A Predefined Time Sliding Mode Control Method for Continuous Stirred Reactors

Abstract

The present invention provides a predefined time sliding mode control method for a continuous stirred reactor, which belongs to the technical field of chemical industry process control. The predefined time sliding mode control method for a continuous stirred reactor includes establishing a continuous stirred reactor model; defining a given temperature x 2d The error e between the actual position and the actual position is used to construct a sliding surface; on the basis of the sliding surface, the control law is designed in combination with the predefined time stability theory and the Lyapunov stability theory to obtain a predefined time sliding mode controller; the coolant temperature output by the predefined time sliding mode controller is applied to the continuous stirred reactor; the invention can solve the problems that the effective control algorithm of the existing CSTR cannot further shorten the convergence time of the continuous stirred reactor and it is difficult to ensure that the controlled variables of the system can accurately track the given values.

Description

Technical Field

[0001] The invention belongs to the technical field of chemical industry process control, and in particular relates to a predefined time sliding mode control method for a continuous stirred reactor. Background Art

[0002] The continuous stirred tank reactor (CSTR) is a commonly used reaction vessel in the chemical process industry. The CSTR is a control object with strong nonlinearity, high complexity and high sensitivity. It usually converts production raw materials into products through a series of physical and chemical reactions at a specified temperature. The CSTR generally operates around an equilibrium point related to the optimal output or optimal productivity; but when the system is disturbed by external factors, the control steady state is easily destroyed, causing the CSTR to deviate from the specified operating point, which will inevitably damage the product quality and cause serious safety hazards. Therefore, it is necessary to study the precise control algorithm of the CSTR and provide technical guidance for the actual production process based on the CSTR, which is of great significance for improving product quality and production efficiency.

[0003] Nowadays, different control algorithms have been proposed for the control problem of CSTR. For example, PI controller with modeling error compensation and self-oscillation consideration; feedback controller with state estimation; fault-tolerant controller for dealing with faults, etc. Sliding mode control is a special type of nonlinear control that can overcome system uncertainty and has strong robustness to disturbances and unmodeled dynamics, especially for nonlinear systems. Therefore, it has a wide range of applications in various control fields.

[0004] Although various effective control algorithms for CSTR have been proposed, most of them are aimed at solving the stability problem of CSTR, which makes it difficult to improve the convergence time, further shorten the convergence time of the system and enable the controlled variables of the system to accurately track the given values. Summary of the invention

[0005] In view of this, the present invention provides a predefined time sliding mode control method for a continuous stirred reactor, which can solve the problem that the effective control algorithm of the existing CSTR cannot further shorten the convergence time of the continuous stirred reactor and it is difficult to ensure that the controlled variables of the system can accurately track the given values.

[0006] The present invention is achieved in that:

[0007] The present invention provides a predefined time sliding mode control method for a continuous stirred tank reactor, which comprises the following steps:

[0008] S10: Establish a continuous stirred tank reactor model;

[0009] S20: Define a given temperature x 2d The error e between the actual position and the sliding surface is constructed;

[0010] S30: Based on the sliding surface, a control law is designed in combination with a predefined time stability theory and a Lyapunov stability theory to obtain a predefined time sliding mode controller, wherein the predefined time sliding mode controller is used to control the continuous stirred tank reactor model to converge and stabilize within a predefined time;

[0011] S40: applying the coolant temperature output by the predefined time sliding mode controller to the continuous stirred reactor;

[0012] S50: verifying the effectiveness and feasibility of the steps S10-S40, respectively analyzing the conditions without interference and with interference, and comparing and analyzing the finite time sliding mode control with the predefined time sliding mode control.

[0013] On the basis of the above technical solution, the predefined time sliding mode control method for a continuous stirred reactor of the present invention can also be improved as follows:

[0014] The specific steps of establishing the continuous stirred tank reactor model include:

[0015] According to the principles of energy conservation and mass conservation, the kinetic model of the continuous stirred reactor was established, and the kinetic model was normalized and dimensionless to obtain a simplified CSTR mathematical model.

[0016] The CSTR mathematical model is:

[0017]

[0018] Among them, x1 is the system concentration variable; x2 is the temperature variable; are the derivatives corresponding to x1 and x2 respectively; u is the coolant temperature, representing the control input; d1 and d2 are the system disturbances; γ, β, D a , B and x 2c is the system parameter.

