Temperature control method of hot working furnace for thick and wide plates based on stable control of distributed parameter system

Abstract

The present application provides a method for controlling the temperature of a wide and thick plate hot working furnace based on the stable control of a distributed parameter system. The method comprises: dividing the internal space of the wide and thick plate hot working furnace into a plurality of subspaces according to the position of each flame nozzle in the wide and thick plate hot working furnace; constructing a distributed parameter system model of the wide and thick plate hot working control furnace; constructing a distributed dynamic feedback controller; applying the constructed distributed dynamic feedback controller to the distributed parameter system model to obtain a distributed parameter control system joint closed-loop model; constructing a Lyapunov function based on the Lyapunov stability theory, solving and obtaining sufficient conditions for the distributed dynamic feedback controller to achieve the stability of the distributed parameter control system joint closed-loop model, and then determining the control parameters of the distributed dynamic feedback controller. In this way, by applying the distributed dynamic feedback controller to the distributed parameter system model, the wide and thick plates in the furnace are heated uniformly and the furnace temperature meets the target temperature state for safe operation.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial furnace temperature, and in particular to a method for controlling wide and thick plate hot working furnace temperature based on distributed parameter system stable control. Background Art

[0002] The internal space of a thick plate hot working furnace can be divided into several sections, each defined as a node. Considering that the temperature inside the thick plate hot working furnace is primarily controlled by the flame nozzles within the furnace (the flame nozzles within the furnace can also be defined as spatial nodes), energy transfer occurs between each node within the furnace, and this energy exhibits a specific change trend over time. This indicates that the thick plate hot working furnace temperature control system, with its spatiotemporal characteristics, is a typical distributed parameter system.

[0003] During the hot working of steel, maintaining uniform and stable temperatures at all points within the furnace is crucial for uniform heating of the billet. This uniformity significantly impacts steel performance. Uneven temperatures within and outside the billet lead to uneven elongation during rolling, which in turn can cause stress and cracks in the rolled piece, impacting steel performance. This is particularly true for high-performance, thick and wide steel plates. Uneven heating can lead to surface quality issues such as pitting, non-metallic inclusions, cracks, and fissures, severely impacting steel performance. Summary of the Invention

[0004] Based on this, a method for controlling the furnace temperature of hot processing of thick and wide plates based on stable control of a distributed parameter system is provided, which makes the heating of high-performance thick and wide steel plates more uniform.

[0005] In a first aspect, a method for controlling the temperature of a wide and thick plate hot working furnace based on stable control of a distributed parameter system is provided, the method comprising:

[0006] According to the position of each flame nozzle in the wide and thick plate hot processing furnace, the internal space of the wide and thick plate hot processing furnace is divided into subspaces;

[0007] Taking the difference between the temperature state of each subspace and the target temperature state required for hot working of thick plates as a variable, and based on the temporal and spatial variation characteristics of the temperature state of the hot working furnace of thick plates and the distributed parameter system theory, a distributed parameter system model of the hot working control furnace of thick plates is constructed;

[0008] Based on the distributed parameter system model, a distributed dynamic feedback controller is constructed, wherein the distributed dynamic feedback controller includes a control system state generator and an intermittent feedback output sub-controller, the control system state generator is constructed based on the influence of the spatial diffusion process of the energy output state of the flame nozzle in each subspace, the influence of the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, and the influence of the coupling effect of the distributed parameter system state in each subspace; the control system state generator is used to determine the control state basic variables of the distributed dynamic feedback controller in each subspace; the intermittent feedback output sub-controller is constructed by designing the intermittent gain based on the control state basic variables of the distributed dynamic feedback controller in each subspace;

[0009] The constructed distributed dynamic feedback controller is applied to the distributed parameter system model to obtain the distributed parameter control system closed-loop model.

[0010] Based on Lyapunov stability theory, a Lyapunov function is constructed to solve the sufficient conditions for the distributed dynamic feedback controller to achieve the stability of the distributed parameter control system's simultaneous closed-loop model;

[0011] The control parameters of the distributed dynamic feedback controller are determined according to the sufficient conditions.

[0012] Optionally, the distributed parameter system model is:

[0013] (1)

[0014] in, Indicates the The temperature difference state between the current temperature state and the target temperature state of the subspace, represents the space-time region in the distributed parameter system, represents a spatial variable, is the time variable, represents the space of positive real numbers, The space inside the furnace for hot processing of thick plates has a smooth boundary bounded regions; n represents the number of subspaces in the interior of a wide and thick plate hot processing furnace; , represents the temperature diffusion Laplace operator inside the subspace, Indicates the number of spatial dimensions; is the diffusion coefficient, and ; Represents node space Temperature difference state to node space The influencing factor of the temperature difference state, is a constant; Indicates the hot working furnace number of each wide and thick plate The distributed parameter system corresponding to the subspace is controlled by the input, and the control input represents the energy input of each flame nozzle in the wide and thick plate hot processing furnace.

