction and apply to heater.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of control, and particularly relates to a method and system for partition control of a temperature field of a copper material heat treatment furnace. BACKGROUND

[0002] The heat treatment of copper materials is usually carried out in a heating furnace or a heating workshop. The furnace is usually divided into multiple temperature zones, and each temperature zone is independently controlled by a heating or cooling actuator. However, due to the existence of thermal radiation and thermal convection, there is a strong correlation between the temperature zones, and the control input of one temperature zone will not only affect its own temperature, but also affect the adjacent or even more distant temperature zones. Most existing control methods separately control a heating device, and lack of correlation management between the heating devices. Model predictive control (MPC) predicts the future output of the system by establishing a dynamic model of the object, and obtains the optimal control sequence at the current time by solving a finite-time open-loop optimization problem in each control cycle. The characteristics of model-based and rolling optimization enable MPC to better control the temperature of the temperature field. However, implicit MPC needs to solve a large amount of constraint optimization problems online at each sampling time, which is too heavy for online calculation and limits real-time application. Explicit model predictive control (eMPC) solves a multi-parameter programming problem offline, and pre-calculates the optimal control law as a piecewise affine function of the state space. In online application, only the current state needs to be looked up to obtain the control amount, which reduces the online calculation load. However, if the number of partitions in the state space is too large, the offline calculation and storage requirements will become impractical. Moreover, when the system state switches between different partition boundaries, the sudden change of the control law is likely to cause oscillation, affecting the smoothness of the control. Therefore, how to reduce the complexity of eMPC, improve its control performance, and ensure the smoothness of the control switching is a key problem to be solved. SUMMARY

[0003] In order to reduce the smoothness of the temperature control and the calculation amount of eMPC in the heat treatment of copper materials, in a first aspect, a method for partition control of a temperature field of a copper material heat treatment furnace is provided, comprising the following steps:

[0004] constructing a state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace;

[0005] In an offline stage, a multi-parameter programming problem is solved to generate a series of affine control laws for performance and energy consumption indicators of different process stages; and the state space is divided based on the coupling strength of each partition in the furnace to obtain multiple explicit control partitions, and each explicit control partition is associated with a set of candidate control laws composed of the affine control laws;

[0006] In the online stage, a current explicit control partition to which the current state vector belongs is determined, a quadratic performance cost is calculated for each control law in the set of candidate control laws associated with the current explicit control partition by short-time domain forward prediction, and the control law with the minimum cost is selected as the current optimal control law; when the state at the next time predicted by using the current optimal control law enters a boundary transition zone between the current partition and an adjacent partition, an adjacent optimal control law is selected for the set of candidate control laws associated with the adjacent partition by using the same prediction and evaluation method, and the current optimal control law and the adjacent optimal control law are smoothed and weighted to generate a control output; otherwise, the current optimal control law is directly used as the control output.

[0007] The control output is applied to the partition actuators of the heat treatment furnace.

[0008] Optionally, the state space model representing the thermodynamic transmission characteristics in the copper material heat treatment furnace is constructed, including:

[0009] The heating power of each partition heater is taken as a model input, and the temperature sensor measurement value of each partition is taken as a model state variable, input and output data are collected by applying a pseudo-random binary sequence excitation signal near a steady-state operating point, and the state space model is established by using a subspace identification method.

[0010] Optionally, the performance and energy consumption indicators for different process stages are used to solve a multi-parameter programming problem to generate a series of affine control laws, including:

[0011] A cost function is constructed with the quadratic norm of temperature tracking error and the quadratic norm of control input increment in the future prediction time domain as optimization objectives, wherein the weight matrix Q of the temperature tracking error is a diagonal matrix with diagonal elements of 1.5, and the weight matrix R of the control input increment is a diagonal matrix with diagonal elements of 0.2.

[0012] The solving is performed under the constraints that the heating power change rate is not greater than 5 kW / min and the partition temperature does not exceed the upper and lower limits of the process requirement by 5℃.

[0013] Optionally, the state space is divided into a plurality of explicit control partitions based on the coupling strength of each partition in the furnace, including:

[0014] The relative gain matrix is calculated according to the steady-state gain matrix of the state space model.

[0015] Two partitions with a relative gain value greater than 0.7 are taken as strongly coupled partitions, and all partitions with strong coupling relationship are merged into one explicit control partition.

[0016] The above process is repeated until all partitions are merged to obtain the plurality of explicit control partitions.

