A Fuzzy PID Temperature Regulation Method for Reheating Steel Billets in Hot Continuous Rolling of Strip Steel

Abstract

The present invention provides a fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production, belonging to the field of hot strip continuous rolling production. The method includes: performing T-S fuzzy partial differential equation modeling on the nonlinear billet internal temperature evolution dynamic model with spatio-temporal distribution characteristics to obtain the T-S fuzzy partial differential equation model of the nonlinear billet internal temperature evolution dynamic; adopting the feedback control technology based on an observer to construct a T-S fuzzy observer according to the T-S fuzzy partial differential equation model; applying the PID control strategy to construct a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer; determining the control parameters of the fuzzy PID temperature measurement tracking regulator, and applying the fuzzy PID temperature measurement tracking regulator to the nonlinear billet internal temperature evolution dynamic model to drive the temperature of the lower surface of the billet to the desired temperature value. By adopting the present invention, non-invasive surface measurement and regulation of the billet temperature can be realized, so that the temperature of the lower surface of the billet reaches the desired temperature value.

Description

Technical Field

[0001] The present invention relates to the field of hot strip continuous rolling production, and particularly to a fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production. Background Art

[0002] In the process of hot strip continuous rolling production (the hot strip continuous rolling production process flow is as Figure 1 shown), precise temperature control contributes to the industrial upgrading of the steel industry: energy conservation, emission reduction, quality improvement and efficiency increase. This is because both the energy consumption and the quality of steel products in hot continuous rolling are closely related to temperature. Therefore, researching how to develop a simple, effective and reliable control algorithm to drive the heating unit to make the temperature distribution of the billet reach the expectation (the schematic diagram of billet reheating is as Figure 2 shown), which has important practical application value for the industrial upgrading of the steel industry.

[0003] The dynamic evolution of the internal temperature of the billet is more complex, which is not only related to time but also depends on the spatial position, and is usually characterized by partial differential equations. At the same time, the non-linear characteristics of the temperature evolution dynamics, such as the specific heat coefficient and the conduction coefficient of the billet are related to temperature and it is difficult to obtain their accurate expressions, which increases the design difficulty of the temperature control system.

[0004] In addition, restricted by the existing sensor measurement and control drive technology, the surface temperature measurement and regulation of the billet are non-invasive, that is, the internal temperature distribution information of the billet cannot be directly obtained by the sensor and directly regulated by the heating unit. Therefore, the billet temperature measurement and heating can only be carried out on its surface, which belongs to the category of boundary control of distributed parameter systems.

[0005] Although PID control is widely used in the industrial field and has become one of the effective ways to solve the tracking control problem, the problem of billet surface temperature regulation is essentially a boundary output tracking control problem of a quasi-linear distributed parameter system. At present, how to use PID control to solve the boundary output tracking problem of non-linear distributed parameter systems is still a difficult point, especially the corresponding PID parameter tuning and its performance analysis methods. Summary of the Invention

[0006] The embodiment of the present invention provides a fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production, which can realize non-invasive surface measurement and regulation of billet temperature, so that the temperature of the lower surface of the billet reaches the desired temperature value. The technical solution is as follows:

[0007] The embodiment of the present invention provides a fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production, including:

[0008] Model the dynamic model of the internal temperature evolution of a nonlinear billet with spatio-temporal distribution characteristics using Takagi-Sugeno (T-S) fuzzy partial differential equations to obtain a T-S fuzzy partial differential equation model for the dynamic internal temperature evolution of the nonlinear billet;

[0009] Adopt observer-based feedback control technology to construct a T-S fuzzy observer according to the T-S fuzzy partial differential equation model;

[0010] Apply the PID control strategy to construct a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer, where the fuzzy PID temperature measurement tracking regulator adopts a boundary control law;

[0011] Determine the control parameters of the fuzzy PID temperature measurement tracking regulator and apply the fuzzy PID temperature measurement tracking regulator to the dynamic model of the internal temperature evolution of the nonlinear billet to drive the temperature of the lower surface of the billet to the desired temperature value.