[0015] Optionally, the distributed parameter system model is transformed into a matrix form as follows:

[0016] (2)

[0017] in, Represents the state of the system by distributed parameters The distributed parameter system state variable matrix is ​​composed of represents a one-dimensional real number space, Indicates the dimension The real matrix space of ; Indicated by the parameter The diagonal matrix parameters formed; Indicated by the parameter The matrix parameters of the distributed parameter system model are constructed; Indicates the control input status The control input matrix formed;

[0018] The initial boundary conditions of the distributed parameter system are:

[0019] , (3)

[0020] or

[0021] , (4)

[0022] in, For smooth boundaries The unit external normal vector of .

[0023] Optionally, the distributed dynamic feedback controller is:

[0024] (5)

[0025] in, Indicates the spatial diffusion process of the energy output state of each subspace flame nozzle, Indicates the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, Indicates the influence of the coupling effect of the system state of each subspace distribution parameter, Indicates the The basic variables of the control state of each subspace; is the diffusion coefficient of the control state; Indicates the number of spatial dimensions; Represents node space Controller state to node space The influencing factor of the controller state, Represents node space The distributed parameter system temperature difference state to the node space The influencing factors of the controller state, and are all constants, represents the distributed parameter system control input corresponding to the i-th subspace of each wide and thick plate hot processing furnace, is the intermittent feedback control gain parameter variable, satisfy:

[0026] (6)

[0027] in, represents the feedback control gain coefficient, To control the cycle, Indicates the current control cycle number, is the control signal duty cycle, satisfying .

[0028] Optionally, the distributed dynamic feedback controller is transformed into a matrix form as follows:

[0029] (7)

[0030] in, Represents the system state by the distributed dynamic feedback controller The controller system state variable matrix constructed;

[0031] Represents the gain parameter variable controlled by intermittent feedback The control gain matrix formed by

[0032] , , ;

[0033] The initial boundary conditions of the distributed dynamic feedback controller system are:

[0034] , (8)

[0035] or

[0036] , (9)

[0037] Optionally, the distributed dynamic feedback controller is applied to the distributed parameter system to obtain a distributed parameter control system simultaneous closed-loop model, wherein the distributed parameter control system simultaneous closed-loop model is:

[0038] (10)

[0039] in, represents the state matrix of the distributed parameter control system closed-loop model, represents the diffusion parameter matrix of the distributed parameter control system closed-loop model, represents an all-zero matrix; Represents the parameter matrix of the simultaneous closed-loop model of the distributed parameter control system.

[0040] Optionally, sufficient conditions include:

[0041] Given system parameters Under the condition that there exists a positive definite symmetric matrix ,matrix and positive constants , When the following conditions are met:

[0042] (11)

[0043] (12)

[0044] (13)

[0045] (14)

[0046] The distributed parameter model reaches stability, where , ,matrix , is the Lyapunov function parameter matrix, is the identity matrix of appropriate dimension, Represents the symmetric terms of a symmetric matrix.

[0047] Optionally, determining the control parameters of the distributed dynamic feedback controller according to the sufficient condition includes:

[0048] According to the sufficient condition, the matrix form of the distributed dynamic feedback control is solved to obtain the control parameters of the distributed dynamic feedback controller, wherein the control parameters at least include the intermittent control gain , constant matrix B and the constant matrix .

[0049] In a second aspect, an electronic device is provided, comprising:

[0050] a memory configured to store instructions;

[0051] The processor is configured to call the instructions from the memory and implement the above-mentioned wide and thick plate hot processing furnace temperature control method based on distributed parameter system stable control when executing the instructions.

[0052] In a third aspect, a machine-readable storage medium is provided, characterized in that instructions are stored on the machine-readable storage medium, and the instructions are used to enable the machine to execute the wide and thick plate hot processing furnace temperature control method based on the above-mentioned distributed parameter system stable control.

[0053] The above-mentioned temperature control method for a wide and thick plate hot working furnace based on stable control of a distributed parameter system divides the internal space of the wide and thick plate hot working furnace into multiple subspaces according to the position of each flame nozzle in the wide and thick plate hot working furnace; takes the difference state between the temperature state of each subspace and the target temperature state required for wide and thick plate hot working as a variable, and constructs a distributed parameter system model of the wide and thick plate hot working furnace based on the distributed parameter system theory according to the temporal and spatial variation characteristics of the temperature state of the wide and thick plate hot working furnace; based on the distributed parameter system model, a distributed dynamic feedback controller is constructed; wherein, the distributed dynamic feedback controller includes a control system state generator and an intermittent feedback output subcontroller, wherein the control system state generator is constructed based on the influence of the spatial diffusion process of the energy output state of the flame nozzle in each subspace, the influence of the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot working furnace, and the influence of the coupling effect of the distributed parameter system state in each subspace; the control system state generator is used to determine the control state basic variables of the distributed dynamic feedback controller in each subspace; and the intermittent feedback output subcontroller is constructed by designing the intermittent gain based on the control state basic variables of the distributed dynamic feedback controller in each subspace. The constructed distributed dynamic feedback controller is applied to the distributed parameter system model to obtain a distributed parameter control system closed-loop model; based on the Lyapunov stability theory, a Lyapunov function is constructed and solved to obtain the sufficient conditions for the distributed dynamic feedback controller to achieve stability of the distributed parameter control system closed-loop model, thereby determining the control parameters of the distributed dynamic feedback controller. The beneficial effects of this application are: by fully considering the spatial diffusion of the energy output state during the flame nozzle control implementation process, a distributed dynamic feedback controller is constructed, the distributed parameter system model is combined with the distributed dynamic feedback controller, and a distributed intermittent control scheme is constructed to achieve uniform and safe heating of wide and thick plates in the furnace. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 11 is a flow chart of a method for controlling the temperature of a wide and thick plate hot working furnace based on stable control of a distributed parameter system provided in an embodiment of the present application;

