A pulse control method for flame nozzle of wide and thick plate hot processing furnace

Abstract

The present invention discloses a pulse control method for a flame nozzle of a wide and thick plate hot working furnace, comprising the following steps: based on the distributed parameter system theory and based on the temperature transfer process of the subspace in the furnace of the wide and thick plate hot working furnace, constructing a distributed parameter system based on the time-space transformation of the temperature in the furnace of the wide and thick plate hot working furnace; combining the wide and thick plate hot working heating curve, obtaining a distributed parameter error model between the temperature change function of each subspace of the wide and thick plate hot working furnace and the target temperature; constructing a pulse control scheme for the flame nozzle of the wide and thick plate hot working furnace to achieve stable control of the distributed parameter system error model; based on Lyapunov stability theory, solving and obtaining sufficient conditions for achieving asymptotic stable control of the distributed parameter system error model; performing numerical simulation, and solving the pulse control parameters based on the obtained sufficient conditions.

Description

Technical Field

[0001] The invention relates to the field of heating furnaces, and in particular to a pulse control method for a flame nozzle of a wide and thick plate hot processing furnace. Background Art

[0002] As a key foundational material for high-end equipment manufacturing and large-scale engineering construction (such as ships, bridges, pressure vessels, and offshore platforms), heavy plate's comprehensive performance (such as strength, toughness, weldability, and fatigue resistance) depends heavily on the quality control of its thermal processing processes (such as rolling and heat treatment). The hot working furnace is the core thermal equipment in the heavy plate production process, responsible for heating the slab to the target process temperature while maintaining the necessary uniformity.

[0003] In traditional thick plate heating furnaces, the flame nozzles typically operate in a continuous combustion mode. However, given the unique challenges of thick plate, such as large thickness, large size, and complex heating curves, this traditional continuous combustion mode has gradually exposed problems such as insufficient temperature uniformity, delayed control response, and high energy consumption. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a pulse control method for a flame nozzle of a wide and thick plate hot processing furnace with a simple algorithm and high control accuracy.

[0005] The technical solution of the present invention to solve the above technical problems is: a pulse control method for a flame nozzle of a wide and thick plate hot processing furnace, comprising the following steps:

[0006] S1: Based on the distributed parameter system theory and the subspace temperature transfer process in the furnace of thick plate hot processing furnace, a distributed parameter system based on the spatiotemporal transformation of the furnace temperature is constructed;

[0007] S2: Based on the heating curve of wide and thick plate hot working, the distribution parameter error model between the temperature change function of each subspace of the wide and thick plate hot working furnace and the target temperature is obtained;

[0008] S3: Construct a pulse control scheme for the flame nozzle of a thick plate hot working furnace to achieve stable control of the distributed parameter system error model. The pulse control scheme is divided into two parts: the basic control output part and the pulse control output part. The basic control output part approximates the heating curve of the thick plate hot working by constructing a basic control output function, while the pulse control output part achieves precise control of the distributed parameter error model system state.

[0009] S4: Based on Lyapunov stability theory, we solve and derive sufficient conditions for achieving asymptotically stable control of distributed parameter system error models;

[0010] S5: Perform numerical simulation and solve the pulse control parameters based on the obtained sufficient conditions.

[0011] The pulse control method of the flame nozzle of the wide and thick plate hot processing furnace is as follows: in step S1, the internal space of the wide and thick plate hot processing furnace is divided into subspaces, each subspace is defined as a spatial node, and each spatial node has a flame nozzle to adjust the temperature of the spatial node; considering the time-varying energy transfer within each subspace in the furnace and the energy interaction between each spatial node, the furnace temperature change of the wide and thick plate hot processing furnace with spatiotemporal characteristics is defined as a distributed parameter system, that is, the spatial temperature transformation of the wide and thick plate hot processing furnace can be modeled and described using a distributed parameter system.

[0012] The pulse control method of the flame nozzle of the thick plate hot processing furnace is as follows: The time variation function of the spatial temperature state distribution in the subspace is: , represents a spatial variable; As a time variable, considering the spatiotemporal transformation characteristics of the temperature in the hot processing furnace for thick and wide plates, the following distributed parameter system is constructed to describe the temperature variation law of each subspace in the hot processing furnace:

[0013] (1);

[0014] in, represents the time and space region in the thick plate hot working furnace, ; represents the space of positive real numbers; For smooth boundaries The bounded area is the space inside the furnace of the wide and thick plate hot processing furnace. , represents the Euclidean norm, express Spatial variables within The norm is bounded, is the numerical parameter that satisfies the conditions, represents positive infinity; , represents a one-dimensional real number space, express dimensional real space, represents the number of spatial dimensions; and , represents the spatial dimension measurement function, Express requirements The dimension of is greater than zero; For the The temperature diffusion coefficient of the subspace is ; For the The control input state of the subspace; let ,but Represents the temperature diffusion laplace operator inside the subspace; represents the total dimension of the space, represents the spatial dimension ordinal number, Represented as dimensional variables in space; is the temperature transfer time lag; Indicates the The subspace state pairs The influence factor of the subspace state, Indicates the The time-delayed state of the subspace is The influencing factors of the subspace states; , Indicates the The subspace of Subspace releases energy; , Indicates the The subspace of The subspace absorbs energy.