[0012] Furthermore, the T-S fuzzy partial differential equation modeling of the dynamic model of the internal temperature evolution of the nonlinear billet with spatio-temporal distribution characteristics to obtain a T-S fuzzy partial differential equation model for the dynamic internal temperature evolution of the nonlinear billet includes:

[0013] Simplify the dynamic model of the internal temperature evolution of the nonlinear billet with spatio-temporal distribution characteristics to obtain a simplified model;

[0014] For the nonlinear terms existing in the simplified model, use the local spatial dependence sector nonlinear method to establish a T-S fuzzy partial differential equation model to describe the nonlinear dynamics of the internal temperature evolution of the billet.

[0015] Furthermore, the dynamic model of the internal temperature evolution of the nonlinear billet with spatio-temporal distribution characteristics is expressed as:

[0016]

[0017] Among them, β(T) represents the specific heat coefficient of the billet, T represents the temperature; T(x,t) represents the temperature distribution of the billet along the thickness direction, x represents the spatial variable of the billet temperature distribution, t represents the time variable of the billet temperature distribution; α(T) is a nonlinear term representing the thermal conductivity of the billet; u(t) represents the radiation source temperature; L represents the thickness of the billet; T out (t) represents the measured value of the temperature of the lower surface of the billet; T(x,0), T 0 (x) both represent the initial temperature distribution of the billet.

[0018] Furthermore, the simplified model is expressed as:

[0019]

[0020] Among them, β represents the specific heat coefficient constant.

[0021] Furthermore, the T-S fuzzy partial differential equation model is expressed as:

[0022]

[0023] α(T) ∈ [a 1 , a 2

[0024]

[0025]

[0026]

[0027] Among them, i ∈ {1, 2}, a 1 , a 2 are both abbreviated forms, h 1 (α(T)), h 2 (α(T)) both represent fuzzy membership functions, T min , T max respectively represent the lower limit value and the upper limit value of the billet temperature distribution, h 1 (α(T)), h 2 (α(T)) ∈ [0, L].

[0028] Furthermore, the constructed T-S fuzzy observer is expressed as:

[0029]

[0030] Among them, represents the estimated value of the temperature distribution of the billet along the thickness direction, j ∈ {1, 2}, and L 0j represents the undetermined T-S fuzzy observer gain; represents the estimated value of the lower surface temperature of the billet; both represent the estimated value of the initial temperature distribution of the billet.

[0031] Furthermore, by applying the PID control strategy, the fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer includes:

[0032] Introduce the billet surface temperature measurement tracking error T e (t) = T out (t) - T d and its integral form and differential form dT e ​∫(t)dt = dT out ∫(t)dt, where T e (t) represents the tracking error of the measured surface temperature of the billet, and T d represents the desired temperature value, and T Ie (t) represents T e (t) in integral form;

[0033] Based on the tracking error T e (t) of the measured surface temperature of the billet and its integral and differential forms, the estimated value provided by the T-S fuzzy observer equation Combined with the PID control strategy, a fuzzy PID temperature measurement tracking regulator is constructed.

[0034] Furthermore, the constructed fuzzy PID temperature measurement tracking regulator is expressed as:

[0035]

[0036] where j ∈ {1, 2}, and the constant k j 、k Pj 、k Ij all represent undetermined control gains, and k Dj represents a given control gain, is a boundary control law.

[0037] Furthermore, the determination of the control parameters of the fuzzy PID temperature measurement tracking regulator includes:

[0038] Applying Lyapunov techniques and combining with a variant form of the Poincaré-Wengel inequality, sufficient conditions for the existence of the fuzzy PID temperature measurement tracking regulator are given, and the problem of the existence of the fuzzy PID temperature measurement tracking regulator is transformed into a feasibility problem of solving a set of linear matrix inequality constraints.

[0039] The beneficial effects brought by the technical solutions provided in the embodiments of the present invention at least include:

[0040] In the embodiments of the present invention, a T-S fuzzy partial differential equation model of the internal temperature evolution dynamics of a nonlinear billet with spatio-temporal distribution characteristics is established through T-S fuzzy partial differential equation modeling, obtaining a T-S fuzzy partial differential equation model of the internal temperature evolution dynamics of the nonlinear billet; a T-S fuzzy observer is constructed based on the T-S fuzzy partial differential equation model by using an observer-based feedback control technique; a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer is constructed by applying a PID control strategy; the control parameters of the fuzzy PID temperature measurement tracking regulator are determined, and the fuzzy PID temperature measurement tracking regulator is applied to the internal temperature evolution dynamics model of the nonlinear billet to drive the temperature of the lower surface of the billet to the desired temperature value. In this way, not only the dynamic information of the internal nonlinear temperature evolution of the billet in both the time and space dimensions is considered simultaneously, but also a boundary control law is adopted, enabling non-invasive surface measurement and regulation of the billet temperature. Finally, the temperature of the lower surface of the billet reaches the desired temperature value, providing effective technical support and theoretical guidance for application scenarios such as energy conservation, emission reduction, quality improvement, and efficiency enhancement in hot strip continuous rolling production. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0042] Figure 1 It is a schematic diagram of the hot strip continuous rolling production process flow;