[0055] Figure 2 This is a state change trend diagram of each subspace of a wide and thick plate hot processing control furnace in a specific embodiment of the present application;

[0056] Figure 3 This is a state change trend diagram of the distributed controllers of each subspace of the wide and thick plate hot processing control furnace in a specific embodiment of the present application;

[0057] Figure 4 Schematic diagram of the structure of a temperature control device for hot working of thick plates based on distributed parameter system stable control according to an embodiment of the present application;

[0058] Figure 5 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0059] The following will be combined with the accompanying drawings in the embodiments of the present application to clearly describe the technical solutions in the embodiments of the present application. Obviously, the embodiments described are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field are within the scope of protection of this application.

[0060] The terms "first," "second," and the like in the specification and claims of this application are used to distinguish similar objects, and are not used to describe a specific order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of this application can be implemented in an order other than that illustrated or described herein, and that the objects distinguished by "first," "second," and the like are generally of the same type, and do not limit the number of objects; for example, the first object can be one or more. In addition, the term "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0061] The following describes in detail the method for controlling the temperature of a wide and thick plate hot working furnace based on stable control of a distributed parameter system provided in the embodiment of the present application through specific embodiments and application scenarios in conjunction with the accompanying drawings.

[0062] See Figure 1 , is a flow chart of a method for controlling the temperature of a wide and thick plate hot working furnace based on a distributed parameter system stable control according to an embodiment of the present application. Figure 1 As shown, the method includes the following steps S100 to S600.

[0063] Step S100 divides the internal space of the thick plate hot working furnace into subspaces;

[0064] Step S200: Using the difference between the temperature state of each subspace and the target temperature state required for hot working of thick plates as a variable, and based on the distributed parameter system theory and the temporal and spatial variation characteristics of the temperature state of the hot working furnace, a distributed parameter system model of the hot working furnace for thick plates is constructed;

[0065] Step S300: Based on the distributed parameter system model, a distributed dynamic feedback controller is constructed, wherein the distributed dynamic feedback controller includes a control system state generator and an intermittent feedback output sub-controller, the control system state generator is constructed based on the influence of the spatial diffusion process of the energy output state of the flame nozzle in each subspace, the influence of the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, and the influence of the coupling effect of the distributed parameter system state in each subspace; the control system state generator is used to determine the control state basic variables of the distributed dynamic feedback controller in each subspace; the intermittent feedback output sub-controller is constructed by designing intermittent gains based on the control state basic variables of the distributed dynamic feedback controller in each subspace;

[0066] Step S400: applying the constructed distributed dynamic feedback controller to the distributed parameter system model to obtain a distributed parameter control system simultaneous closed-loop model;

[0067] Step S500: Based on Lyapunov stability theory, construct a Lyapunov function to solve and obtain sufficient conditions for the distributed dynamic feedback controller to achieve stability of the distributed parameter control system's simultaneous closed-loop model;

[0068] Step S600: determining control parameters of the distributed dynamic feedback controller according to the sufficient conditions.

[0069] In this embodiment, to achieve uniform and stable temperatures at all points within a thick plate hot working furnace, the interior of the furnace is divided into n subspaces based on the flame nozzles within the furnace. Each subspace is defined as a node, and each node has a flame nozzle, or control input, that can regulate the temperature of that subspace.

[0070] In an embodiment of the present application, in order to achieve temperature stability in each area of ​​the furnace space of a wide and thick plate hot processing furnace, that is, the temperature of each area reaches a constant temperature, the difference state between the temperature state of each subspace and the target temperature state required for the wide and thick plate hot processing is used as a variable. According to the spatiotemporal variation characteristics of the spatial temperature state of the wide and thick plate hot processing furnace, based on the distributed parameter system theory, a distributed parameter system model of the wide and thick plate hot processing control furnace is constructed. The spatiotemporal variation characteristics of the spatial temperature of the wide and thick plate hot processing furnace can be understood as the time characteristics and spatial characteristics of the spatial temperature of the wide and thick plate hot processing furnace. The time characteristics can be understood as the dynamic change law of the furnace temperature over time, including the heating rate, the stability of the insulation stage, the controllability of the cooling process, etc. The spatial characteristics can be understood as the temperature distribution differences at different positions in the furnace, including the temperature gradients along the furnace length, furnace width, and furnace height, as well as the temperature uniformity of the steel plate cross section (thickness, width direction).