[0015] In the pulse control method for the flame nozzle of the thick plate hot working furnace, in step S2, the thick plate hot working heating curve is set to meet the following requirements:

[0016] (2);

[0017] in, Represents the spatial target temperature variation curve of the distributed parameter system; Represents the time-varying rate function of the spatial target temperature of the distributed parameter system;

[0018] To achieve the control target, set the The error function between the temperature change function of the subspace and the target temperature is: ,satisfy:

[0019] (3);

[0020] Combining formula (1) and formula (3), we can get the following distribution parameter error model:

[0021] (4);

[0022] in, Indicates the The temperature error state of the subspace is The influencing factors of the temperature error state in each subspace, Indicates the The time-delayed temperature error state of the subspace is The influencing factors of the temperature error state in each subspace;

[0023] when When satisfied: , ;

[0024] when When satisfied: , .

[0025] In the pulse control method for the flame nozzle of the wide and heavy plate hot working furnace, in step S2, two control objectives are set. The first control objective is to achieve that the furnace temperature of the wide and heavy plate hot working furnace continuously matches the target temperature for hot working of the wide and heavy plate steel in engineering terms; the second control objective is to achieve uniform distribution of the furnace temperature of the wide and heavy plate hot working furnace.

[0026] In the theoretical solution process, when the distribution parameter error model reaches asymptotic stability, the uniform distribution of furnace temperature in the wide and thick plate hot processing furnace is achieved; when the distribution parameter error model reaches asymptotic stability, it satisfies According to the definition of formula (3), when the distributed parameter error model reaches asymptotic stability, the furnace temperature of the wide and thick plate hot processing furnace continues to match the target temperature of the wide and thick plate hot processing steel. Therefore, when the designed control scheme achieves the asymptotic stability of the distributed parameter error model, the two set control objectives are achieved.

[0027] According to the distributed parameter error model, in order to simplify the description, the distributed parameter system is rewritten into a matrix form:

[0028] (5);

[0029] in, , the superscript T represents the transpose of the matrix, is the system matrix variable, ; System state diffusion coefficient , Indicated by The diagonal matrix formed by represents the identity of a diagonal matrix; , , Represented by the function The dimensions of the composition are Matrix function of ; , Indicated by The dimensions of the composition are Matrix parameters of ; , Indicated by The dimensions of the composition are Matrix parameters of ; Indicates that the dimension formed by the elements in the brackets is Matrix of , , Indicated by The control input matrix variable composed of the control input states of the nodes;

[0030] Based on the actual engineering process of time-space transformation of thick plate hot processing furnace, the initial boundary conditions of the distributed parameter system are set as follows:

[0031] , (6);

[0032] or

[0033] , (7);

[0034] , (8);

[0035] in for The unit external normal vector of is a smooth function.

[0036] The pulse control method of the flame nozzle of the thick plate hot processing furnace, in step S3, the pulse control output part: set The pulse control scheme The moment of pulse control satisfies:

[0037] (9);

[0038] definition is the control interval of pulse control, ;

[0039] In the pulse control output part, that is, At this moment, the impulse control constructs the impulse control gain for the distributed parameter error model system state to achieve the regulation of the distributed parameter error model system state;

[0040] Basic control output part: When , the basic control output satisfies:

[0041] (10);

[0042] in Indicates the The basic control output function of the subspace is constructed based on historical data. To achieve the approximation of the heating transformation curve for hot working of wide and thick plates;

[0043] Therefore, combined with the distributed parameter error model, the impulse control scheme model can be obtained as follows:

[0044] (11);

[0045] in, , Indicates the The instantaneous state after the pulse controller acts in the subspace, , Indicates the The instantaneous state before the pulse controller acts in the subspace, Indicates the The first subspace The gain of the pulse control.

[0046] In the above-mentioned pulse control method for the flame nozzle of the wide and thick plate hot processing furnace, in step S3, to simplify the description, the pulse control scheme model is changed to the following matrix form:

[0047] (12);

[0048] in, Pulse control is performed when Indicates the instantaneous moment after pulse control; Indicates the instant before pulse control;

[0049] , , Indicated by Error function at time The system matrix variables constituted; Indicated by Error function at time The system matrix variables are composed of , ; express The pulse control parameter matrix at time , Indicated by The dimensions of the composition are The nonlinear function of .

