Wide and thick plate hot working burner period intermittent control method considering input saturation

Abstract

The invention discloses a wide and thick plate hot working burner period intermittent control method considering input saturation. The method comprises the steps that burner heat supply controllable areas are divided according to burner distribution positions in the length direction of a wide and thick plate; on the basis of the operation time sequence of the wide and thick plate in the furnace, a burner heat supply controllable area distribution parameter model is established according to the temperature sensor distribution position and temperature information. And designing a burner period intermittent control method considering input saturation. And on the basis of a Lyapunov functional and a linear matrix inequality theory, calculating and designing sufficient conditions for finite time stability of a burner heat supply controllable area distribution parameter system under the control method. Through the steps, the temperature control performance of the heating furnace can be improved, sufficient combustion of fuel in the furnace is achieved, and it is ensured that wide and thick plates are heated evenly and the target temperature reaches the standard.

Description

Technical Field

[0001] The invention relates to the technical field of steel rolling, and in particular to a periodic intermittent control method for a wide and thick plate hot processing burner taking input saturation into consideration. Background Art

[0002] The uniformity of heating of steel billets has a great influence on the performance of steel. If the temperature inside and outside the steel billets is uneven, the extension during rolling will be uneven, which will cause stress and cracks in the rolled parts, thus affecting the performance of the steel. Especially for high-performance wide and thick steel plates, if the heating is uneven, the wide and thick plates formed by rolling will have more pitting, and there will also be non-metallic inclusions, cracks, cracks and other surface quality problems, which seriously affect the performance of steel. Therefore, optimizing the combustion process of the heating furnace is of great significance to ensure and improve the performance of steel.

[0003] As the core component of the heating furnace, the burner plays a decisive role in the temperature field and flow field inside the heating furnace. Since the burners are usually distributed inside the heating furnace according to a certain rule, the space inside the furnace can be divided into several parts according to the distribution of the burners, and each space is defined as a node. The node space can be heated by controlling the burner, and the heat between each node space is transferred through thermal convection, so that the temperature of each node space shows a specific change trend. Therefore, the wide and thick plate hot processing furnace temperature control system with time and space characteristics can be regarded as a typical distributed parameter system.

[0004] In this system, the furnace temperature of each node is measured by thermocouples, and the burner switch time is controlled according to the difference between the measured furnace temperature and the set furnace temperature, so that the temperature control of each node in the heating furnace can be achieved. In existing engineering technology, wide and thick plate hot processing control furnaces all use continuous constant heating to achieve furnace temperature stability. Although this can ensure that the furnace has enough energy to ensure normal production, this control scheme often causes incomplete combustion of fuel in the furnace, resulting in great energy waste. In addition, there is a lag in the nozzle's control of the furnace temperature, and there is an upper limit to the nozzle's thermal power. Therefore, it is necessary to consider the system's control time lag and input saturation to avoid a decrease in temperature control performance or even instability in actual engineering. Summary of the invention

[0005] In order to solve the technical problems of energy waste and unstable control performance caused by the existing continuous constant heating method, the present invention provides a periodic intermittent control method for wide and thick plate hot processing burners considering input saturation. According to the characteristics of heat conduction, the present invention establishes a wide and thick plate hot processing control furnace temperature system with time and space characteristics as a burner heating controllable area distributed parameter model, and designs a periodic intermittent controller considering input saturation for the distributed parameter system. Based on the Lyapunov functional and linear matrix inequality theory, the sufficient conditions for the finite time stability of the burner heating controllable area distributed parameter system under the designed control method are calculated.

[0006] In order to achieve the above technical purpose, the technical solution of the present invention is:

[0007] A method for periodic intermittent control of a burner for hot processing of wide and thick plates considering input saturation comprises the following steps:

[0008] Step S1, dividing a plurality of burner heating controllable areas along the length direction of the wide and thick plate according to the distribution positions of the burners;

[0009] Step S2, based on the running time of the wide and thick plate in the hot processing furnace and according to the real-time temperature information of each burner heating controllable area, a burner heating controllable area distribution parameter model considering input saturation is established;

[0010] Step S3, establishing a burner periodic intermittent control method based on the model in step 2 under the premise of considering input saturation;

[0011] Step S4, based on Lyapunov functional and linear matrix inequality theory, calculate the sufficient conditions for making the burner heating controllable area distributed parameter system finite time stable in the method of step S3.