[0071] In the embodiments of this application, a distributed parameter system (DPS) can be understood as a system whose state variables vary not only in time but also in space. This type of system is characterized by its state being dependent on spatial location. Therefore, it cannot be fully described by the values ​​of a finite number of points, but requires a continuous spatial function. The distributed parameter system model for a thick plate hot working control furnace can be expressed as:

[0072] (1)

[0073] in, Indicates the The temperature difference state between the current temperature state and the target temperature state of the subspace, represents the space-time region in the distributed parameter system, represents a spatial variable, is the time variable, represents the space of positive real numbers, The space inside the furnace for hot processing of thick plates has a smooth boundary bounded regions; n represents the number of subspaces in the interior of a wide and thick plate hot processing furnace; , represents the temperature diffusion Laplace operator inside the subspace, Indicates the number of spatial dimensions; is the diffusion coefficient, and ; Represents node space Temperature difference state to node space The influencing factor of the temperature difference state, is a constant; Indicates the hot working furnace number of each wide and thick plate The distributed parameter system corresponding to the subspace is controlled by the input, and the control input represents the energy input of each flame nozzle in the wide and thick plate hot processing furnace.

[0074] In this embodiment, a distributed parameter system model for a thick plate hot working furnace is constructed based on the temperature variation patterns within the furnace, with the goal of achieving a stable and uniform temperature distribution within the furnace that matches the target temperature of the thick plate hot working material over time. The model uses the temperature difference between the current and target temperatures as a variable. To achieve stable temperature control of the thick plate hot working furnace, a distributed dynamic feedback controller is constructed. The distributed dynamic feedback controller comprises a control system state generator and an intermittent feedback output subcontroller. The distributed dynamic feedback controller can be understood as a flame nozzle control scheme within the thick plate hot working furnace. The control system state generator is constructed based on the spatial diffusion process of the flame nozzle energy output state within each subspace, the coupling effect of the energy output states of other flame nozzles within the thick plate hot working furnace, and the coupling effect of the distributed parameter system states within each subspace. The control system state generator is used to determine the basic control state variables of the distributed dynamic feedback controller within each subspace. By designing intermittent control gains based on the basic variables of the control state of the distributed dynamic feedback controller in each subspace, an intermittent feedback output subcontroller can be constructed, thus completing the construction of the distributed dynamic feedback controller. The intermittent feedback output subcontroller can be used to output the regulation state based on the basic state of the flame nozzle output energy. Applying the constructed distributed dynamic feedback controller to the distributed parameter system model can obtain a distributed parameter control system closed-loop model. Based on Lyapunov stability theory, a Lyapunov function is constructed and solved to obtain the sufficient conditions for the distributed dynamic feedback controller to achieve asymptotic stability of the distributed parameter control system closed-loop model, namely, the furnace temperature of the thick plate hot processing furnace is stably and uniformly distributed and can match the target temperature of the thick plate hot processing steel over time.

[0075] The present invention provides a method for controlling the temperature of a thick plate hot working furnace based on stable control of a distributed parameter system. Its key innovation lies in the construction of a distributed control scheme, combined with an intermittent control scheme, to achieve temperature control for thick plate hot working furnaces. This method takes into account the spatiotemporal transformation of energy transfer during flame nozzle energy output (the spatiotemporal transformation of the distributed parameter system). Specifically, considering the energy output form of the flame nozzle, in practical engineering, it is difficult for the flame nozzle (i.e., the control device) to directly perform feedback control based on the spatial temperature state within the thick plate hot working furnace. Therefore, this method constructs a distributed dynamic feedback controller, which includes a control system state generator and an intermittent feedback output sub-controller. The innovation lies in the fact that the basic feedback control state of the constructed distributed dynamic feedback controller is not the traditional system state. Instead, the control system state generator is constructed based on the energy diffusion process in the flame nozzle space. The intermittent feedback output sub-controller is constructed in conjunction with the intermittent control scheme to achieve a stable and uniform temperature distribution in the thick plate hot working furnace, and to match the target temperature of the thick plate hot working steel material over time. This results in asymptotic stability of the distributed parameter control system's simultaneous closed-loop model.

[0076] In the present embodiment, Lyapunov stability theory is an important method for analyzing the stability of dynamic systems. Its basic concept is to determine whether a system is stable near a certain equilibrium point by constructing an appropriate Lyapunov function. By solving the Lyapunov function, it is possible to derive sufficient conditions for a distributed dynamic feedback controller to achieve stability in a simultaneous closed-loop model of a distributed parameter control system. This is the sufficient condition for achieving the target temperature in a furnace flame nozzle control scheme for hot working thick plates.

[0077] In the embodiment of the present application, by determining the sufficient conditions for the stability of the distributed parameter system model, the control parameters of the distributed dynamic feedback controller can be calculated. Specifically, the distributed dynamic feedback controller can be transformed into a matrix form, which can be expressed as:

[0078] (7)

[0079] Then, the control parameters of the distributed dynamic feedback controller can be obtained by solving the problem. The control parameters may include but are not limited to the intermittent control gain , constant matrix B and the constant matrix This control solution can achieve more precise control of the furnace temperature for hot processing of wide and thick plates.