[0050] In the above-mentioned pulse control method for the flame nozzle of the wide and thick plate hot processing furnace, in step S4, in order to facilitate the drawing of relevant conclusions, the following conditions are given:

[0051] Assumption 1: For the constructed nonlinear function , satisfying the following Lipschitz conditions:

[0052] (13);

[0053] in is the Lipschitz condition parameter of hypothesis 1, ;

[0054] Next, we will use Lyapunov theory to derive sufficient conditions for the existence of an asymptotically stable pulse controller for distributed parameter systems. We will then solve for the specific parameters of the pulse control scheme, ensuring that the distributed parameter system is asymptotically stable under the pulse control scheme. This means that the temperatures of each subspace in the thick plate hot working furnace reach the target control temperature.

[0055] Conclusion 1: Under given parameters, if the following conditions are met, the matrix form impulse control scheme model is asymptotically stable;

[0056] Condition A: For all , such that:

[0057] (14);

[0058] Among them, 0 represents an all-zero matrix; represents the identity matrix; formula (14) is a symmetric matrix, represents the symmetric term of a symmetric matrix; 、 Both represent the parameters of the Lyapunov functional and are positive definite symmetric matrices to be solved; is a positive constant greater than zero;

[0059] Condition B: For each , ,exist

[0060] (15);

[0061] in, represents the largest eigenvalue of the matrix, For the The proportional constant of the pulse control state satisfies: ;

[0062] Condition C: For all ,have:

[0063] (16);

[0064] in, is the exponential stability constant of the system, .

[0065] In the pulse control method for the flame nozzle of the thick plate hot working furnace, in step S4, the proof process of conclusion 1 is as follows:

[0066] Based on Lyapunov stability theory, the following Lyapunov functional is constructed :

[0067] (17);

[0068] in: is the time integration parameter, is the time integral differential;

[0069] Let the intermediate amount , intermediate amount ,but ;

[0070] Next, we will find the sufficient conditions for the stable control of the matrix form impulse control scheme model based on Lyapunov stability theory; considering the existence of state instantaneous transition in impulse control, in the solution process, we will find the sufficient conditions for the stable control of the matrix form impulse control scheme model based on Lyapunov stability theory. Time and When , the derivative of Lyapunov functional is solved, and the derivative of Lyapunov functional is obtained. The sufficient condition is that , Decreasing, then Decrease to reach asymptotically stable state;

[0071] when When:

[0072] (18);

[0073] (19);

[0074] in, for The derivative of for The derivative of for The derivative of for The derivative of

[0075] because , Representation matrix The minimum eigenvalue of Representation matrix The minimum eigenvalue of ;

[0076] Combining formulas (18) and (19), and using assumption 1, we can obtain:

[0077] (20);

[0078] in, for The derivative of is the intermediate variable matrix defined, satisfying: ;

[0079] According to formula (20), considering , so when When , if there is:

[0080] (twenty one);

[0081] Then it satisfies:

[0082] (twenty two);

[0083] That is When , if formula (21) holds, then formula (22) holds;

[0084] Based on formula (22), we can get When there is:

[0085] (twenty three);

[0086] when When:

[0087] ;

[0088] definition:

[0089] (twenty four);

[0090] Therefore, when condition B exists, that is, formula (24) is established, it satisfies:

[0091] (25);

[0092] Combining formula (23) with formula (25), we can obtain the following recursive solution:

[0093]

[0094] For all ,exist ,definition:

[0095] (26);

[0096] Therefore, when condition C exists, that is, formula (26) is established, it satisfies:

[0097] (27);

[0098] According to formula (27), we can get Decreasing, the exponential is stable; therefore, Conclusion 1 is proved.

[0099] In the pulse control method for the flame nozzle of the thick plate hot processing furnace, in step S5, the numerical simulation process is as follows:

[0100] The specific parameters are set as follows: Set the wide and thick plate hot working control furnace to contain 4 sub-spaces, that is, set , the heat transfer relationship of each subspace satisfies , , , ;

[0101] According to conclusion 1 condition A, use LMI toolbox to solve the optimal Satisfies the A condition, and the corresponding positive definite symmetric matrix , for:

[0102] , ;

[0103] According to Conclusion 1 Condition C , numerical simulation analysis settings meet the conditions;

[0104] Based on the flame nozzle control implementation process of the wide and thick plate processing furnace in actual engineering, numerical simulation analysis is used to set the spatial temperature pulse control cycle in the wide and thick plate hot processing furnace ,Right now , and then according to condition C, we can solve Satisfy the conditions; so the numerical simulation analysis sets the proportional constant of the pulse control state meet the conditions;

[0105] According to condition B in conclusion 1, the gain of pulse control is obtained meet the conditions;

[0106] Based on the conditions of Conclusion 1, the control parameters are solved and numerical simulation is performed based on the control parameters to obtain the temperature error state change trend diagram of each node subspace.

[0107] The beneficial effects of the present invention are: the present invention constructs a basic control scheme The basic control output scheme is based on the complex heating curve required in the hot working process of thick and wide plates, and the controller output adjustment function model is constructed. When the basic control output acts on the distributed parameter system, the temperature change of the wide and thick plate hot processing furnace can be closer to the temperature curve required for wide and thick plate hot processing; the control scheme constructed by the present invention combines pulse control with basic control, which can significantly reduce the pulse control adjustment range and increase the accuracy of the pulse control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 It is the overall flow chart of the present invention.