[0012] The method described, step S1 comprises:

[0013] Based on the burner positions evenly arranged on the top and bottom sides of the hot working furnace, the burner heat controllable areas are divided along the length direction of the wide and thick plates, so that in each burner heat controllable area, there is a burner on the top and bottom sides of the hot working furnace.

[0014] In the method described, in step S2, the real-time temperature information of each burner heat-controllable area is obtained by evenly distributing temperature sensors next to the burners on the top and bottom sides of the hot processing furnace, and using the average real-time temperature measured by the temperature sensors on the top and bottom sides as the real-time temperature of the corresponding burner heat-controllable area.

[0015] The method, in step S2, considers the distribution parameter model of the temperature change of the controllable area of ​​the burner heating supply with saturated input as follows:

[0016]

[0017] Among them, x is the spatial parameter representing the x, y, and z axes of the three-dimensional space, x∈(x1,x2,x3)∈Ω∈R 3 , R represents Euclidean space, and the furnace space Ω is a space with smooth boundaries The subscripts 1, 2, and 3 of the spatial parameter x represent the x, y, and z directions, respectively; t is the time parameter, z i (x, t) represents the state variable of the difference between the temperature of the ith controllable area and the target temperature at the tth time; di is the thermal diffusion coefficient of the wide and thick plate material in the x, y, and z directions of the three-dimensional space, i is 1, 2, or 3, representing the x, y, and z axes of the three-dimensional space, respectively, and Δ represents the Laplace operator. The superscript 3 of Σ indicates the thermal diffusion dimension, i.e., the x, y, and z axes in the three-dimensional space, and l is the subscript used to indicate the thermal diffusion dimension; f(z i (x, t)) is a smooth nonlinear vector-valued function; a ij and b ji is a constant, where i represents the i-th node on the wide and thick plate, and j represents other nodes except the i-th node. When i≠j, a ij and b ji Represents the influence factor of other node spaces on the i-th node space. When i=j, a ij and b ji represents the self-excited term that affects the node inside node i; h(t) represents the time delay of heat propagation in the wide and thick plate, satisfying 0≤h(t)≤τ, τ is a constant representing the upper limit of the time delay of heat propagation; sat(u i (x, t)) is the control input considering input saturation; u i (x, t) is the original control input; n is the total number of controllable areas in the furnace.

[0018] The method described above, the i-th node on the wide and thick plate, refers to dividing the steel billet into n small cubes evenly and taking the center position z of each small cube i As a node.

[0019] In the method, in step S2, the initial value and initial boundary condition of the controllable region distribution parameter model are:

[0020] z i (x,t)=Φ i (x,t),(x,t)∈Ω×[-τ,0]

[0021]

[0022] Where n is the smooth boundary The unit external normal vector of i (x, t) is a bounded continuous function in the furnace space Ω;

[0023] The distribution parameter model is transformed into a matrix form:

[0024]

[0025] Where D represents the thermal diffusion coefficient of the wide and thick plate material, that is, D = diag (d1, d2, d3); A = (a ij )3×3 , B=(b ij ) 3×3 is a constant matrix; f(z(x, t)) = f(z1(x, t), z2(x, t), z3(x, t)) T , u(x, t)=(u1(x, t), u2(x, t), u3(x, t)) T , where the superscript T represents the matrix transpose.

[0026] In the method described above, in step S3, the control input expression of the burner periodic intermittent control method considering input saturation is:

[0027] sat(u(x, t))=(sat(u1(x, t)), sat(u2(x, t)), sat(u3(x, t))) T ,

[0028] where

[0029]

[0030] u M and u m are the upper and lower bounds of the control input quantity respectively.