[0017] Optionally, the secondary performance cost is calculated by short-time domain forward prediction for each control law in the candidate control law set associated with the explicit control partition, including:

[0018] The step of short-time domain forward prediction is set to 5 control steps;

[0019] For each affine control law in the candidate set, the state trajectory and control sequence of the future 5 control steps are iteratively calculated based on the current state vector and the state space model;

[0020] The quadratic performance cost composed of temperature tracking error and control input increment in the 5 control steps is accumulated to obtain the total evaluation value.

[0021] Optionally, the current optimal control law and the adjacent optimal control law are mixed by smooth weighted to generate the control output, including:

[0022] The boundary transition zone is defined as an area extending from the boundary of the current partition and the adjacent partition to the inside of the current partition by a preset width D;

[0023] When the state at the next time predicted by the current optimal control law enters the boundary transition zone, the vertical distance d of the predicted state point to the boundary of the current partition and the adjacent partition is calculated;

[0024] The weighting coefficient The calculation formula is:

[0025] The current control output calculated by the current optimal control law The adjacent control output calculated by the adjacent optimal control law are mixed by smooth weighted to generate the control output The calculation formula is: .

[0026] In another aspect, the application also provides a partition control system for temperature field of copper material heat treatment furnace, including the following modules:

[0027] A model construction module is used to construct a state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace;

[0028] An offline stage module is used to solve a multi-parameter programming problem to generate a series of affine control laws for performance and energy consumption indicators of different process stages; and divide the state space based on the coupling strength of each partition in the furnace to obtain a plurality of explicit control partitions, and associate each of the explicit control partitions with a candidate control law set composed of the affine control laws;

[0029] an online phase module configured to determine a current explicit control partition to which a current state vector belongs, to calculate a quadratic performance cost of each control law in a set of candidate control laws associated with the current explicit control partition by short-time domain forward prediction, and to select a control law with the minimum cost as a current optimal control law; when a state at a next time instant predicted by using the current optimal control law enters a boundary transition zone between the current partition and an adjacent partition, to select an adjacent optimal control law for a set of candidate control laws associated with the adjacent partition by using the same prediction and evaluation method, and to generate a control output by smoothing and weighted mixing the current optimal control law and the adjacent optimal control law; otherwise, to directly use the current optimal control law as the control output;

[0030] a control module configured to apply the control output to a partition actuator of the heat treatment furnace.

[0031] Optionally, the state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace is constructed by:

[0032] applying a pseudo-random binary sequence excitation signal near a steady state working point to collect input and output data, and establishing the state space model by using a subspace identification method.

[0033] Optionally, the performance and energy consumption indicators for different process stages are used to solve a multi-parameter programming problem to generate a series of affine control laws, including:

[0034] a cost function is constructed with a quadratic norm of temperature tracking error and a quadratic norm of control input increment in a future prediction time domain as optimization objectives, wherein a weight matrix Q of the temperature tracking error is a diagonal matrix with diagonal elements of 1.5, and a weight matrix R of the control input increment is a diagonal matrix with diagonal elements of 0.2;

[0035] the solving is performed under the constraints that a heating power change rate is not greater than 5 kW / min and a partition temperature does not exceed an upper limit and a lower limit of a process requirement by 5°C.

[0036] Optionally, the state space is divided into a plurality of explicit control partitions based on coupling strengths of the partitions in the furnace, including:

[0037] a relative gain matrix is calculated according to a steady state gain matrix of the state space model;

[0038] two partitions with a relative gain value greater than 0.7 are taken as strongly coupled partitions, and all the partitions with strong coupling relationship are merged into one explicit control partition;

[0039] the above process is repeated until all the partitions are merged to obtain the plurality of explicit control partitions.

[0040] Optionally, the short-time domain forward prediction calculation of each control law in the candidate control law set associated with the explicit control partition obtains a quadratic performance cost, comprising:

[0041] The step length of the short-time domain forward prediction is set to 5 control steps;

[0042] For each affine control law in the candidate set, based on the current state vector and the state space model, the state trajectory and control sequence of the next 5 control steps are iteratively calculated;

[0043] The quadratic performance cost composed of the temperature tracking error and the control input increment in the 5 control steps is accumulated to obtain the total evaluation value.

[0044] Optionally, the smoothing weighted mixing of the current optimal control law and the adjacent optimal control law generates a control output, comprising:

[0045] The boundary transition zone is defined as a region extending from the boundary of the current partition and the adjacent partition to the inside of the current partition by a preset width D;

[0046] When the state at the next time predicted by the current optimal control law enters the boundary transition zone, the vertical distance d of the predicted state point to the boundary of the current partition and the adjacent partition is calculated;

[0047] The weighting coefficient The calculation formula is:

[0048] The current control output calculated by the current optimal control law The adjacent control output calculated by the adjacent optimal control law are smoothing weighted mixed to generate a control output The calculation formula is: .