[0109] Figure 2 Schematic diagram of the instantaneous state of pulse control.

[0110] Figure 3 This is the temperature error state change trend diagram of the first subspace during numerical simulation.

[0111] Figure 4 This is the temperature error state change trend diagram of the second subspace during numerical simulation.

[0112] Figure 5 This is the temperature error state change trend diagram of the third subspace during numerical simulation.

[0113] Figure 6 This is the temperature error state change trend diagram of the fourth subspace during numerical simulation. DETAILED DESCRIPTION

[0114] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0115] like Figure 1 As shown, a pulse control method for a flame nozzle of a wide and thick plate hot processing furnace includes the following steps:

[0116] S1: Based on the distributed parameter system theory and the subspace temperature transfer process in the furnace of thick plate hot processing furnace, a distributed parameter system based on the spatiotemporal transformation of the furnace temperature is constructed.

[0117] In the step S1, the internal space of the thick plate hot working furnace is divided into subspaces, each subspace is defined as a spatial node, and each spatial node has a flame nozzle to adjust the temperature of the spatial node; considering the time-varying energy transfer within each subspace in the furnace and the energy interaction between each spatial node, the furnace temperature change of the wide and thick plate hot processing furnace with spatiotemporal characteristics is defined as a distributed parameter system, that is, the spatial temperature transformation of the wide and thick plate hot processing furnace can be modeled and described using a distributed parameter system.

[0118] S2: Combined with the heating curve of wide and thick plate hot processing, the distribution parameter error model between the temperature change function of each subspace of the wide and thick plate hot processing furnace and the target temperature is obtained.

[0119] In step S2, define The time variation function of the spatial temperature state distribution in the subspace is: , represents a spatial variable; As a time variable, considering the spatiotemporal transformation characteristics of the temperature in the hot processing furnace for thick and wide plates, the following distributed parameter system is constructed to describe the temperature variation law of each subspace in the hot processing furnace:

[0120] (1);

[0121] in, represents the time and space region in the thick plate hot working furnace, ; represents the space of positive real numbers; For smooth boundaries The bounded area is the space inside the furnace of the wide and thick plate hot processing furnace. , represents the Euclidean norm, express Spatial variables within The norm is bounded, is the numerical parameter that satisfies the conditions, represents positive infinity; , represents a one-dimensional real number space, express dimensional real space, represents the number of spatial dimensions; and , represents the spatial dimension measurement function, Express requirements The dimension of is greater than zero; For the The temperature diffusion coefficient of the subspace is ; For the The control input state of the subspace; let ,but Represents the temperature diffusion laplace operator inside the subspace; represents the total dimension of the space, represents the spatial dimension ordinal number, Represented as dimensional variables in space; is the temperature transfer time lag; Indicates the The subspace state pairs The influence factor of the subspace state, Indicates the The time-delayed state of the subspace is The influencing factors of the subspace states; , Indicates the The subspace of Subspace releases energy; , Indicates the The subspace of The subspace absorbs energy.

[0122] During the hot working process of thick and heavy plates in a hot working furnace, in order to achieve the optimal hot working treatment of the thick and heavy plate steel, it is necessary to make the temperature of the internal space of the hot working furnace change with time to meet a specific curve (the focus of the present invention is not on the specific parameters of the curve, but on designing a specific control scheme to ensure that the furnace temperature change of the thick and heavy plate hot working furnace matches the hot working temperature curve of the thick and heavy plate steel). Therefore, in the present invention, the hot working heating curve of the thick and heavy plate is set to meet the following:

[0123] (2);

[0124] in, Represents the spatial target temperature variation curve of the distributed parameter system; Represents the time-varying rate function of the spatial target temperature of the distributed parameter system;

[0125] To achieve the control target, set the The error function between the temperature change function of the subspace and the target temperature is: ,satisfy:

[0126] (3);

[0127] Combining formula (1) and formula (3), we can get the following distribution parameter error model:

[0128] (4);

[0129] in, Indicates the The temperature error state of the subspace is The influencing factors of the temperature error state in each subspace, Indicates the The time-delayed temperature error state of the subspace is The influencing factors of the temperature error state in each subspace;

[0130] when When satisfied: , ;

[0131] when When satisfied: , .

[0132] Two control objectives were set. The first was to ensure that the furnace temperature of the wide and heavy plate hot processing furnace consistently matched the target temperature for hot processing of wide and heavy plate steel. The second was to ensure that the furnace temperature of the wide and heavy plate hot processing furnace was evenly distributed.