[0080] In the embodiment of the present application, after the control parameters of the distributed dynamic feedback controller are obtained, the effectiveness of the control scheme and the sufficient conditions can be verified based on the control parameters.

[0081] Through steps S100 to S600, the interior of the thick plate hot working furnace is divided into multiple subspaces based on the position of each flame nozzle within the furnace. Based on the difference between the temperature of each subspace and the target control temperature, and taking into account the spatiotemporal temperature variation characteristics of the wide and thick plate hot working furnace, a distributed parameter system model of the wide and thick plate hot working furnace is constructed. Based on the distributed parameter system model, a distributed dynamic feedback controller is constructed. Based on Lyapunov stability theory, a Lyapunov function is constructed to solve the sufficient conditions for the distributed dynamic feedback controller to achieve stability of the distributed parameter system model, thereby determining the control parameters of the distributed dynamic feedback controller. In this way, by combining the distributed parameter system model with the distributed dynamic feedback controller, a distributed intermittent control scheme is constructed, achieving uniform and safe heating of the thick plate within the furnace.

[0082] In some embodiments, the distributed parameter system model is:

[0083] (1)

[0084] in, Indicates the The temperature difference state between the current temperature state and the target temperature state of the subspace, represents the space-time region in the distributed parameter system, represents a spatial variable, is the time variable, represents the space of positive real numbers, The space inside the furnace for hot processing of thick plates has a smooth boundary bounded regions; n represents the number of subspaces in the interior of a wide and thick plate hot processing furnace; , represents the temperature diffusion Laplace operator inside the subspace, Indicates the number of spatial dimensions; is the diffusion coefficient, and ; Represents node space Temperature difference state to node space The influencing factor of the temperature difference state, is a constant; Indicates the hot working furnace number of each wide and thick plate The distributed parameter system corresponding to the subspace is controlled by the input, and the control input represents the energy input of each flame nozzle in the wide and thick plate hot processing furnace.

[0085] Specifically, in the present application, since the control object is the three-dimensional space of the wide and thick plate hot processing furnace, it is possible to set .

[0086] In some embodiments, the distributed parameter system model is transformed into a matrix form as follows:

[0087] (2)

[0088] in, Represents the state of the system by distributed parameters The distributed parameter system state variable matrix is ​​composed of represents a one-dimensional real number space, Indicates the dimension The real matrix space of ; Indicated by the parameter The diagonal matrix parameters formed; Indicated by the parameter The matrix parameters of the distributed parameter system model are constructed; Indicates the control input status The control input matrix formed;

[0089] The initial boundary conditions of the distributed parameter system are:

[0090] , (3)

[0091] or

[0092] , (4)

[0093] in, For smooth boundaries The unit external normal vector of .

[0094] In some embodiments, the distributed dynamic feedback controller is:

[0095] (5)

[0096] in, Indicates the spatial diffusion process of the energy output state of each subspace flame nozzle, Indicates the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, Indicates the influence of the coupling effect of the system state of each subspace distribution parameter, Indicates the The basic variables of the control state of each subspace; is the diffusion coefficient of the control state; Indicates the number of spatial dimensions; Represents node space Controller state to node space The influencing factor of the controller state, Represents node space The distributed parameter system temperature difference state to the node space The influencing factors of the controller state, and are all constants, represents the distributed parameter system control input corresponding to the i-th subspace of each wide and thick plate hot processing furnace, is the intermittent feedback control gain parameter variable, satisfy:

[0097] (6)

[0098] in, represents the feedback control gain coefficient, To control the cycle, Indicates the current control cycle number, Indicates the duty cycle of the control signal, satisfying .

[0099] The distributed dynamic feedback controller is transformed into a matrix form as follows:

[0100] (7)

[0101] in, , represents the system state of the distributed dynamic feedback controller The controller system state variable matrix constructed;

[0102] Represents the gain parameter variable controlled by intermittent feedback The control gain matrix formed by

[0103] , , ;

[0104] The initial boundary conditions of the distributed dynamic feedback controller system are:

[0105] , (8)

[0106] or

[0107] , (9).

[0108] Specifically, the physical meaning of the matrix model (7) of the distributed dynamic feedback controller represents the first The flame nozzle output of each subspace is the energy transfer process between nodes in its subspace and the furnace space. The regulation of the flame nozzle output is described as the regulation of the feedback control gain coefficient in the distributed dynamic feedback controller (5).

[0109] In some embodiments, the distributed dynamic feedback controller is applied to the distributed parameter system to obtain a distributed parameter control system simultaneous closed-loop model, wherein the distributed parameter control system simultaneous closed-loop model is:

[0110] (10)

[0111] in, Represents the state matrix of the simultaneous closed-loop model of the distributed parameter control system; represents the diffusion parameter matrix of the distributed parameter control system closed-loop model, represents an all-zero matrix; Represents the parameter matrix of the simultaneous closed-loop model of the distributed parameter control system.