[0049] The present application places the optimization calculation in the offline stage, reduces the online calculation burden of model predictive control, and adopts a state space partition strategy based on the coupling strength of the partition to simplify the partition complexity of the explicit control. At the same time, through short-time domain prediction and optimization of the candidate control law set in the online stage, compared with the simple lookup table method, higher optimization effect is obtained with very small calculation increment. The smoothing weighted mixing mechanism of the control law introduced at the partition boundary ensures the continuity and stability of the control output at the state switching, effectively eliminates the control chattering, and improves the uniformity of the temperature field control. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The flowchart of the first embodiment;

[0051] Figure 2 schematic diagram for partitioning of a furnace;

[0052] Figure 3 schematic diagram for partitioning and control law. DETAILED DESCRIPTION

[0053] For the purpose, technical solutions and advantages of the embodiments of the present application to be clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0054] The plurality involved in the present application refers to two or more than two. In addition, it should be understood that in the description of the present application, the words "first", "second", etc. are only used for the purpose of distinguishing the description and cannot be understood as indicating or implying relative importance or indicating or implying order.

[0055] In the first embodiment, the present application provides a method for partitioning control of temperature field of copper material heat treatment furnace, as shown in Figure 1 , including the following steps:

[0056] S1, constructing a state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace;

[0057] When the copper material passes through the heating furnace, partition temperature control will be performed, as shown in Figure 2 , including multiple partitions and multiple heating devices. By analyzing the furnace structure, material thermal physical property parameters and internal heat transfer process, an energy conservation partial differential equation is established for each temperature zone in the furnace, which includes the power input of the heating element, the radiation and convection heat transfer of the temperature zone to the workpiece and the furnace wall, the heat exchange between the temperature zones and the heat loss to the environment; the nonlinear model is linearized in combination with the typical set point, and the spatial discretization is performed by using finite difference method or finite element method, to obtain a group of ordinary differential equations; the continuous time system is time-discretized, for example, by using Euler method or zero-order holder, to obtain a discrete state space model in the form of x(k+1)=Ax(k)+Bu(k), wherein the state vector x includes the temperatures of all temperature zones, and the control input vector u is the power of the heating actuator of each temperature zone.

[0058] In an optional embodiment, the constructing a state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace comprises:

[0059] The heating power of each partition heater is taken as a model input, and the temperature sensor measurement of each partition is taken as a model state variable, input and output data are collected by applying a pseudo-random binary sequence excitation signal near the steady-state operating point, and the state space model is established by using a subspace identification method.

[0060] The discrete-time state space model is specifically: a state equation x(k+1)=A*x(k)+B*u(k), and an observation equation y(k)=C*x(k)+D*u(k).

[0061] Wherein, x(k) is the measurement value of the temperature sensor of each partition. Assuming that there are n temperature zones, then is an n*1 column vector, representing the temperature of all partitions in the furnace at time k.

[0062] u(k) is the heating power of each partition heater. Assuming that there are p heaters, usually p=n, then is a p*1 column vector, representing the power applied to each heater at time k.

[0063] y(k) is the temperature of each partition. Generally, y(k) and the state x(k) are the same.

[0064] A is a state matrix, n*n dimension, representing the internal state of the system. For example, how does the temperature at the current time affect the temperature at the next time?

[0065] B is an input matrix, n*p dimension, representing how the input, i.e., the heating power, affects the system state, i.e., the temperature. For example, how much will the temperature of the 1st, 2nd,..., nth temperature zones be affected at the next time when 1kW of power is added to the 1st temperature zone?

[0066] C is an output matrix, n*n dimension, representing how to get the external measurement value from the internal state. Since the state is the measurement value, C is a unit matrix I.

[0067] D is a feedforward matrix, n*p dimension, representing how the input affects the output. The heating power does not instantaneously change the temperature, but there is a lag process.

[0068] During the process of applying a pseudo-random binary sequence PRBS signal to the power of each heating zone, the input power P(k) of all heating zones and the temperature T(k) of all temperature zones are recorded at a fixed sampling period. With the input data u(k) and the output data y(k) (i.e., the temperature T(k)), the matrices A, B, C, and D can be calculated using a subspace identification method such as N4SID. The subspace identification method solving process is known in the art, and will not be described here.