[0133] In the theoretical solution process, when the distribution parameter error model reaches asymptotic stability, the uniform distribution of furnace temperature in the wide and thick plate hot processing furnace is achieved; when the distribution parameter error model reaches asymptotic stability, it satisfies According to the definition of formula (3), when the distributed parameter error model reaches asymptotic stability, the furnace temperature of the wide and thick plate hot processing furnace continues to match the target temperature of the wide and thick plate hot processing; therefore, when the designed control scheme achieves the asymptotic stability of the distributed parameter error model, the two set control objectives are achieved.

[0134] According to the distributed parameter error model, in order to simplify the description, the distributed parameter system is rewritten into a matrix form:

[0135] (5);

[0136] in, , the superscript T indicates the transpose of the matrix, is the system matrix variable, ; System state diffusion coefficient , Indicated by The diagonal matrix formed by represents the identity of a diagonal matrix; , , Represented by the function The dimensions of the composition are Matrix function of ; , Indicated by The dimensions of the composition are Matrix parameters of ; , Indicated by The dimensions of the composition are Matrix parameters of ; Indicates that the dimension formed by the elements in the brackets is Matrix of , , Indicated by The control input matrix variable composed of the control input states of the nodes;

[0137] Based on the actual engineering process of time-space transformation of thick plate hot processing furnace, the initial boundary conditions of the distributed parameter system are set as follows:

[0138] , (6);

[0139] or

[0140] , (7);

[0141] , (8);

[0142] in for The unit external normal vector of is a smooth function.

[0143] S3: Construct a pulse control scheme for the flame nozzle of a wide and thick plate hot processing furnace to achieve stable control of the distributed parameter system error model; the pulse control scheme is divided into two parts: the basic control output part and the pulse control output part. The basic control output part constructs a basic control output function to achieve approximation of the heating curve of wide and thick plate hot processing, and the pulse control output part achieves precise control of the distributed parameter error model system state.

[0144] Pulse control output part: setting The pulse control scheme The moment of pulse control satisfies:

[0145] (9);

[0146] definition is the control interval of pulse control, ;

[0147] In the pulse control output part, that is, At this moment, the pulse control constructs the pulse control gain for the distributed parameter error model system state, realizes the regulation of the distributed parameter error model system state, and then realizes the precise control of the distributed parameter error model system state.

[0148] Basic control output part: When , the basic control output satisfies:

[0149] (10);

[0150] in Indicates the The basic control output function of the subspace is constructed based on historical data. To achieve the approximation of the heating transformation curve for hot working of wide and thick plates;

[0151] Therefore, combined with the distributed parameter error model, the impulse control scheme model can be obtained as follows:

[0152] (11);

[0153] in, , Indicates the The instantaneous state after the pulse controller acts in the subspace, , Indicates the The instantaneous state before the pulse controller acts in the subspace. The instantaneous state of the pulse control is as follows: Figure 2 As shown; Indicates the The first subspace The gain of the pulse control.

[0154] To simplify the description, the pulse control scheme model is changed to the following matrix form:

[0155] (12);

[0156] in, Pulse control is performed when Indicates the instantaneous moment after pulse control; Indicates the instant before pulse control;

[0157] , , Indicated by Error function at time The system matrix variables constituted; Indicated by Error function at time The system matrix variables are composed of , ; express The pulse control parameter matrix at time , Indicated by The dimensions of the composition are The nonlinear function of .

[0158] S4: Based on Lyapunov stability theory, we solve the sufficient conditions for achieving asymptotically stable control of distributed parameter system error models.

[0159] In order to draw relevant conclusions, the following conditions are given:

[0160] Assumption 1: For the constructed nonlinear function , satisfying the following Lipschitz conditions:

[0161] (13);

[0162] in is the Lipschitz condition parameter of hypothesis 1, ;

[0163] Next, we will use Lyapunov theory to derive sufficient conditions for the existence of an asymptotically stable pulse controller for distributed parameter systems. We will then solve for the specific parameters of the pulse control scheme, ensuring that the distributed parameter system is asymptotically stable under the pulse control scheme. This means that the temperatures of each subspace in the thick plate hot working furnace reach the target control temperature.

[0164] Conclusion 1: Under given parameters, if the following conditions are met, the matrix form impulse control scheme model is asymptotically stable;

[0165] Condition A: For all , such that:

[0166] (14);

[0167] Where 0 represents an all-zero matrix of appropriate dimension; represents the identity matrix; formula (14) is a symmetric matrix, represents the symmetric term of a symmetric matrix; 、 Both represent the parameters of the Lyapunov functional and are positive definite symmetric matrices to be solved; is a positive constant greater than zero;

[0168] Condition B: For each , ,exist

[0169] (15);

[0170] in, represents the largest eigenvalue of the matrix, For the The proportional constant of the pulse control state satisfies: ;

[0171] Condition C: For all ,have:

[0172] (16);

[0173] in, is the exponential stability constant of the system, .