[0031] In the method described above, in step S3, when considering input saturation, the expression of the control input u(x, t) for implementing intermittent control is:

[0032] When ||z||≠0 and lT≤t≤(l + θ)T, where ||z|| represents the norm of z, z is the state variable, T is the control period, and θ is the proportion of the working duration of the control period, there is

[0033]

[0034] When ||z|| = 0 or (l + θ)T < t < (l + 1)T,

[0035] u(x, t)=0

[0036] where k1, k2, and k3 are gain parameters, s represents the integral variable of time t, M is the total volume of the wide and thick plate, M = mes(Ω), mes represents the measure of the spatial region, and η is an empirical parameter for control convergence, 0 < η < 1.

[0037] In the method described above, in step S4, the Lyapunov functional is:

[0038]

[0039] In the method described above, in step S4, the sufficient conditions include:

[0040] When there are positive constants k1, k3 and q that satisfy the following conditions:

[0041] Condition 1.1: For any spatial parameter x∈R 3 , there exists a positive constant ρ∈R such that the function f(·) satisfies the Lipschitz continuity condition:

[0042] ||f(x)||≤ρ||x||

[0043] Condition 1.2: There exists a positive real number h0 such that the time delay h(t) of heat propagation through a thick plate satisfies:

[0044]

[0045] in represents the derivative of h(t);

[0046] Condition 1.3:

[0047] Where G represents the weight matrix, G = diag(g1, g2, g3), g = min(g1, g2, g3), 0 <g≤1,

[0048]

[0049] Condition 1.4:

[0050] Condition 1.5: θk3g-(1-θ)q>0

[0051] in, l j It represents the length of the wide and thick plate in the x, y, and z axis directions in the three-dimensional space; q is an empirical parameter used to affect the finite time convergence, q>0;

[0052] Considering the input saturated burner heating controllable area distributed parameter system will reach stability, the corresponding convergence time t * for:

[0053]

[0054] The technical effect of the present invention is that the present invention establishes a wide and thick plate hot processing control furnace temperature system with time and space characteristics as a burner heating controllable area distributed parameter model, and designs a periodic intermittent controller considering input saturation for the distributed parameter system. Based on the Lyapunov functional and linear matrix inequality theory, the sufficient conditions for the finite time stability of the burner heating controllable area distributed parameter system under the designed control method are calculated. Under this condition, the intermittent periodic heating method can achieve furnace temperature stability, and the quality of wide and thick plate steel can be guaranteed while efficiently utilizing energy. Therefore, the present invention can achieve energy conservation and emission reduction to a large extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of the present invention.

[0056] Figure 2 It is a state diagram of the error change between the node temperature in the furnace and the target temperature controlled at each time point in an embodiment of the present invention.

[0057] Figure 3 It is a state diagram of the control system of the embodiment of the present invention at each time point. DETAILED DESCRIPTION

[0058] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] This embodiment provides a method for controlling the periodic intermittent operation of a burner for hot processing of wide and thick plates taking into account input saturation. The flow chart is as follows: Figure 1 As shown, the following steps are included:

[0060] Step S1, evenly arranging a plurality of burners on the top and bottom sides of the heat treatment furnace, and dividing the controllable heat supply area accordingly, so that each controllable heat supply area has a burner on the top and bottom sides.

[0061] Step S2, a number of electric thermocouples are evenly distributed beside the burners on the top and bottom sides of the hot processing furnace, and the average temperature measured by the thermocouples on the top and bottom sides is used as the real-time temperature of the corresponding burner heating controllable area. According to the division of the heating controllable area, based on the spatiotemporal variation characteristics of the node temperature, and considering the input saturation phenomenon existing in actual engineering, a distribution parameter model of the burner heating controllable area considering input saturation is constructed.

[0062] Step S3, considering the input saturation phenomenon of the burner in the actual project, a burner periodic intermittent control method considering input saturation is designed for the heating furnace burner, and based on the actual node temperature and target temperature measured by the thermocouple, a specific control scheme mathematical model expression is designed.

[0063] Step S4, based on the Lyapunov functional and linear matrix inequality theory, the sufficient conditions for the finite-time stability of the distributed parameter system of the burner heating controllable area under the designed method are calculated.