[0069] Take a tunnel furnace with 10 temperature zones as an example, the input vector of the model is the real-time heating power of the 10 heaters, such as P1 to P10, in kilowatts. The state variable vector of the model corresponds to the real-time temperature values measured by the thermocouples in the 10 temperature zones, such as T1 to T10, in degrees Celsius. The temperature in each zone of the furnace is stabilized at a certain common process set point, such as 850 degrees Celsius. Then, a pseudo-random binary sequence signal with an amplitude of five percent of the rated power is superimposed on the set value of the power of each heater, which randomly switches between plus and minus five percent, with a minimum switching time interval of 60 seconds. Under this excitation, the heating power input data and the temperature response data of each zone are continuously collected for 2 hours, with a sampling period of 10 seconds. The thousands of input and output data sequences collected are applied to the subspace identification algorithm to calculate the state space matrices A, B, C, D that can represent the dynamic response of the system, and the model is established.

[0070] S2, in the offline stage, a series of affine control laws are generated by solving a multi-parameter programming problem for performance and energy consumption indicators of different process stages; and the state space is divided based on the coupling strength of each partition in the furnace to obtain a plurality of explicit control partitions, and each of the explicit control partitions is associated with a set of candidate control laws composed of the affine control laws;

[0071] In the offline calculation, a quadratic performance index function is defined, which includes a penalty term for temperature tracking error and a penalty term for control energy consumption, and the upper and lower limits of heating power and temperature rise rate are set as constraint conditions; the optimization problem is constructed as a multi-parameter quadratic programming problem, where the current state vector x(k) is used as a parameter; a multi-parameter programming solver is used to solve the problem offline to obtain a state space division composed of a group of non-overlapping polytopes, and an affine control law corresponding to each zone As shown in Figure 3 The influence coefficients between the temperature zones are calculated using the steady-state gain matrix or dynamic response data of the system, and a clustering algorithm such as K-means is used to divide the temperature zones with close coupling into a group, thereby reducing the dimensionality of the state space to a plurality of explicit control partitions; for each explicit control partition, the original affine control laws contained in its spatial range are collected to form a set of candidate control laws exclusive to the partition.

[0072] In an optional embodiment, the generation of a series of affine control laws by solving a multi-parameter programming problem for performance and energy consumption indicators of different process stages includes:

[0073] A cost function is constructed with the quadratic norm of the temperature tracking error and the quadratic norm of the control input increment in the future prediction horizon as the optimization objective, where the weight matrix Q of the temperature tracking error is a diagonal matrix with diagonal elements of 1.5, and the weight matrix R of the control input increment is a diagonal matrix with diagonal elements of 0.2;

[0074] The solution is obtained under the constraints that the heating power change rate is not greater than 5 kW / min and the zone temperature does not exceed the upper and lower limits of the process requirement by 5℃.

[0075] The diagonal elements of the weight matrix Q are uniformly set to 1.5, and any deviation from the target temperature will be strongly penalized for all temperature zones. In contrast, the diagonal elements of the weight matrix R are set to 0.2, indicating that a smaller penalty is applied to the dramatic change of the control power, allowing the controller to make larger adjustments when necessary, but still inhibiting unnecessary frequent fluctuations and protecting the heating equipment.

[0076] During the solving process, constraints are set. For example, for a heater with a rated power of 100 kilowatts, the power change rate is limited to 5 kilowatts per minute, avoiding damage to the equipment caused by current surges. At the same time, if the process temperature requirement of a certain zone is 900 degrees Celsius, the allowed fluctuation range is strictly limited to 895 degrees Celsius to 905 degrees Celsius, and control strategies exceeding this range will be excluded. The multi-parameter programming solver will divide the entire state space into hundreds of polytope regions based on the above objectives and constraints, and calculate an optimal control law for each polytope region.

[0077] The multi-parameter programming solver converts the entire optimization problem (including the objective function and constraints) into a geometric problem. For a certain region in the state space, the optimal control strategy for all state points in the region satisfies a simple linear formula, i.e. an affine control law. By starting from an initial region, iteratively searching for boundaries and identifying adjacent regions, the solver completely covers the entire feasible state space with these polytope regions. Each time a new polytope region is found, the affine control law specific to that region is calculated. The solver output includes hundreds of polytope regions, each corresponding to an optimal control law formula. In specific implementation, the ppopt library in python is used for solving.

[0078] In one embodiment, the state space is divided based on the coupling strength of each zone in the furnace to obtain a plurality of explicit control zones, including:

[0079] According to the steady-state gain matrix of the state space model, a relative gain matrix is calculated;

[0080] two partitions with relative gain value greater than 0.7 are regarded as strongly coupled partitions, and all the partitions with strong coupling relationship are merged into one explicit control partition;

[0081] The above process is repeated until all the partitions are merged, and the multiple explicit control partitions are obtained.