[0019] The kinetic model of the continuous stirred reactor given above is described by function:

[0020]

[0021] Furthermore, the given temperature x 2d The error e between the actual position is:

[0022] e=x2-x 2d ;

[0023] Among them, x 2d is the expected temperature value.

[0024] Furthermore, the function of the sliding surface is:

[0025] s=x2+Ψ;

[0026] in, α1, β1 and η are constants, where α1, β1>0, 0<η1<1; is the Lyapunov function; T c1 is the predefined time of the sliding phase.

[0027] Furthermore, the specific steps of designing a control law based on the sliding surface and combining the predefined time stability theory and the Lyapunov stability theory to obtain a predefined time sliding mode controller include:

[0028] The first step is to establish an uncertain dynamic system;

[0029] The second step is to introduce a radially unbounded Lyapunov function to determine the trajectory of the uncertain dynamical system;

[0030] The third step is to obtain a formula of a sliding mode control law of the predefined time sliding mode controller according to the function of the sliding mode surface;

[0031] The fourth step is to analyze the stability of the predefined time sliding mode controller.

[0032] Furthermore, the uncertain dynamic system is:

[0033]

[0034] in, is the derivative corresponding to x; t is the time variable, x∈R n is the system state variable, d∈R m is an unknown but bounded disturbance; f: R + ×R n ×R m →R n is a nonlinear function.

[0035] Furthermore, the radially unbounded Lyapunov function is:

[0036]

[0037] Where V(x) is a radially unbounded Lyapunov function; is the derivative of the radially unbounded Lyapunov function; T c>0 is a predefined constant, η∈(0,1) and 0<∈<∞ are system parameters; α is a constant;

[0038] The residual of the solution of the uncertain dynamical system is:

[0039]

[0040] Among them, 0<μ<1; T pc To adjust the time,

[0041] Furthermore, the formula of the sliding mode control law of the predefined time sliding mode controller is:

[0042]

[0043] Where u is the sliding mode control law of the predefined time sliding mode controller, is another Lyapunov function, T c2 is the predefined time of the arrival phase; f d =Dtanh(sD / ω), ω is a constant greater than zero, D is the upper limit of disturbance; β2, α2 and η2 are system parameters.

[0044] Furthermore, the specific steps of analyzing the stability of the predefined time sliding mode controller are:

[0045] Verify the predefined time stability of the arrival phase and the sliding phase respectively;

[0046] The verification process of the predefined time stability of the arrival stage is to drive the tracking error of the continuous stirred tank reactor model onto the defined sliding mode surface within the predefined time by using the control law of the designed predefined time sliding mode controller stability;

[0047] The verification process of the predefined time stability of the sliding stage is to make the sliding mode motion of the designed predefined time sliding mode controller make the tracking error of the continuous stirred tank reactor model converge to zero within the predefined time and remain stable thereafter, that is, to ensure the predefined time stability of the sliding stage.

[0048] Furthermore, the specific process of verifying the predefined time stability of the sliding stage includes:

[0049] The sliding surface function satisfies s=0,

[0050]

[0051] Define the error Lyapunov function:

[0052]

[0053] The derivative is:

[0054]

[0055] The error e obtained by solving will be c1 reaches 0 within 1 second; among them, is the derivative of the error e;

[0056] The specific process of verifying the predefined time stability of the arrival stage includes:

[0057] The Lyapunov function of the sliding surface is defined as:

[0058]

[0059] The derivative is:

[0060]

[0061] Substituting the formula of the sliding mode control law of the predefined time sliding mode controller into the formula, we can obtain:

[0062]

[0063] in, is the derivative of s; is the derivative of Ψ;

[0064] According to the inequality 0≤|z|-ztanh(z / ∈)<ζ∈, where z∈R,∈>0, ζ satisfies ζ=e -ζ-1 , i.e. ζ=0.2785;

[0065] so,

[0066]

[0067] Here, σ = ζω is bounded, so s can be in a predefined time T c2 Converges to 0 internally;

[0068] According to the validation process of the predefined time stability of the sliding phase and the reaching phase, the continuous stirred tank reactor model is c1 +T c2 reaches equilibrium within a certain period of time.