[0064] Combining the burner heating controllable area distributed parameter model considering input saturation in step S2 and the burner periodic intermittent control method considering input saturation in S3, the sufficient conditions for the finite time stability of the burner heating controllable area distributed parameter system under the designed control method are calculated based on Lyapunov stability theory and linear matrix inequality theory. Based on this, the specific parameter expression of the periodic intermittent control of each spatial node burner is calculated to complete a periodic intermittent control method for wide and thick plate hot processing burners considering input saturation.

[0065] In this embodiment, the steps specifically include:

[0066] In step S1, the burner heating controllable area is divided along the length direction of the wide and thick plate based on the burner positions evenly arranged on the top and bottom sides of the hot working furnace, so that in each burner heating controllable area, there is a burner on the top and bottom sides of the hot working furnace.

[0067] In step S2, the real-time temperature information of each burner heat-controllable area is obtained by evenly distributing temperature sensors next to the burners on the top and bottom sides of the hot processing furnace, and using the average real-time temperature measured by the temperature sensors on the top and bottom sides as the real-time temperature of the corresponding burner heat-controllable area.

[0068] The distributed parameter model of the temperature change in the controllable area of ​​the burner heating with saturated input is:

[0069]

[0070] Among them, x is the spatial parameter representing the x, y, and z axes of the three-dimensional space, x∈(x1,x2,x3)∈Ω∈R 3 , R represents Euclidean space, and the furnace space Ω is a space with smooth boundaries The subscripts 1, 2, and 3 of the spatial parameter x represent the x, y, and z directions, respectively. t is the time parameter, z i (x, t) represents the state variable of the difference between the temperature of the ith controllable area and the target temperature at the tth time. i is the thermal diffusion coefficient of the wide and thick plate material in the x, y, and z directions of the three-dimensional space, i is 1, 2, or 3, representing the x, y, and z axes of the three-dimensional space, respectively, and Δ represents the Laplace operator. The superscript 3 of Σ indicates the heat diffusion dimension, i.e., the x, y, and z axes in the three-dimensional space, and l is the subscript used to indicate the heat diffusion dimension. i (x,t)) is a smooth nonlinear vector-valued function.ij and b ji is a constant, where i represents the i-th node on the wide and thick plate, and j represents other nodes except the i-th node. When i≠j, a ij and b ji Represents the influence factor of other node spaces on the i-th node space. When i=j, a ij and b ji In this embodiment, the i-th node on the wide and thick plate means that the steel billet is evenly divided into n small cubes, and the center position z of each small cube is taken. i As a node. h(t) represents the time delay of heat propagation in a wide and thick plate, satisfying 0≤h(t)≤τ, where τ is a constant representing the upper limit of the time delay of heat propagation. sat(u i (x, t)) is the control input considering input saturation. i (x, t) is the original control input. n is the total number of controllable areas in the furnace.

[0071] In the above step S2, the initial values ​​and initial boundary conditions of the controllable region distribution parameter model are:

[0072] z i (x,t)=Φ i (x,t),(x,t)∈Ω×[-τ,0]

[0073]

[0074] Where n is the smooth boundary The unit external normal vector of . Φ i (x, t) is a bounded continuous function in the furnace space Ω.

[0075] The distribution parameter model is transformed into a matrix form:

[0076]

[0077] Where D represents the thermal diffusion coefficient of the wide and thick plate material, that is, D = diag (d1, d2, d3). ij ) 3×3 , B=(b ij ) 3×3 is a constant matrix. f(z(x,t))=f(z1(x,t),z2(x,t),z3(x,t)) T ,u(x,t)=(u1(x,t),u2(x,t),u3(x,t)) T , the superscript T indicates the matrix transpose.

[0078] In step S3 of this embodiment, the control input expression of the burner periodic intermittent control method considering input saturation is:

[0079] sat(u(x,t))=(sat(u1(x,t)), sat(u2(x,t)), sat(u3(x,t))) T ,

[0080] where,

[0081]

[0082] u M and u m are the upper and lower bounds of the control input quantity, respectively.