[0082] The steady-state gain matrix of the system is derived from the state-space model, and in one embodiment, the steady-state gain matrix is calculated as The steady-state gain matrix represents the influence of each heater power input on the steady-state temperature of all the zones. Based on the gain matrix, the relative gain matrix is obtained by calculating the element-wise product of the gain matrix and the transpose of its inverse. Each element value of the relative gain matrix, for example, the element in the i-th row and j-th column, represents the relative influence degree of the j-th heater on the temperature control of the i-th zone.

[0083] For example, in an 8-zone heat treatment furnace, the calculated relative gain matrix shows that the relative gain value between the 2nd zone and the 3rd zone is 0.85, and the relative gain value between the 3rd zone and the 4th zone is 0.78. Since both values are greater than the set threshold value of 0.7, the 2nd zone and the 3rd zone are first merged into one control partition. Since the 4th zone has strong coupling with the member of the new partition, the 3rd zone, the 4th zone is also merged into the new partition, forming a larger partition containing the 2nd, 3rd and 4th zones. Since the relative gain values between the 1st zone and other zones are all less than 0.7, the 1st zone is independent as a partition. In this way, the 8 zones can be divided into three explicit control partitions, for example, the first partition contains the 1st zone, the second partition contains the 2nd, 3rd and 4th zones, and the third partition contains the 5th, 6th, 7th and 8th zones.

[0084] S3, in the online phase, determining the explicit control partition to which the current state vector belongs, calculating the quadratic performance cost of each control law in the candidate control law set associated with the explicit control partition through short-time domain forward prediction, and selecting the control law with the minimum cost as the current optimal control law; when the state at the next time predicted by the current optimal control law enters the boundary transition zone between the current partition and an adjacent partition, selecting the adjacent optimal control law for the candidate control law set associated with the adjacent partition using the same prediction evaluation method, and generating the control output by smoothing and weighted mixing the current optimal control law and the adjacent optimal control law; otherwise, directly using the current optimal control law as the control output;

[0085] At the beginning of each control cycle, real-time temperature data of each zone in the furnace is collected to form the current state vector x(k); it is determined in which explicit control partition x(k) falls; then, all the affine control laws in the candidate control law set associated with the partition are traversed, and for any control law , a state space model is used to make a N-step rolling prediction, N is a short prediction horizon, to get a predicted state trajectory; according to the predicted trajectory and the corresponding control sequence, a quadratic performance cost value is calculated; the cost values generated by all candidate control laws are compared, and the control law corresponding to the minimum cost value is selected as the current optimal control law.

[0086] In the offline phase, a boundary transition zone with a thickness of ε is defined for each two adjacent explicit control partitions; in online operation, the current optimal control law is applied to the current state x(k), and the state x(k+1) at the next time is predicted; it is judged whether x(k+1) is located in any boundary transition zone; if not, the calculation result of the current optimal control law is directly taken as the final control output; if it is located in the boundary transition zone between the current partition and a certain adjacent partition, the evaluation of the candidate control law set of the adjacent partition is enabled, and the same short-horizon forward prediction and cost evaluation method as the previous step is adopted to select the optimal control law of the adjacent partition, that is, the adjacent optimal control law; a weighting factor α is calculated according to the relative position of the predicted state x(k+1) in the transition zone, for example, the weighting factor is proportional to the normalized distance of the state point to the partition boundary; the final control output is generated by weighted mixing through the formula of .

[0087] In a specific embodiment, the short-horizon forward prediction is performed on each control law in the candidate control law set associated with the explicit control partition to calculate a quadratic performance cost, including:

[0088] The step length of the short-horizon forward prediction is set to 5 control steps;

[0089] For each affine control law in the candidate set, based on the current state vector and the state space model, the state trajectory and control sequence of the future 5 control steps are iteratively calculated;

[0090] The quadratic performance cost composed of the temperature tracking error and the control input increment in the 5 control steps is accumulated to obtain the total evaluation value.

[0091] Suppose the current system state is in the explicit partition P1, but very close to the boundaries of partitions P2 and P3. At this time, the three affine control laws associated with P1, P2 and P3 are selected as candidate control laws. For the control law corresponding to P1, the current temperature state vector and the state space model are used to forward deduce for 5 control periods. For example, if the control period is 1 minute, the next 5 minutes are predicted. In the first prediction, the control amount is calculated according to the current state, and then the state of the next minute is obtained; based on this new state, the second control amount is calculated, and the state of the next minute is predicted, and so on for five times.