[0112] In the embodiment of the present application, based on Lyapunov stability theory, sufficient conditions are obtained for the distributed dynamic feedback controller (5) to achieve the stability of the distributed parameter system model (1), that is, sufficient conditions for the asymptotic stability of the distributed parameter control system closed-loop model (10).

[0113] The method provided in this embodiment is now demonstrated based on the following lemma:

[0114] Let function exist is continuous and non-negative, if there exists a constant , , and positive integers Make the following formula:

[0115] (15)

[0116] and If established, then there is .

[0117] The sufficient conditions for the distributed dynamic feedback controller (5) to achieve the stability of the distributed parameter system model (1), that is, the sufficient conditions for the asymptotic stability of the distributed parameter control system closed-loop model (10), include:

[0118] Conclusion 1: Given system parameters Under the condition that there exists a positive definite symmetric matrix , matrix M, B, , and positive constants , When the following conditions are met:

[0119] (11)

[0120] (12)

[0121] (13)

[0122] (14)

[0123] The distributed parameter model reaches stability, where , ,matrix , is the Lyapunov function parameter matrix, is the identity matrix of appropriate dimension, Represents the symmetric terms of a symmetric matrix.

[0124] In the embodiment of the present application, the proof process is as follows:

[0125] Constructing Lyapunov functions satisfy:

[0126] (16)

[0127] in is the Lyapunov function parameter, which is a positive definite symmetric matrix; For space The spatial element.

[0128] Consider when When, combined with the above definition, the matrix Medium parameter matrix is the control parameter matrix to be solved.

[0129] .

[0130] in,

[0131] .

[0132] Similarly: .

[0133] Consider system parameters , , , so there is ;in is a matrix The maximum eigenvalue of .

[0134] So there exists: , so:

[0135] .

[0136] .

[0137] So, if ,but

[0138] .

[0139] Consider controller parameters , , B is implicit in the matrix In the matrix inequality The controller parameters cannot be directly obtained during the solution process. Therefore, the matrix will be transformed to facilitate the solution of the controller parameters.

[0140] definition:

[0141] , (17)

[0142] in is the identity matrix of appropriate dimension; is a positive definite symmetric matrix; is a reversible matrix; the matrix , is the appropriate parameter matrix.

[0143] consider ,but

[0144] (18)

[0145] definition:

[0146] , (19)

[0147] consider , that is, it must meet the following requirements:

[0148] , (20).

[0149] That is, formula (13) in Conclusion 1 needs to hold.

[0150] So, yes Multiply left by left and right multiplication ,exist:

[0151] .

[0152] From formulas (17) to (20), we can get that in the case of formula (11) in conclusion 1, Established. That is, in the case of formula (11) in Conclusion 1, it satisfies

[0153] .

[0154] Consider when When, combined with the above definition, the matrix Medium parameters is a zero matrix.

[0155] .

[0156] .

[0157] So, if .

[0158] but:

[0159] (twenty one)

[0160] According to the formula , similarly, under the conditions of formula (13) in conclusion 1, formula (21) holds. That is, under the conditions of formula (13) in conclusion 1,

[0161] .

[0162] Therefore, when formulas (11) and (12) in Conclusion 1 are satisfied, we can get

[0163] .

[0164] According to Lemma 1, we can satisfy the following assumptions: When (i.e., formula (14) in Conclusion 1), there exists:

[0165] .

[0166] This proves Conclusion 1.

[0167] In the embodiment of the present application, by solving Conclusion 1, the specific data of the parameters in the matrix mode (7) of the distributed dynamic feedback controller can be calculated. Through this control scheme, more precise control can be achieved.

[0168] The effectiveness of the method provided in this embodiment is further illustrated by a specific example below:

[0169] In order to illustrate the effectiveness of the control scheme constructed in this design, consider the following combined model of the spatial temperature transformation distributed parameter system and distributed control system in the hot processing furnace of thick and wide plates

[0170] (twenty two)

[0171] In order to simplify the simulation, the wide and thick plate hot working control furnace is set to contain 4 subspaces, that is, the parameters are set , the heat transfer relationship of each subspace satisfies the matrix , diffusion coefficients of system state and control state satisfy: .

[0172] Set the sampling period of space temperature in the hot processing furnace of thick and wide plates , the control signal duty ratio of the distributed intermittent control scheme is .

[0173] According to the conditions (11)-(14) of Conclusion 1, set the parameters , According to the conclusion 1, we can solve the matrix Specific parameters of each module, including distributed dynamic feedback control parameters , The specific data are as follows:

[0174] ,

[0175] .

[0176] For the intermittent feedback control gain matrix, when When the intermittent feedback control gain ;when When the intermittent feedback control gain ;in: is an all-zero matrix;

[0177] .