[0083] Meanwhile, when considering input saturation, the expression of the control input u(x,t) for implementing intermittent control is:

[0084] When ||z||≠0 and lT≤t≤(l + θ)T, where ||z|| represents the norm of z, z is the state variable, T is the control period, and θ is the proportion of the working duration of the control period, there is

[0085]

[0086] When ||z|| = 0 or (l + θ)T < t < (l + 1)T,

[0087] u(x,t) = 0

[0088] where, k1, k2, and k3 are gain parameters, s represents the integral variable of time t, M is the total volume of the wide and thick plate, M = mes(Ω), mes represents the measure of the spatial region, and η is an empirical parameter for control convergence, 0 < η < 1.

[0089] In step S4 of this embodiment, the Lyapunov functional is:

[0090]

[0091] The sufficient conditions include:

[0092] When there exist positive constants k1, k3, and q satisfying the following conditions:

[0093] Condition 1.1: For any spatial parameter x ∈ R 3 , there exists a positive constant ρ ∈ R such that the function f(·) satisfies the Lipschitz continuity condition:

[0094] ||f(x)|| ≤ ρ||x||

[0095] Condition 1.2: There exists a positive real number h0 such that the time delay h(t) of heat propagation through a thick plate satisfies:

[0096]

[0097] in represents the derivative of h(t).

[0098] Condition 1.3:

[0099] Where G represents the weight matrix, G = diag(g1, g2, g3), g = min(g1, g2, g3), 0 <g≤1,

[0100]

[0101] Condition 1.4:

[0102] Condition 1.5: θk3g-(1-θ)q>0

[0103] in, l j It represents the length of the wide and thick plate in the x, y, and z directions of the three-dimensional space. q is an empirical parameter used to affect the finite time convergence, q>0.

[0104] Considering the input saturated burner heating controllable area distributed parameter system will reach stability, the corresponding convergence time t * for:

[0105]

[0106] The constants k2 and η are given positive constants. In this way, the convergence time t can be obtained according to the above sufficient conditions 1.1-1.5 and the final convergence time calculation formula. * At the same time, the convergence time t can also be determined according to actual requirements. * , combined with sufficient conditions 1.1-1.5, the convergence time calculation formula is used to calculate the values ​​of constant k2 and constant η that meet the requirements. Since the adjustment range of constant k2 and constant η is relatively large, even if t is required in advance * In this case, a satisfactory solution can still be calculated, which is also the advantage of this embodiment.

[0107] The following four lemmas are given to demonstrate the method provided in this embodiment:

[0108] Lemma 1: Define the function g i for:

[0109]

[0110] Obviously there is 0 <g i ≤1, and sat(u i (x,t))=g i (u i (x,t)), i=1,2,…n. Therefore:

[0111] sat(u(x,t))=diag(g1,g2,g3)u(x,t)=Gu(x,t)

[0112] Let g = min(g1,g2,g3), we have:

[0113] 0 <g<g i ≤1

[0114] Assume Ω is a cube |x k | <l k , (k=1,2,…q), and g(x) belongs to C 1 (Ω) and satisfies have:

[0115]

[0116] Where x = (x1, x2, x3) T ∈Ω

[0117] Lemma 2: If Y, Z are real matrices of suitable dimensions, for any constant μ>0, the following inequality always holds:

[0118]

[0119] Lemma 3: Assume that the continuous positive definite function V(t) satisfies the following differential inequality:

[0120]

[0121] Among them, α>0, 0<η<1, p>0, and they are all constants. Therefore, for any t0, V(t) satisfies the following inequality:

[0122]

[0123] and in,

[0124] Lemma 4: Assume that the function V(t) is continuous, non-negative when t∈[0,∞], and satisfies the following conditions:

[0125]

[0126] Where p and q are constants greater than zero, and l∈N. If θp-(1-θ)q>0, then the following holds:

[0127]

[0128] According to Lemma 3, if V(t) satisfies Lemma 4, in finite time Within, V(t) will tend to 0, and when t>t1, V(t)=0.