[0174] In step S4, the proof process of conclusion 1 is as follows:

[0175] Based on Lyapunov stability theory, the following Lyapunov functional is constructed :

[0176] (17);

[0177] in: is the time integration parameter, is the time integral differential;

[0178] Let the intermediate amount , intermediate amount ,but ;

[0179] Next, we will find the sufficient conditions for the stable control of the matrix form impulse control scheme model based on Lyapunov stability theory; considering the existence of state instantaneous transition in impulse control, in the solution process, we will find the sufficient conditions for the stable control of the matrix form impulse control scheme model based on Lyapunov stability theory. Time and When , the derivative of Lyapunov functional is solved, and the derivative of Lyapunov functional is obtained. The sufficient condition is that , Decreasing, then Decrease to reach asymptotically stable state;

[0180] when When:

[0181] (18);

[0182] (19);

[0183] in, for The derivative of for The derivative of for The derivative of for The derivative of

[0184] because , Representation matrix The minimum eigenvalue of Representation matrix The minimum eigenvalue of ;

[0185] Combining formulas (18) and (19), and using assumption 1, we can obtain:

[0186] (20);

[0187] in, for The derivative of is the intermediate variable matrix defined, satisfying: ;

[0188] According to formula (20), considering , so when When , if there is:

[0189] (twenty one);

[0190] Then it satisfies:

[0191] (twenty two);

[0192] That is When , if formula (21) holds, then formula (22) holds;

[0193] Based on formula (22), we can get When there is:

[0194] (twenty three);

[0195] when When:

[0196]

[0197] definition:

[0198] (twenty four);

[0199] Therefore, when condition B exists, that is, formula (24) is established, it satisfies:

[0200] (25);

[0201] Combining formula (23) with formula (25), we can obtain the following recursive solution:

[0202]

[0203] For all ,exist ,definition:

[0204] (26);

[0205] Therefore, when condition C exists, that is, formula (26) is established, it satisfies:

[0206] (27);

[0207] According to formula (27), we can get Decreasing, the exponential is stable; therefore, Conclusion 1 is proved.

[0208] S5: Perform numerical simulation and solve the pulse control parameters based on the obtained sufficient conditions.

[0209] In step S5, the numerical simulation process is as follows:

[0210] The specific parameters are set as follows: Set the wide and thick plate hot working control furnace to contain 4 subspaces, that is, set the parameters , the heat transfer relationship of each subspace satisfies , , , .

[0211] According to conclusion 1 condition A, use LMI toolbox to solve the optimal Satisfies the A condition, and the corresponding positive definite symmetric matrix , for:

[0212] , ;

[0213] According to Conclusion 1 Condition C , numerical simulation analysis settings meet the conditions;

[0214] Based on the flame nozzle control implementation process of the wide and thick plate processing furnace in actual engineering, numerical simulation analysis is used to set the spatial temperature pulse control cycle in the wide and thick plate hot processing furnace ,Right now , and then according to condition C, we can solve Satisfy the conditions; so the numerical simulation analysis sets the proportional constant of the pulse control state meet the conditions;

[0215] According to condition B in conclusion 1, the gain of pulse control is obtained The conditions are met; solve the parameters based on Conclusion 1 and perform simulation.

[0216] like Figure 3-Figure 6As shown in Figure 2, it can be found that under the action of the impulse control scheme, the distributed parameter system reaches an asymptotically stable state, that is, the error between the temperature of each subspace and the target temperature tends to zero, and the target temperature state is reached.

Claims

1. A pulse control method for a flame nozzle of a wide and thick plate hot processing furnace, characterized in that: The following steps are involved: S1: Based on the distributed parameter system theory and the subspace temperature transfer process in the furnace of thick plate hot processing furnace, a distributed parameter system based on the spatiotemporal transformation of the furnace temperature is constructed; S2: Based on the heating curve of wide and thick plate hot working, the distribution parameter error model between the temperature change function of each subspace of the wide and thick plate hot working furnace and the target temperature is obtained; S3: Construct a pulse control scheme for the flame nozzle of a thick plate hot working furnace to achieve stable control of the distributed parameter system error model. The pulse control scheme is divided into two parts: the basic control output part and the pulse control output part. The basic control output part approximates the heating curve of the thick plate hot working by constructing a basic control output function, while the pulse control output part achieves precise control of the distributed parameter error model system state. S4: Based on Lyapunov stability theory, we solve and derive sufficient conditions for achieving asymptotically stable control of distributed parameter system error models; S5: Perform numerical simulation and solve the pulse control parameters based on the obtained sufficient conditions.

2. The pulse control method for the flame nozzle of a wide and thick plate hot processing furnace according to claim 1 is characterized in that: In the step S1, the internal space of the thick plate hot working furnace is divided into subspaces, each subspace is defined as a spatial node, and each spatial node has a flame nozzle to adjust the temperature of the spatial node; considering the time-varying energy transfer within each subspace in the furnace and the energy interaction between each spatial node, the furnace temperature change of the wide and thick plate hot processing furnace with spatiotemporal characteristics is defined as a distributed parameter system, that is, the spatial temperature transformation of the wide and thick plate hot processing furnace can be modeled and described using a distributed parameter system.