[0092] In each of the 5 steps, a cost is calculated, which is the sum of two parts: one is the weighted sum of square of difference between predicted temperature and target temperature, the other is the weighted sum of square of control power variation. The total cost of applying P1 control law is the sum of the cost of the 5 steps. The same process is applied to P2 and P3 control laws, and the total cost of applying P1 control law is J1 = 12.5, the total cost of applying P2 control law is J2 = 10.8, and the total cost of applying P3 control law is J3 = 15.1. By comparing the total cost, one can determine which control law will achieve the best control result with the least cost in the next short time.

[0093] In one embodiment, the step of generating the control output by smoothing and weighting the current optimal control law and the adjacent optimal control law comprises:

[0094] defining the boundary transition zone as a region extending from the boundary between the current partition and the adjacent partition to a preset width D inside the current partition;

[0095] calculating the vertical distance d of the predicted state point to the boundary between the current partition and the adjacent partition when the next time state predicted by the current optimal control law enters the boundary transition zone;

[0096] the weighting coefficient The calculation formula is:

[0097] the current control output calculated by the current optimal control law the adjacent control output calculated by the adjacent optimal control law are smoothed and weighted to generate the control output The calculation formula is: .

[0098] Suppose the state is moving from explicit partition A to partition B. To avoid the jump of control output when crossing the boundary, a virtual transition zone with a width of D is defined near the boundary between A and B inside partition A. The width D can be set to the distance value 2.0 under the state space norm. When the controller predicts that the next time state will enter this transition zone, the smoothing and weighting mechanism is started. For example, if the vertical distance d of the predicted state point to the boundary between A and B is 0.4, the calculated weighting coefficient is 0.8. The controller will calculate two control outputs at the same time. One is the current control output obtained by applying the current optimal control law of partition A to the current state, which is assumed to be a heating power of 35 kW. The other is the adjacent control output obtained by applying the adjacent optimal control law of partition B to the same current state, which is assumed to be a heating power of 40 kW. The actual control output applied to the heater is 39 kW. The control output is thus transitioned from 35 kW to 40 kW.

[0099] S4, applying the control output to the zone actuators of the heat treatment furnace.

[0100] The calculated final control output vector is sent to a programmable logic controller (PLC) or a distributed control system (DCS). The control system converts each element value in the vector into a power setpoint signal for the corresponding heating zone, such as a 4-20 mA current signal or a 0-10 V voltage signal, to drive the corresponding solid-state relay or thyristor power regulator, which adjusts the electrical power applied to the heating wires in each zone, thereby achieving control of the temperature field in the furnace.

[0101] In a second embodiment, the present application also provides a temperature field partition control system for a copper material heat treatment furnace, comprising the following modules:

[0102] a model construction module for constructing a state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace;

[0103] an offline stage module for solving a multi-parameter programming problem to generate a series of affine control laws for performance and energy consumption indicators of different process stages; and dividing the state space based on the coupling strength of each zone in the furnace to obtain multiple explicit control zones, and associating each of the explicit control zones with a set of candidate control laws composed of the affine control laws;

[0104] an online stage module for determining the explicit control zone to which the current state vector belongs, calculating the quadratic performance cost for each control law in the set of candidate control laws associated with the explicit control zone through short-time domain forward prediction, and selecting the control law with the minimum cost as the current optimal control law; when the state at the next time predicted using the current optimal control law enters the boundary transition zone between the current zone and an adjacent zone, selecting the adjacent optimal control law for the set of candidate control laws associated with the adjacent zone using the same prediction evaluation method, and generating a control output by smoothing and weighted mixing the current optimal control law and the adjacent optimal control law; otherwise, directly using the current optimal control law as the control output;

[0105] a control module for applying the control output to the zone actuators of the heat treatment furnace.

[0106] In a specific embodiment, the state space model representing the thermodynamic transfer characteristics in the copper material heat treatment furnace is constructed by:

[0107] The heating power of each zone heater is taken as the model input, and the temperature sensor measurement of each zone is taken as the model state variable. By applying a pseudo-random binary sequence excitation signal near the steady-state operating point, input and output data are collected, and a subspace identification method is used to establish the state space model.

[0108] In one specific embodiment, the performance and energy consumption indicators for different process stages are used to solve a multi-parameter programming problem to generate a series of affine control laws, including:

[0109] A cost function is constructed with the quadratic norm of temperature tracking error and the quadratic norm of control input increment in the future prediction time domain as optimization objectives, wherein the weight matrix Q of the temperature tracking error is a diagonal matrix with diagonal elements of 1.5, and the weight matrix R of the control input increment is a diagonal matrix with diagonal elements of 0.2;

[0110] The solving is performed under the constraints that the heating power change rate is not greater than 5 kW / min and the partition temperature does not exceed the upper and lower limits of the process requirement by 5℃.