[0129] The specific proof process is as follows:

[0130] The derivative of the Lyapunov functional constructed above is:

[0131]

[0132] According to the boundary conditions of the system and Lemma 1, we have:

[0133]

[0134] According to condition 1.1 and Lemma 2, we can deduce that:

[0135] 2z T (x,t)f(z(x,t))≤z T (x,t)Δz(x,t)+ρ 2 z T (x,t)Δz(x,t)=z T (x,t)(1+ρ 2 )Iz(x,t),2z T (x,t)Bz(x,th(t))≤z T (x,t)BB T z(x,t)+z

[0136] When ||z||≠0 and lT≤t≤(l+θ)T, we have:

[0137]

[0138] Therefore, under this condition, we have:

[0139]

[0140] Similarly, when lT≤t≤(l+θ)T, we have:

[0141]

[0142] According to Lemma 4, the distributed parameter system can achieve global stability. Its stable convergence time can be estimated by the following formula:

[0143]

[0144] Thus, the proof is completed.

[0145] The following is a practical numerical example to further illustrate the effectiveness of the method provided in this embodiment:

[0146] Suppose the distributed parameter system and its control system are as follows:

[0147]

[0148] The initial conditions of the given system are as follows: Φ1(x,0) = 10sin6.5x, Φ2(x,0) = 5cos3x, Φ3(x,0) = sin(2 - 5x), Φ4(x,0) = 5sin(2x). Suppose When ρ = 3.5, f(ξ) satisfies the Lipschitz continuity condition. Suppose Ω = {0 < x < 3}, then L = -1 / 9, M = 3.

[0149] In periodic intermittent control, set θ = 0.6, u m = u M = 300.

[0150] Set d i = 1.5 (i = 1, 2, 3, 4), η = 3 / 4, h(t) = 0.01(1 - e -10t )(h0 = 0.1), k2 = k1 / 2.

[0151] According to the above parameters, using the LMI toolbox in Matlab, the control system parameters can be obtained: q = 18.7, k1 = 107.7, k3 = 65.6, G = diag(0.8 0.3 0.5 0.9).

[0152] According to the convergence time calculation formula, it can be known that t* = 20.3s.

[0153] The simulation results are as Figure 2 and Figure 3 shown. It can be seen from Figure 3 that the control input variable u i (x,t) is intermittent and getting smaller and smaller, which indicates that the control intensity applied to the system is also getting lower and lower. It can be seen from Figure 2 that the state variable z i (x,t) also tends to be stable and reaches the equilibrium state after 20.3s. This indicates that under the satisfaction of the said conditions, the system can reach stability under the proposed control method.

Claims

1. A method for periodic intermittent control of a burner for hot working of wide and thick plates considering input saturation, characterized in that: It includes the following steps: Step S1: Along the length direction of the heavy plate, divide multiple controllable regions for burner heating according to the distribution positions of the burners. Step S2: Based on the running time of the heavy plate in the hot working furnace and according to the real-time temperature information of each controllable region for burner heating, establish a distribution parameter model of the controllable regions for burner heating considering input saturation. Step S3: On the premise of considering input saturation, establish a burner periodic intermittent control method based on the model in Step 2. Step S4: Based on the Lyapunov functional and linear matrix inequality theory, calculate the sufficient conditions for the finite-time stability of the distribution parameter system of the controllable regions for burner heating in the method of Step S3.

2. The method according to claim 1, characterized in that The said Step S1 includes: Divide the controllable regions for burner heating along the length direction of the heavy plate based on the positions of the burners uniformly arranged on the top and bottom sides of the hot working furnace, so that there is one burner on both the top and bottom sides of the hot working furnace in each controllable region for burner heating.

3. The method according to claim 2, characterized in that In the said Step S2, the real-time temperature information of each controllable region for burner heating is obtained by uniformly arranging temperature sensors beside the burners on the top and bottom sides of the hot working furnace, and taking the average real-time temperature measured by the temperature sensors on the top and bottom sides as the real-time temperature of the corresponding controllable region for burner heating.