3. The pulse control method for the flame nozzle of a wide and thick plate hot processing furnace according to claim 2, characterized in that: In step S2, define The time variation function of the spatial temperature state distribution in the subspace is: , represents a spatial variable; As a time variable, considering the spatiotemporal transformation characteristics of the temperature in the hot processing furnace for thick and wide plates, the following distributed parameter system is constructed to describe the temperature variation law of each subspace in the hot processing furnace: （1） in, represents the time and space region in the thick plate hot working furnace, ; represents the space of positive real numbers; For smooth boundaries The bounded area is the space inside the furnace of the wide and thick plate hot processing furnace. , represents the Euclidean norm, express Spatial variables within The norm is bounded, is the numerical parameter that satisfies the conditions, represents positive infinity; , represents a one-dimensional real number space, express dimensional real space, represents the number of spatial dimensions; and , represents the spatial dimension measurement function, Express requirements The dimension of is greater than zero; For the The temperature diffusion coefficient of the subspace is ; For the The control input state of the subspace; let ,but Represents the temperature diffusion laplace operator inside the subspace; represents the total dimension of the space, represents the spatial dimension ordinal number, Represented as dimensional variables in space; is the temperature transfer time lag; Indicates the The subspace state pairs The influence factor of the subspace state, Indicates the The time-delayed state of the subspace is The influencing factors of the subspace states; , Indicates the The subspace of Subspace releases energy; , Indicates the The subspace of The subspace absorbs energy.

4. The pulse control method for the flame nozzle of a wide and thick plate hot processing furnace according to claim 3 is characterized in that: In step S2, the wide and thick plate hot working heating curve is set to meet the following requirements: （2） in, Represents the spatial target temperature variation curve of the distributed parameter system; Represents the time-varying rate function of the spatial target temperature of the distributed parameter system; To achieve the control target, set the The error function between the temperature change function of the subspace and the target temperature is: ,satisfy: （3） Combining formula (1) and formula (3), we can get the following distribution parameter error model: （4） in, Indicates the The temperature error state of the subspace is The influencing factors of the temperature error state in each subspace, Indicates the The time-delayed temperature error state of the subspace is The influencing factors of the temperature error state in each subspace; when When satisfied: , ; when When satisfied: , .

5. The pulse control method for the flame nozzle of a wide and thick plate hot processing furnace according to claim 4 is characterized in that: In step S2, two control objectives are set. The first control objective is to ensure that the furnace temperature of the wide and heavy plate hot processing furnace continuously matches the target temperature of the wide and heavy plate steel hot processing in engineering. The second control objective is to ensure that the furnace temperature of the wide and heavy plate hot processing furnace is evenly distributed. In the theoretical solution process, when the distribution parameter error model reaches asymptotic stability, the uniform distribution of furnace temperature in the wide and thick plate hot processing furnace is achieved; when the distribution parameter error model reaches asymptotic stability, it satisfies According to the definition of formula (3), when the distributed parameter error model reaches asymptotic stability, the furnace temperature of the wide and thick plate hot processing furnace continues to match the target temperature of the wide and thick plate hot processing steel. Therefore, when the designed control scheme achieves the asymptotic stability of the distributed parameter error model, the two set control objectives are achieved. According to the distributed parameter error model, in order to simplify the description, the distributed parameter system is rewritten into a matrix form: （5） in, , the superscript T represents the transpose of the matrix, is the system matrix variable, ; System state diffusion coefficient , Indicated by The diagonal matrix formed by represents the identity of a diagonal matrix; , , Represented by the function The dimensions of the composition are Matrix function of ; , Indicated by The dimensions of the composition are Matrix parameters of ; , Indicated by The dimensions of the composition are Matrix parameters of ; Indicates that the dimension formed by the elements in the brackets is Matrix of , , Indicated by The control input matrix variable composed of the control input states of the nodes; Based on the actual engineering process of time-space transformation of thick plate hot processing furnace, the initial boundary conditions of the distributed parameter system are set as follows: ， （6） or ， （7） ， （8） in for The unit external normal vector of is a smooth function.

6. The pulse control method for the flame nozzle of a wide and thick plate hot processing furnace according to claim 5, characterized in that: In the step S3, Pulse control output part: setting The pulse control scheme The moment of pulse control satisfies: （9） definition is the control interval of pulse control, ; In the pulse control output part, that is, At this moment, the impulse control constructs the impulse control gain for the distributed parameter error model system state to achieve the regulation of the distributed parameter error model system state; Basic control output part: When , the basic control output satisfies: （10） in Indicates the The basic control output function of the subspace is constructed based on historical data. To achieve the approximation of the heating transformation curve for hot working of wide and thick plates; Therefore, combined with the distributed parameter error model, the impulse control scheme model can be obtained as follows: （11） in, , Indicates the The instantaneous state after the pulse controller acts in the subspace, , Indicates the The instantaneous state before the pulse controller acts in the subspace, Indicates the The first subspace The gain of the pulse control.