[0178] Importing the solved parameters into the model (22), simulation analysis can obtain: the state change trend diagram of each subspace of the wide and thick plate hot working control furnace and the state change trend diagram of the distributed controller of each subspace of the wide and thick plate hot working control furnace. Figure 2 A schematic diagram shows the state change trend of each subspace of a wide and thick plate hot working control furnace in a specific embodiment of the present application. Figure 3 The schematic diagram shows the state change trend of each subspace distributed controller of the wide and thick plate hot processing control furnace of a specific embodiment of the present application. Figure 2 and Figure 3 It can be found that the distributed parameter system can reach a stable state after a period of time under the action of the distributed dynamic feedback controller.

[0179] See Figure 4, is a schematic structural diagram of a temperature control device for a wide and thick plate hot working furnace based on a distributed parameter system stable control according to an embodiment of the present application. A second aspect of an embodiment of the present application provides a temperature control device for a wide and thick plate hot working furnace based on a distributed parameter system stable control, comprising:

[0180] The division module is used to divide the internal space of the thick plate hot processing furnace into subspaces;

[0181] The first construction module is used to construct a distributed parameter system model of the wide and thick plate hot processing control furnace based on the distributed parameter system theory, taking the difference between the temperature state of each subspace and the target temperature state required for the wide and thick plate hot processing as a variable, according to the spatiotemporal variation characteristics of the temperature state of the wide and thick plate hot processing furnace space;

[0182] The second construction module is used to construct a distributed dynamic feedback controller based on the distributed parameter system model, wherein the distributed dynamic feedback controller includes a control system state generator and an intermittent feedback output sub-controller, the control system state generator is constructed based on the influence of the spatial diffusion process of the energy output state of the flame nozzle in each subspace, the influence of the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, and the influence of the coupling effect of the distributed parameter system state in each subspace; the control system state generator is used to determine the control state basic variables of the distributed dynamic feedback controller in each subspace; the intermittent feedback output sub-controller is constructed by designing intermittent gains based on the control state basic variables of the distributed dynamic feedback controller in each subspace;

[0183] An action module is used to apply the constructed distributed dynamic feedback controller to the distributed parameter system model to obtain a distributed parameter control system joint closed-loop model;

[0184] The third construction module is used to construct a Lyapunov function based on Lyapunov stability theory, and solve and obtain sufficient conditions for the distributed dynamic feedback controller to achieve stability of the distributed parameter control system's simultaneous closed-loop model;

[0185] A determination module is used to determine the control parameters of the distributed dynamic feedback controller according to the sufficient condition.

[0186] The wide and thick plate hot processing furnace temperature control device based on distributed parameter system stable control provided in the second aspect of the embodiment of the present application can realize the various processes implemented in the above method embodiment and achieve the same beneficial effects. To avoid repetition, it will not be repeated here.

[0187] See Figure 5, is a structural diagram of an electronic device provided in an embodiment of the present application. An embodiment of the present application provides an electronic device 5000, including a processor 5100 and a memory 5200. The memory 5200 stores machine executable instructions that can be executed by the processor 5100. The processor 5100 can execute the machine executable instructions to implement the above-mentioned wide and thick plate hot processing furnace temperature control method based on distributed parameter system stable control.

[0188] An embodiment of the present application provides a machine-readable storage medium having instructions stored thereon. When the instructions are executed by a processor, the processor implements the above-mentioned method for controlling the temperature of a wide and thick plate hot working furnace based on stable control of a distributed parameter system.

[0189] In some embodiments, the embodiments of the present application also provide a computer program product, including a computer program, which, when executed by a processor, implements the wide and thick plate hot processing furnace temperature control method based on distributed parameter system stable control according to the above embodiment.

[0190] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0191] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, 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 device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including the instruction device, which implements the function specified in the process. Figure 1 a process or multiple processes and / or boxes Figure 1These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0192] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0193] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0194] Computer-readable media includes permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media (transitory media), such as modulated data signals and carrier waves.

[0195] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0196] The above are merely embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should all be included within the scope of the claims of the present application.

[0197] In addition, the various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.

Claims

1. A method for controlling the temperature of a wide and thick plate hot working furnace based on a distributed parameter system stable control, characterized in that: The method comprises: According to the position of each flame nozzle in the wide and thick plate hot processing furnace, the internal space of the wide and thick plate hot processing furnace is divided into subspaces; Taking the difference between the temperature state of each subspace and the target temperature state required for hot processing of thick plates as a variable, and based on the temporal and spatial variation characteristics of the temperature state of the wide and thick plate hot processing furnace and the distributed parameter system theory, a distributed parameter system model of the wide and thick plate hot processing furnace is constructed; Based on the distributed parameter system model, a distributed dynamic feedback controller is constructed, wherein the distributed dynamic feedback controller includes a control system state generator and an intermittent feedback output sub-controller, the control system state generator is constructed based on the influence of the spatial diffusion process of the energy output state of the flame nozzle in each subspace, the influence of the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, and the influence of the coupling effect of the distributed parameter system state in each subspace; the control system state generator is used to determine the control state basic variables of the distributed dynamic feedback controller in each subspace; the intermittent feedback output sub-controller is constructed by designing the intermittent gain based on the control state basic variables of the distributed dynamic feedback controller in each subspace; The constructed distributed dynamic feedback controller is applied to the distributed parameter system model to obtain the distributed parameter control system closed-loop model. Based on Lyapunov stability theory, a Lyapunov function is constructed to solve the sufficient conditions for the distributed dynamic feedback controller to achieve the stability of the distributed parameter control system's simultaneous closed-loop model; The control parameters of the distributed dynamic feedback controller are determined according to the sufficient conditions.