4. The method according to claim 1, characterized in that: In the said Step S2, the distribution parameter model of the temperature change of the controllable regions for burner heating considering input saturation is: Among them, x is the spatial parameter representing the x, y, and z axes of the three-dimensional space, x∈(x1,x2,x3)∈Ω∈R 3 , R represents Euclidean space, and the furnace space Ω is a space with smooth boundaries The subscripts 1, 2, and 3 of the spatial parameter x represent the x, y, and z directions, respectively; t is the time parameter, z i (x, t) represents the state variable of the difference between the temperature of the ith controllable area and the target temperature at the tth time; d i is the thermal diffusion coefficient of the wide and thick plate material in the x, y, and z directions of the three-dimensional space, i is 1, 2, or 3, representing the x, y, and z axes of the three-dimensional space, respectively, and Δ represents the Laplace operator. The superscript 3 of Σ indicates the thermal diffusion dimension, i.e., the x, y, and z axes in the three-dimensional space, and l is the subscript used to indicate the thermal diffusion dimension; f(z i (x, t)) is a smooth nonlinear vector-valued function; a ij and b ji is a constant, where i represents the i-th node on the wide and thick plate, and j represents other nodes except the i-th node. When i≠j, a ij and b ji Represents the influence factor of other node spaces on the i-th node space. When i=j, a ij and b ji represents the self-excited term that affects the node inside node i; h(t) represents the time delay of heat propagation in the wide and thick plate, satisfying 0≤h(t)≤τ, where τ is a constant representing the upper limit of the time delay of heat propagation; sat(u i (x, t)) is the control input considering input saturation; u i (x, t) is the original control input; n is the total number of controllable areas in the furnace.

5. The method according to claim 4, characterized in that The i-th node on the wide and thick plate means that the billet is evenly divided into n small cubes, and the center position z of each small cube is taken i As a node.

6. The method according to claim 4, characterized in that In the said Step S2, the initial values and initial boundary conditions of the distribution parameter model of the controllable regions are: z i (x,t)=Φ i (x,t),(x,t)∈Ω×[-τ,0] Where n is the smooth boundary The unit external normal vector of i (x, t) is a bounded continuous function in the furnace space Ω; Transform the distribution parameter model into matrix form as: Where D represents the thermal diffusion coefficient of the wide and thick plate material, that is, D = diag (d1, d2, d3); A = (a ij ) 3×3 , B=(b ij ) 3×3 is a constant matrix; f(z(x,t))=f(z1(x,t),z2(x,t),z3(x,t)) T ,u(x,t)=(u1(x,t),u2(x,t),u3(x,t)) T , the superscript T indicates the matrix transpose.

7. The method according to claim 4, characterized in that In the said Step S3, the control input expression of the burner periodic intermittent control method considering input saturation is: sat(u(x,t))=(sat(u1(x,t)),sat(u2(x,t)),sat(u3(x,t))) T , Wherein, u M and u m are the upper and lower bounds of the control input respectively.

8. The method according to claim 7, characterized in that In the said Step S3, when considering input saturation, the expression of the control input u(x,t) for performing intermittent control is: When ||z||≠0 and lT≤t≤(l + θ)T, where ||z|| represents the norm of z, z is the state variable, T is the control period, and θ is the proportion of the working duration of the control period, there is When ||z||=0 or (l + θ)T<t<(l + 1)T, u(x,t)=0 Wherein, k1, k2, and k3 are gain parameters, s represents the integral variable of time t, M is the total volume of the heavy plate, M = mes(Ω), mes represents the measure of the spatial region, η is an empirical parameter for control convergence, and 0<η<1.

9. The method according to claim 8, characterized in that In the said Step S4, the Lyapunov functional is:

10. The method according to claim 8, characterized in that In the said Step S4, the sufficient conditions include: When there exist positive constants k1, k3, and q satisfying the following conditions: Condition 1.1: For any spatial parameter x∈R 3 , there exists a positive constant ρ∈R such that the function f(·) satisfies the Lipschitz continuity condition: ||f(x)||≤ρ||x|| Condition 1.2: There exists a positive real number h0 such that the time delay h(t) of the heat propagation of the heavy plate satisfies: in represents the derivative of h(t); Condition 1.3: Where G represents the weight matrix, G = diag(g1,g2,g3), g = min(g1,g2,g3), 0<g≤1, Condition 1.4: Condition 1.5: θk3g - (1 - θ)q>0 in, l j It represents the length of the wide and thick plate in the x, y, and z axis directions in the three-dimensional space; q is an empirical parameter used to affect the finite time convergence, q>0; Considering the input saturated burner heating controllable area distributed parameter system will reach stability, the corresponding convergence time t * for:

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