[0111] In one specific embodiment, the state space is divided based on the coupling strength of each partition in the furnace to obtain a plurality of explicit control partitions, including:

[0112] According to the steady-state gain matrix of the state space model, a relative gain matrix is calculated;

[0113] Two partitions with a relative gain value greater than 0.7 are regarded as strongly coupled partitions, and all partitions with strong coupling relationship are merged into one explicit control partition;

[0114] The above process is repeated until all partitions are merged to obtain the plurality of explicit control partitions.

[0115] In one specific embodiment, a quadratic performance cost is calculated for each control law in the set of alternative control laws associated with the explicit control partition through short-time domain forward prediction, including:

[0116] The step length of the short-time domain forward prediction is set to 5 control steps;

[0117] For each affine control law in the alternative set, the state trajectory and control sequence of the future 5 control steps are iteratively calculated based on the current state vector and the state space model;

[0118] The quadratic performance cost composed of the temperature tracking error and the control input increment in the 5 control steps is accumulated to obtain a total evaluation value.

[0119] In one specific embodiment, the current optimal control law and the adjacent optimal control law are mixed by smooth weighting to generate a control output, including:

[0120] The boundary transition zone is defined as an area extending from the boundary between the current partition and the adjacent partition to the inside of the current partition by a preset width D;

[0121] When the state at the next time predicted by the current optimal control law enters the boundary transition region, calculate the vertical distance d of the predicted state point to the boundary of the current partition and the adjacent partition;

[0122] Weighting coefficient The calculation formula is:

[0123] The current control output calculated by the current optimal control law The adjacent control output calculated by the adjacent optimal control law are weighted and mixed to generate the control output The calculation formula is: .

[0124] Those skilled in the art will understand that embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk memory, Compact Disc Read-Only Memory (CD-ROM), optical memory, etc.) having computer-usable program code embodied therein.

[0125] The present application is described in reference to the flowcharts and / or block diagrams of the methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus create a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in the flowcharts and / or block diagrams.

[0126] The above description is merely illustrative of the embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the scope of the claims of the present application.

Claims

1. A method for zoned control of the temperature field in a copper heat treatment furnace, characterized in that, Includes the following steps: Construct a state-space model representing the thermodynamic transfer characteristics within a copper heat treatment furnace; In the offline phase, a series of affine control laws are generated by solving a multi-parameter programming problem to address the performance and energy consumption indicators of different process stages. The state space is divided based on the coupling strength of each zone in the furnace to obtain multiple explicit control zones. Each explicit control zone is associated with a set of alternative control laws composed of the affine control laws. During the online phase, the explicit control partition is determined based on the current state vector. For each control law in the set of candidate control laws associated with that explicit control partition, a short-time-domain forward prediction calculation is performed to obtain a quadratic performance cost. The control law with the lowest cost is selected as the current optimal control law. When the state predicted by the current optimal control law enters the boundary transition zone between the current partition and an adjacent partition, the same prediction and evaluation method is used to select the adjacent optimal control law from the set of candidate control laws associated with the adjacent partition. The current optimal control law and the adjacent optimal control law are then smoothly weighted and mixed to generate the control output. Otherwise, the current optimal control law is directly used as the control output. The control output is applied to the actuators of each zone of the heat treatment furnace; The step of smoothly weighting and mixing the current optimal control law with adjacent optimal control laws to generate a control output includes: The boundary transition area is defined as a region extending from the boundary between the current partition and the adjacent partition into the interior of the current partition with a preset width D. When the state predicted by the current optimal control law enters the boundary transition zone, the vertical distance d from the predicted state point to the boundary between the current partition and the adjacent partition is calculated. Weighting coefficients The calculation formula is: ; The current control output calculated from the current optimal control law. The adjacent control output calculated from the adjacent optimal control law Perform smooth weighted mixing to generate control output. The calculation formula is: .

2. The method according to claim 1, characterized in that, The construction of the state-space model representing the thermodynamic transfer characteristics within the copper heat treatment furnace includes: The heating power of each zone heater is used as the model input, and the temperature sensor measurement values ​​of each zone are used as the model state variables. By applying pseudo-random binary sequence excitation signals near the steady-state operating point, input and output data are collected, and the state space model is established using the subspace identification method.

3. The method according to claim 1, characterized in that, The method involves solving a multi-parameter programming problem to generate a series of affine control laws for performance and energy consumption indicators at different process stages, including: A cost function is constructed with the second norm of the temperature tracking error in the future prediction time domain and the second norm of the control input increment as the optimization objective. The weight matrix Q of the temperature tracking error is a diagonal matrix with diagonal elements of 1.5, and the weight matrix R of the control input increment is a diagonal matrix with diagonal elements of 0.