[0043] Figure 2 It is a schematic diagram of billet reheating;

[0044] Figure 3 It is a schematic flow diagram of the fuzzy PID temperature regulation method for billet reheating in hot strip continuous rolling production provided by the embodiments of the present invention;

[0045] Figure 4 It is a schematic principle diagram of the fuzzy PID temperature regulation method for billet reheating in hot strip continuous rolling production provided by the embodiments of the present invention;

[0046] Figure 5 It is a schematic diagram of the fuzzy membership function of the billet heat conduction system provided by the embodiments of the present invention;

[0047] Figure 6 It is a schematic diagram of the evolution profile of the internal temperature distribution of the billet in the closed-loop system provided by the embodiments of the present invention;

[0048] Figure 7 It is the internal temperature T(·,t) of the billet provided by the embodiments of the present invention 2 Schematic diagram of the closed-loop trajectory;

[0049] Figure 8 The output T of the lower surface temperature measurement of the steel billet provided by the embodiment of the present invention out (t) trajectory schematic diagram;

[0050] Figure 9 The trajectory schematic diagram of the control heat source u(t) for adjusting the temperature measurement output of the steel billet provided by the embodiment of the present invention. Detailed implementation manners

[0051] To make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0052] As Figure 3 - Figure 4 shown, the embodiment of the present invention provides a fuzzy PID temperature regulation method for reheating steel billets in hot strip continuous rolling production, including:

[0053] S101, performing T-S fuzzy partial differential equation modeling on the non-linear internal temperature evolution dynamic model of the steel billet with spatio-temporal distribution characteristics to obtain a T-S fuzzy partial differential equation model of the non-linear internal temperature evolution dynamic of the steel billet; specifically, it may include the following steps:

[0054] A1, simplifying the non-linear internal temperature evolution dynamic model of the steel billet with spatio-temporal distribution characteristics to obtain a simplified model;

[0055] In this embodiment, the non-linear internal temperature evolution dynamic model of the steel billet with spatio-temporal distribution characteristics is expressed as:

[0056]

[0057] Among them, β(T) represents the specific heat coefficient of the steel billet, T represents the temperature; T(x, t) represents the temperature distribution of the steel billet along the thickness direction, x represents the spatial variable of the steel billet temperature distribution, and t represents the time variable of the steel billet temperature distribution; α(T) is a non-linear term representing the thermal conductivity of the steel billet; u(t) represents the radiation source temperature; L represents the thickness of the steel billet; T out (t) represents the measured value of the lower surface temperature of the steel billet; T(x, 0), T 0 (x) both represent the initial temperature distribution of the steel billet.

[0058] In this embodiment, considering that in practice, the change of the specific heat coefficient β(T) of the steel billet with respect to the change of temperature is not obvious compared with the change of the thermal conductivity of the steel billet with temperature, it is regarded as a constant, and a simplified model of the non-linear internal temperature evolution dynamic model of the steel billet is obtained, which is expressed as:

[0059]

[0060] Among them, β represents the specific heat coefficient constant.

[0061] A2. For the nonlinear term α(T) existing in the simplified model, a T-S fuzzy partial differential equation model is established by using the local space-dependent sector nonlinear method to describe the nonlinear dynamic evolution of the internal temperature of the billet. In this way, the information of the nonlinear temperature dynamic evolution of the billet in both time and space dimensions is fully considered, and a T-S fuzzy partial differential equation model is established, thereby overcoming the control design difficulties brought by the nonlinear characteristics of the internal temperature evolution dynamic model of the billet and obtaining good control performance.