2. The method according to claim 1, characterized in that The distributed parameter system model is: (1) in, Indicates the The temperature difference state between the current temperature state and the target temperature state of the subspace, represents the space-time region in the distributed parameter system, represents a spatial variable, is the time variable, represents the space of positive real numbers, The space inside the furnace for hot processing of thick plates has a smooth boundary bounded regions; n represents the number of subspaces in the interior of a wide and thick plate hot processing furnace; , represents the temperature diffusion Laplace operator inside the subspace, Indicates the number of spatial dimensions; is the diffusion coefficient, and ; Represents node space Temperature difference state to node space The influencing factor of the temperature difference state, is a constant; Indicates the hot working furnace number of each wide and thick plate The distributed parameter system control input corresponding to the subspace represents the energy input of each flame nozzle in the wide and thick plate hot processing furnace.

3. The method according to claim 1, characterized in that The method further comprises: The distributed parameter system model is transformed into a matrix form: (2) in, Represents the state of the system by distributed parameters The distributed parameter system state variable matrix is ​​composed of represents a one-dimensional real number space, Indicates the dimension The real matrix space of ; Indicated by the parameter The diagonal matrix parameters formed; Indicated by the parameter The matrix parameters of the distributed parameter system model are constructed; Indicates the control input status The control input matrix formed; The initial boundary conditions of the distributed parameter system are: , (3) or , (4) in, For smooth boundaries The unit external normal vector of .

4. The method according to claim 1, wherein The distributed dynamic feedback controller is: (5) in, Indicates the spatial diffusion process of the energy output state of each subspace flame nozzle, Indicates the coupling effect of the energy output state of other flame nozzles in the wide and thick plate hot processing furnace, Indicates the influence of the coupling effect of the system state of each subspace distribution parameter, Indicates the The basic variables of the control state of the subspace; is the diffusion coefficient of the control state; Indicates the number of spatial dimensions; Represents node space Controller state to node space The influencing factor of the controller state, Represents node space The distributed parameter system temperature difference state to the node space The influencing factors of the controller state, and are all constants, represents the distributed parameter system control input corresponding to the i-th subspace of each wide and thick plate hot processing furnace, is the intermittent feedback control gain parameter variable, satisfy: (6) in, represents the feedback control gain coefficient, To control the cycle, Indicates the current control cycle number, is the control signal duty cycle, satisfying .

5. The method according to claim 4, characterized in that The method further comprises: The distributed dynamic feedback controller is transformed into a matrix form as follows: (7) in, , represents the system state of the distributed dynamic feedback controller The controller system state variable matrix constructed; Represents the gain parameter variable controlled by intermittent feedback The control gain matrix formed by ， ， ； The initial boundary conditions of the distributed dynamic feedback controller system are: ， (8) or ， (9)。 6. The method according to claim 1, characterized in that The method further comprises: The distributed dynamic feedback controller is applied to the distributed parameter system to obtain a distributed parameter control system simultaneous closed-loop model. The distributed parameter control system simultaneous closed-loop model is: (10) in, Represents the state matrix of the simultaneous closed-loop model of the distributed parameter control system; represents the diffusion parameter matrix of the distributed parameter control system closed-loop model, represents an all-zero matrix; Represents the parameter matrix of the simultaneous closed-loop model of the distributed parameter control system.

7. The method according to claim 1, characterized in that The sufficient conditions include: Given system parameters Under the condition that there exists a positive definite symmetric matrix ,matrix and positive constants , When the following conditions are met: (11) (12) (13) (14) The distributed parameter control system achieves stability through the simultaneous closed-loop model, where , ,matrix , is the Lyapunov function parameter matrix, is the identity matrix of appropriate dimension, Represents the symmetric terms of a symmetric matrix.

8. The method according to claim 1, characterized in that Determining the control parameters of the distributed dynamic feedback controller according to the sufficient condition includes: According to the sufficient condition, the matrix form of the distributed dynamic feedback control is solved to obtain the control parameters of the distributed dynamic feedback controller, wherein the control parameters at least include the intermittent control gain , constant matrix B and constant matrix .

9. An electronic device, characterized in that: include: a memory configured to store instructions; The processor is configured to call the instructions from the memory and implement the wide and thick plate hot processing furnace temperature control method based on distributed parameter system stable control according to any one of claims 1 to 8 when executing the instructions.

10. A machine-readable storage medium, characterized in that The machine-readable storage medium stores instructions for enabling a machine to execute the method for controlling furnace temperature in hot working of thick plates based on distributed parameter system stable control according to any one of claims 1 to 8.

Images