2. The solution is performed under the constraints that the rate of change of heating power is no greater than 5 kW / min and the zone temperature does not exceed the upper or lower limit of the process requirements by 5℃.

4. The method according to claim 1, characterized in that, The state space is divided based on the coupling strength of each zone within the furnace, resulting in multiple explicit control zones, including: The relative gain matrix is ​​calculated based on the steady-state gain matrix of the state-space model. Two partitions with a relative gain greater than 0.7 are designated as strongly coupled partitions, and all partitions with strong coupling relationships are merged into one explicitly controlled partition. Repeat the above process until all partitions are merged, resulting in the multiple explicitly controlled partitions.

5. The method according to claim 1, characterized in that, The step of performing short-time forward prediction calculations on each control law in the set of candidate control laws associated with the explicit control partition to obtain the quadratic performance cost includes: The step size for short-time forward prediction is set to 5 control steps; For each affine control law in the candidate set, based on the current state vector and state space model, iteratively calculate the state trajectory and control sequence for the next 5 control steps; The total evaluation value is obtained by summing the secondary performance costs consisting of temperature tracking error and control input increment within 5 control steps.

6. A zoned control system for the temperature field of a copper heat treatment furnace, characterized in that, Includes the following modules: The model building module is used to construct a state-space model representing the thermodynamic transfer characteristics inside a copper heat treatment furnace. The offline phase module is used to solve multi-parameter programming problems and generate a series of affine control laws for performance and energy consumption indicators at different process stages. The state space is divided based on the coupling strength of each zone in the furnace to obtain multiple explicit control zones. Each explicit control zone is associated with a set of alternative control laws composed of the affine control laws. The online phase module is used to determine the explicit control partition to which the current state vector belongs, perform short-time forward prediction calculation on each control law in the set of candidate control laws associated with the explicit control partition to obtain the quadratic performance cost, and select the control law with the minimum cost as the current optimal control law; when the state predicted by the current optimal control law enters the boundary transition zone between the current partition and the adjacent partition, the same prediction and evaluation method is used to select the adjacent optimal control law from the set of candidate control laws associated with the adjacent partition, and the current optimal control law and the adjacent optimal control law are smoothly weighted and mixed to generate the control output; otherwise, the current optimal control law is directly used as the control output. A control module is used to apply the control output to the actuators of each zone of the heat treatment furnace; The step of smoothly weighting and mixing the current optimal control law with adjacent optimal control laws to generate a control output includes: The boundary transition area is defined as a region extending from the boundary between the current partition and the adjacent partition into the interior of the current partition with a preset width D. When the state predicted by the current optimal control law enters the boundary transition zone, the vertical distance d from the predicted state point to the boundary between the current partition and the adjacent partition is calculated. Weighting coefficients The calculation formula is: ; The current control output calculated from the current optimal control law. The adjacent control output calculated from the adjacent optimal control law Perform smooth weighted mixing to generate control output. The calculation formula is: .

7. The system according to claim 6, characterized in that, The construction of the state-space model representing the thermodynamic transfer characteristics within the copper heat treatment furnace includes: The heating power of each zone heater is used as the model input, and the temperature sensor measurement values ​​of each zone are used as the model state variables. By applying pseudo-random binary sequence excitation signals near the steady-state operating point, input and output data are collected, and the state space model is established using the subspace identification method.

8. The system according to claim 6, characterized in that, The method involves solving a multi-parameter programming problem to generate a series of affine control laws for performance and energy consumption indicators at different process stages, including: A cost function is constructed with the second norm of the temperature tracking error in the future prediction time domain and the second norm of the control input increment as the optimization objective. The weight matrix Q of the temperature tracking error is a diagonal matrix with diagonal elements of 1.5, and the weight matrix R of the control input increment is a diagonal matrix with diagonal elements of 0.

2. The solution is performed under the constraints that the rate of change of heating power is no greater than 5 kW / min and the zone temperature does not exceed the upper or lower limit of the process requirements by 5℃.

9. The system according to claim 6, characterized in that, The state space is divided based on the coupling strength of each zone within the furnace, resulting in multiple explicit control zones, including: The relative gain matrix is ​​calculated based on the steady-state gain matrix of the state-space model. Two partitions with a relative gain greater than 0.7 are designated as strongly coupled partitions, and all partitions with strong coupling relationships are merged into one explicitly controlled partition. Repeat the above process until all partitions are merged, resulting in the multiple explicitly controlled partitions.

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