[0062] In this embodiment, for the nonlinear term α(T), it is assumed that α(T) ∈ [a 1 , a 2 . and then

[0063]

[0064] Among them, h 1 (α(T)), h 2 (α(T)) ∈ [0, L], and further it can be obtained that:

[0065]

[0066] Among them, h 1 (α(T)), h 2 (α(T)) both represent fuzzy membership functions, as Figure 5 shown;

[0067] For the thermal conductivity α(T) of the billet, when the billet temperature T(x, t) is high, the value is large, and when the billet temperature T(x, t) is low, the value is small. Therefore, the corresponding fuzzy sets are defined as "high" and "low". The simplified model of the nonlinear internal temperature evolution dynamic model of the billet can be accurately described by the T-S fuzzy partial differential equation model of the following two system rules:

[0068] System rule 1:

[0069] If α(T) belongs to "low", then

[0070]

[0071] System rule 2:

[0072] If α(T) belongs to "high", then

[0073]

[0074] Combined with the fuzzy membership functions h 1 (α(T)) and h2 (α(T)), the T-S fuzzy partial differential equation model is obtained as follows:

[0075]

[0076] where i ∈ {1, 2}, a 1 and a 2 are both abbreviated forms, and T min and T max represent the lower limit value and the upper limit value of the billet temperature distribution respectively.

[0077] S102, adopting the feedback control technology based on an observer, construct a T-S fuzzy observer according to the T-S fuzzy partial differential equation model;

[0078] In this embodiment, to overcome the design difficulties caused by the non-coincidence between control and measurement, the feedback control technology based on an observer is adopted, and the following T-S fuzzy observer is constructed according to the T-S fuzzy partial differential equation model shown in Equation (3):

[0079]

[0080] where represents the estimated value of the temperature distribution of the billet along the thickness direction, j ∈ {1, 2}, and L 0j represents the undetermined T-S fuzzy observer gain; T out (t) represents the measured value of the billet lower surface temperature, that is: the temperature measurement output during the billet reheating process; represents the estimated value of the billet lower surface temperature; both represent the estimated value of the billet initial temperature distribution.

[0081] S103, applying the PID control strategy, construct a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer, where the fuzzy PID temperature measurement tracking regulator adopts the boundary control law, and specifically may include the following steps:

[0082] B1, by placing a temperature sensor at x = L on the lower surface of the billet, the lower surface temperature of the billet can be obtained, that is, the temperature measurement output T out (t) = T(L, t), t > 0, introduce the temperature measurement tracking error T e (t) = T out (t) - T d and its integral form and differential form dT e (t)dt = dT out (t)dt, where Te (t) represents the measurement tracking error of the billet surface temperature, T d represents the desired temperature value, T Ie (t) represents T e (t) in integral form;

[0083] In this embodiment, for the integral form there is

[0084] B2, according to the measurement tracking error T of the billet surface temperature e (t) and its integral and differential forms, the estimated value provided by the T-S fuzzy observer equation Combined with the PID control strategy, a fuzzy PID temperature measurement tracking regulator / law (which can also be called: billet reheating fuzzy PID temperature regulator / law) is constructed.

[0085] In this embodiment, the constructed fuzzy PID temperature measurement tracking regulator (or, fuzzy PID temperature measurement tracking regulation law) is expressed as:

[0086]

[0087] where j ∈ {1, 2}, the constant k j 、k Pj 、k Ij all represent undetermined control gains, k Dj represents the given control gain, is a boundary control law.

[0088] In this embodiment, the fuzzy PID temperature measurement tracking regulator effectively solves the design difficulty caused by the non-isotopy between the temperature sensor and the heating unit under the observer-based feedback control technology.

[0089] S104. Determine the control parameters of the fuzzy PID temperature measurement tracking regulator, and apply the fuzzy PID temperature measurement tracking regulator to the nonlinear dynamic model of the billet internal temperature evolution to drive the lower surface temperature of the billet to the desired temperature value.

[0090] In this embodiment, when solving the control parameters of the fuzzy PID temperature measurement tracking regulator, the Lyapunov technique is applied and combined with a variant form of the Poincaré-Wengel inequality to give a sufficient condition for the existence of the fuzzy PID temperature measurement tracking regulator, and the existence problem of the fuzzy PID temperature measurement tracking regulator is transformed into a feasibility problem of solving a set of linear matrix inequality constraints.

[0091] In this embodiment, the steps to obtain the sufficient condition for the existence of the fuzzy PID temperature measurement tracking regulator are as follows:

[0092] First, Lemma 1 gives an important integral inequality - a variant form of the Poincaré-Wirtinger inequality.