7. The pulse control method for the flame nozzle of a wide and thick plate hot working furnace according to claim 6, characterized in that: In step S3, to simplify the description, the pulse control scheme model is changed to the following matrix form: （12） in, Pulse control is performed when Indicates the instantaneous moment after pulse control; Indicates the instant before pulse control; , , Indicated by Error function at time The system matrix variables constituted; Indicated by Error function at time The system matrix variables are composed of , ; express The pulse control parameter matrix at time , Indicated by The dimensions of the composition are The nonlinear function of .

8. The pulse control method for the flame nozzle of a wide and thick plate hot working furnace according to claim 7, characterized in that: In step S4, in order to facilitate drawing relevant conclusions, the following conditions are given: Assumption 1: For the constructed nonlinear function , satisfying the following Lipschitz conditions: （13） in is the Lipschitz condition parameter of hypothesis 1, ; Next, we will use Lyapunov theory to derive sufficient conditions for the existence of an asymptotically stable pulse controller for distributed parameter systems. We will then solve for the specific parameters of the pulse control scheme, ensuring that the distributed parameter system is asymptotically stable under the pulse control scheme. This means that the temperatures of each subspace in the thick plate hot working furnace reach the target control temperature. Conclusion 1: Under given parameters, if the following conditions are met, the matrix form impulse control scheme model is asymptotically stable; Condition A: For all , such that: （14） Among them, 0 represents an all-zero matrix; represents the identity matrix; formula (14) is a symmetric matrix, represents the symmetric term of a symmetric matrix; 、 Both represent the parameters of the Lyapunov functional and are positive definite symmetric matrices to be solved; is a positive constant greater than zero; Condition B: For each , ,exist （15） in, represents the largest eigenvalue of the matrix, For the The proportional constant of the pulse control state satisfies: ; Condition C: For all ,have: （16） in, is the exponential stability constant of the system, .

9. The pulse control method for the flame nozzle of a wide and thick plate hot working furnace according to claim 8, characterized in that: In step S4, the proof process of conclusion 1 is as follows: Based on Lyapunov stability theory, the following Lyapunov functional is constructed : （17） in: is the time integration parameter, is the time integral differential; Let the intermediate amount , intermediate amount ,but ; Next, we will find the sufficient conditions for the stable control of the matrix form impulse control scheme model based on Lyapunov stability theory; considering the existence of state instantaneous transition in impulse control, in the solution process, we will find the sufficient conditions for the stable control of the matrix form impulse control scheme model based on Lyapunov stability theory. Time and When , the derivative of Lyapunov functional is solved, and the derivative of Lyapunov functional is obtained. The sufficient condition is that , Decreasing, then Decrease to reach asymptotically stable state; when When: （18） （19） in, for The derivative of for The derivative of for The derivative of for The derivative of because , Representation matrix The minimum eigenvalue of Representation matrix The minimum eigenvalue of ; Combining formulas (18) and (19), and using assumption 1, we can obtain: （20） in, for The derivative of is the intermediate variable matrix defined, satisfying: ； According to formula (20), considering , so when When , if there is: （21） Then it satisfies: （22） That is When , if formula (21) holds, then formula (22) holds; Based on formula (22), we can get When there is: （23） when When: ； definition: （24） Therefore, when condition B exists, that is, formula (24) is established, it satisfies: （25） Combining formula (23) with formula (25), we can obtain the following recursive solution: ； For all ,exist ,definition: （26） Therefore, when condition C exists, that is, formula (26) is established, it satisfies: （27） According to formula (27), we can get Decreasing, the exponential is stable; therefore, Conclusion 1 is proved.

10. The pulse control method for the flame nozzle of a wide and thick plate hot working furnace according to claim 8, characterized in that: In step S5, the numerical simulation process is as follows: The specific parameters are set as follows: Set the wide and thick plate hot working control furnace to contain 4 sub-spaces, that is, set , the heat transfer relationship of each subspace satisfies , , , ; According to conclusion 1 condition A, use LMI toolbox to solve the optimal Satisfies the A condition, and the corresponding positive definite symmetric matrix , for: ， ； According to Conclusion 1 Condition C , numerical simulation analysis settings meet the conditions; Based on the flame nozzle control implementation process of the wide and thick plate processing furnace in actual engineering, numerical simulation analysis is used to set the spatial temperature pulse control cycle in the wide and thick plate hot processing furnace ,Right now , and then according to condition C, we can solve Satisfy the conditions; so the numerical simulation analysis sets the proportional constant of the pulse control state meet the conditions; According to condition B in conclusion 1, the gain of pulse control is obtained meet the conditions; Based on the conditions of Conclusion 1, the control parameters are solved and numerical simulation is performed based on the control parameters to obtain the temperature error state change trend diagram of each node subspace.

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