[0093] Lemma 1 Assume that \(f(x)\) is a continuously differentiable and square-integrable function defined on \([0,L]\), and its first derivative is also square-integrable. The following integral inequality holds:

[0094]

[0095]

[0096] Theorem 1 Consider the internal temperature distribution of the billet described by Equation (2) and its corresponding T-S fuzzy partial differential equation model (described by Equation (3)). For given constants \(\sigma>0\), \(\varepsilon>0\), \(0 < \delta < 1\), if there exist constants such that the following linear matrix inequalities hold:

[0097]

[0098]

[0099] where \(\Upsilon\) ij denotes the shorthand form of the matrix ;

[0100]

[0101]

[0102]

[0103] Then there exists a temperature measurement output feedback tracking fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer to drive the temperature of the lower surface of the billet to asymptotically converge to the preset desired temperature value \(T\) d and maintain the temperature of the billet uniformly bounded. Among them, the control gains \(k\) j , \(k\) Pj , \(k\) Ij , \(L\) 0j , \(j\in\{1,2\}\) can be obtained by the following formula

[0104]

[0105] In this embodiment, determining the control of the fuzzy PID temperature measurement tracking regulator may include the following steps:

[0106] C1. Construction of the temperature estimation error system

[0107] First, define the billet temperature estimation error, that is, the difference between \(T(x,t)\) and the estimated value The difference between:

[0108]

[0109] Whose spatio-temporal dynamic evolution behavior is characterized by the following equation:

[0110]

[0111] Next, according to the T-S fuzzy partial differential equation model, the fuzzy PID temperature measurement tracking regulator, and the above definition of the billet temperature estimation error, the corresponding closed-loop system can be obtained:

[0112]

[0113] C2, Fuzzy PID Temperature Measurement Tracking Regulator Control Design Based on Lyapunov

[0114] Given constants σ>0, ε>0, 0<δ<1, assuming that the linear matrix inequalities (6) and (7) hold, consider the Lyapunov function V(t) expressed as:

[0115] V(t) = V 1 (t) + V 2 (t) + V 3 (t) + V 4 (t), (9)

[0116] Where,

[0117]

[0118]

[0119]

[0120]

[0121] Where p and w are undetermined Lyapunov parameters, and ε>0, σ>0 are pre-given design parameters that satisfy the inequality (6).

[0122] Let And p>0, it can be obtained that:

[0123]

[0124] Where Ξ represents the shorthand form of the matrix ;

[0125] The Lyapunov function characterized by equation (9) can be rewritten as

[0126]

[0127] Where, and satisfy the following inequalities

[0128]

[0129] where and

[0130] Deriving the functions \(V\) 1 (t), \(V\) 2 (t), \(V\) 3 (t), \(V\) 4 (t) respectively and using integration by parts and Lemma 1, the derivative of \(V(t)\) with respect to time \(t\) is obtained as follows:

[0131]

[0132] where and

[0133]

[0134]

[0135]

[0136]

[0137] According to inequality (7) and considering \(p > 0\), the following inequality can be obtained

[0138] \(\varPhi\) ij =\(\varUpsilon\rho\) ij \(\rho < 0\), \(i,j\in\{1,2\}\)

[0139] where This inequality means that \(\varPhi\) ij +\(\tau I\leq0\), \(i,j\in\{1,2\}\), where \(\tau\) satisfies \(0 < \tau\leq\min\) i,j∈{1,2} \(\lambda\) min (-\(\varPhi\) ij ), and the form \(\lambda\) min (A) represents the minimum eigenvalue of matrix \(A\);

[0140] Furthermore, it can be obtained that:

[0141]

[0142] Combining the triangle inequality and assuming is bounded, the conclusion is obtained that as \(t\rightarrow\infty\), the internal evolution dynamics of the billet temperature exponentially converges to a bounded set in the sense of the norm \(\|\cdot\|\) 2 and \(\|T\) e (t)\|\) 2Bounded means ||T out (t) - T d || 2 Asymptotically converges. This means that under the drive of the control law, the temperature of the lower surface of the billet can be adjusted to the preset desired temperature value T d , thus meeting the reheating temperature requirements of the billet.

[0143] The fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production according to the embodiments of the present invention performs T-S fuzzy partial differential equation modeling on the nonlinear billet internal temperature evolution dynamic model with spatio-temporal distribution characteristics to obtain the T-S fuzzy partial differential equation model of the nonlinear billet internal temperature evolution dynamic; adopts the feedback control technology based on an observer to construct a T-S fuzzy observer according to the T-S fuzzy partial differential equation model; uses the PID control strategy to construct a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer; determines the control parameters of the fuzzy PID temperature measurement tracking regulator, and applies the fuzzy PID temperature measurement tracking regulator to the nonlinear billet internal temperature evolution dynamic model to drive the temperature of the lower surface of the billet to be adjusted to the desired temperature value. In this way, not only the dynamic information of the nonlinear temperature evolution inside the billet in both the time and space dimensions is considered simultaneously, but also the boundary control law is adopted, enabling non-invasive surface measurement and regulation of the billet temperature. Finally, the temperature of the lower surface of the billet reaches the desired temperature value, providing effective technical support and theoretical guidance for application scenarios such as energy conservation, emission reduction, quality improvement, and efficiency enhancement in hot strip continuous rolling production.

[0144] To better understand the fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production according to the embodiments of the present invention, let the thickness of the billet be 1, i.e., L = 1, the initial internal temperature distribution of the billet be T(x, 0) = 120, x ∈ [0, L] and its estimated value and the process parameter β = 383.7667.

[0145] Assume the maximum heating temperature of the reheating furnace (i.e., the upper limit value of the billet temperature distribution) T max = 300, the minimum temperature (i.e., the lower limit value of the billet temperature distribution) T min = 0, and the thermal conductivity satisfies:

[0146] α(T) = α 1 - α 2 T

[0147] where, α 1 = 61.8474, α 2 = 0.0437, the desired temperature value T d= 200. Solve the linear matrix inequalities (LMIs) shown in equations (6) and (7) using the solver feasp in the software MATLAB, and the following control gains k can be obtained j , k Pj , k Ij , j ∈ {1, 2} and the observer gain L 0j , j ∈ {1, 2}:

[0148] k 1 = -0.0549, k 2 = 4.4867, k P1 = 14.2243, k P2 = 13.4147,

[0149] k I1 = 0.2667, k I2 = 0.2954, L 01 = 12.9244, L 02 = 15.2811

[0150] Let k D1 = 0.2 and k D2 = 0.1. Apply the fuzzy PID temperature measurement tracking regulator with the above control parameters to the nonlinear billet temperature evolution dynamic model, specifically referring to: the simplified model of the nonlinear billet internal temperature evolution dynamic model shown in equation (2), from Figure 6 - Figure 9 it can be seen that the fuzzy PID temperature measurement tracking regulator can adjust the lower surface temperature of the billet to the set desired temperature value T d and maintain the internal temperature distribution T(x, t) of the billet uniformly bounded. The above simulation results verify the effectiveness and feasibility of the fuzzy PID temperature measurement tracking regulator.

[0151] In summary, the reheating fuzzy PID temperature regulation method for billets in hot strip continuous rolling production described in the embodiments of the present invention has at least the following beneficial effects:

[0152] 1). Considering the dynamic information of the nonlinear temperature evolution of the billet in two dimensions of time and space, establish a T-S fuzzy partial differential equation model, thereby overcoming the control design difficulties brought by the nonlinear characteristics of the billet internal temperature evolution dynamic model and obtaining good control performance;

[0153] 2). The fuzzy PID temperature measurement tracking regulator is based on the boundary measurement T out (t) = T(L, t) and the boundary control law shown in equation (5), and successfully overcomes the control design difficulties introduced by the non-invasiveness of billet temperature measurement and regulation;

[0154] 3). The development of the fuzzy PID temperature measurement and tracking regulator effectively solves the design difficulties caused by the non-coincidence between the temperature sensor and the heating unit under the framework of the observer-based feedback control technology;

[0155] 4). Based on the above T-S fuzzy control technology, boundary control law, and observer-based output feedback control, combined with the PID control technology, a fuzzy PID temperature measurement and tracking regulator based on the T-S fuzzy observer is designed to drive the temperature of the lower surface of the billet to be adjustable to the desired value.

[0156] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production, characterized in that, it includes: Performing T-S fuzzy partial differential equation modeling on the non-linear billet internal temperature evolution dynamic model with spatio-temporal distribution characteristics to obtain the T-S fuzzy partial differential equation model of the non-linear billet internal temperature evolution dynamic; Adopting the feedback control technology based on an observer to construct a T-S fuzzy observer according to the T-S fuzzy partial differential equation model; Applying the PID control strategy to construct a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer, wherein the fuzzy PID temperature measurement tracking regulator adopts the boundary control law; Determining the control parameters of the fuzzy PID temperature measurement tracking regulator, and applying the fuzzy PID temperature measurement tracking regulator to the non-linear billet internal temperature evolution dynamic model to drive the temperature of the lower surface of the billet to the desired temperature value; Among them, the performing T-S fuzzy partial differential equation modeling on the non-linear billet internal temperature evolution dynamic model with spatio-temporal distribution characteristics to obtain the T-S fuzzy partial differential equation model of the non-linear billet internal temperature evolution dynamic includes: Simplifying the non-linear billet internal temperature evolution dynamic model with spatio-temporal distribution characteristics to obtain a simplified model; For the non-linear terms existing in the simplified model, using the local space-dependent sector non-linearity method to establish a T-S fuzzy partial differential equation model to describe the non-linear dynamics of the billet internal temperature evolution; Among them, the non-linear billet internal temperature evolution dynamic model with spatio-temporal distribution characteristics is expressed as: Among them, β(T) represents the specific heat coefficient of the billet, T represents the temperature; T(x,t) represents the temperature distribution of the billet along the thickness direction, x represents the spatial variable of the billet temperature distribution, and t represents the time variable of the billet temperature distribution; α(T) is a non-linear term representing the thermal conductivity of the billet; u(t) represents the temperature of the radiation source; L represents the thickness of the billet; T out (t) represents the measured value of the temperature of the lower surface of the billet; T(x,0), T 0 (x) both represent the initial temperature distribution of the billet; Among them, the simplified model is expressed as: Among them, β represents the specific heat coefficient constant; Among them, the T-S fuzzy partial differential equation model is expressed as: α(T) ∈ [a 1 , a 2 ​ where \(i\in\{1,2\}\), \(a\) 1 and \(a\) 2 are both abbreviated forms, \(h\) 1 (\(\alpha(T)\)) and \(h\) 2 (\(\alpha(T)\)) both represent fuzzy membership functions, \(T\) min and \(T\) max respectively represent the lower limit value and the upper limit value of the billet temperature distribution, \(h\) 1 (\(\alpha(T)\)) and \(h\) 2 (\(\alpha(T)\)) \(\in[0,L]\); Among them, the constructed T-S fuzzy observer is expressed as: Among them, represents the estimated value of the temperature distribution of the billet along the thickness direction, j ∈ {1, 2}, and L 0j represents the undetermined T-S fuzzy observer gain; represents the estimated value of the lower surface temperature of the billet; both represent the estimated value of the initial temperature distribution of the billet; Among them, the applying the PID control strategy to construct a fuzzy PID temperature measurement tracking regulator based on the T-S fuzzy observer includes: Introduce the measurement and tracking error T of the billet surface temperature e (t) = T out (t) - T d And its integral form And the differential form dT e (t) / dt = dT out (t) / dt, where T e (t) represents the measurement and tracking error of the billet surface temperature, T d represents the desired temperature value, T Ie (t) represents the integral form of T e (t); According to the measurement tracking error T of the billet surface temperature e (t) and its integral and differential forms, the estimated value provided by the T-S fuzzy observer equation Combined with the PID control strategy, a fuzzy PID temperature measurement tracking regulator is constructed; Among them, the constructed fuzzy PID temperature measurement tracking regulator is expressed as: where \(j\in\{1,2\}\), and the constants \(k\) j , \(k\) Pj , \(k\) Ij all represent undetermined control gains, and \(k\) Dj represents a given control gain, which is a boundary control law.

2. The fuzzy PID temperature regulation method for reheating billets in hot strip continuous rolling production according to claim 1, characterized in that, the determining the control parameters of the fuzzy PID temperature measurement tracking regulator includes: Applying Lyapunov technology and combining with a variant form of the Poincaré-Wengel inequality to give the sufficient conditions for the existence of the fuzzy PID temperature measurement tracking regulator, and transforming the existence problem of the fuzzy PID temperature measurement tracking regulator into a feasibility problem of solving a set of linear matrix inequality constraints.

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