[0069] Compared with the prior art, the beneficial effects of the predefined time sliding mode control method for a continuous stirred reactor provided by the present invention are: by establishing a continuous stirred reactor model; defining a given temperature x 2dThe error e between the actual position and the actual position is used to construct a sliding surface; on the basis of the sliding surface, the control law is designed in combination with the predefined time stability theory and the Lyapunov stability theory to obtain a predefined time sliding mode controller; the coolant temperature output by the predefined time sliding mode controller is applied to the continuous stirred reactor; the effectiveness and feasibility of the verification steps are analyzed in the absence of interference and in the presence of interference, and the finite time sliding mode control and the predefined time sliding mode control are compared and analyzed; it can solve the convergence time problem of the continuous stirred reactor in the control process, and it also has good robustness when there is unknown interference in the system, so that the system state trajectory can reach the equilibrium point within the predefined time and remain stable, thereby improving the control efficiency of the continuous stirred reactor and having the ability to handle complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0071] Figure 1 A schematic flow chart of a predefined time sliding mode control method for a continuous stirred tank reactor;

[0072] Figure 2 is a schematic diagram of the CSTR model;

[0073] Figure 3 Concentration response curves for predefined time sliding mode control and finite time sliding mode control;

[0074] Figure 4 Temperature response curves for predefined time sliding mode control and finite time sliding mode control;

[0075] Figure 5 The control input curve of the sliding mode control with a predefined time when there is no disturbance;

[0076] Figure 6 The concentration response curve of the sliding mode control with predefined time when there is no disturbance in the continuous stirred tank reactor model;

[0077] Figure 7 The temperature response curve of the sliding mode control with predefined time when there is no interference in the continuous stirred tank reactor model;

[0078] Figure 8 The concentration response curve of the predefined time sliding mode control when a disturbance is added to the continuous stirred tank reactor model;

[0079] Fig. 9The temperature response curve of the predefined time sliding mode control when a disturbance is added to the continuous stirred tank reactor model;

[0080] Fig.10 Control input curve for predefined time sliding mode control when a disturbance is introduced into the continuous stirred tank reactor model. DETAILED DESCRIPTION

[0081] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0083] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0084] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0085] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0086] like Figure 1-2FIG. 1 is a specific flow chart of a predefined time sliding mode control method for a continuous stirred reactor provided by the present invention, which includes the following steps:

[0087] S10: Establish a continuous stirred tank reactor model;

[0088] S20: Define a given temperature x 2d The error e between the actual position and the sliding surface is constructed;

[0089] S30: Based on the sliding surface, a control law is designed in combination with the predefined time stability theory and the Lyapunov stability theory to obtain a predefined time sliding mode controller, wherein the predefined time sliding mode controller is used to control the continuous stirred tank reactor model to converge and stabilize within a predefined time;

[0090] S40: applying the coolant temperature output by the sliding mode controller at a predefined time to the continuous stirred reactor;

[0091] S50: verify the effectiveness and feasibility of steps S10-S40, analyze them in the absence of interference and with interference, and compare and analyze the finite time sliding mode control and the predefined time sliding mode control.

[0092] Among them, in the above technical solution, the specific steps of establishing the continuous stirred tank reactor model include:

[0093] According to the principles of energy conservation and mass conservation, the kinetic model of the continuous stirred reactor was established, and the kinetic model was normalized and dimensionless to obtain a simplified CSTR mathematical model.

[0094] The CSTR mathematical model is:

[0095]

[0096] Among them, x1 is the system concentration variable; x2 is the temperature variable; are the derivatives corresponding to x1 and x2 respectively; u is the coolant temperature, representing the control input; d1 and d2 are the system disturbances; γ, β, D a , B and x 2c is the system parameter.

[0097] The kinetic model of the continuous stirred reactor given above is described by function:

[0098]

[0099] Furthermore, in the above technical solution, given the temperature x 2d The error e between the actual position is:

[0100] e=x2-x 2d ;

[0101] Among them, x 2d is the expected temperature value.

[0102] Furthermore, in the above technical solution, the function of the sliding surface is:

[0103] s=x2+Ψ;

[0104] in, α1, β1 and η1 are constants, where α1, β1>0, 0<η1<1; is the Lyapunov function; T c1 is the predefined time of the sliding phase.

[0105] Furthermore, in the above technical solution, based on the sliding surface, the control law is designed in combination with the predefined time stability theory and the Lyapunov stability theory, and the specific steps of obtaining the predefined time sliding mode controller include:

[0106] The first step is to establish an uncertain dynamic system;

[0107] In the second step, a radially unbounded Lyapunov function is introduced to determine the trajectory of the uncertain dynamical system;

[0108] The third step is to obtain the formula of the sliding mode control law of the predefined time sliding mode controller according to the function of the sliding surface;

[0109] The fourth step is to analyze the stability of the sliding mode controller with predefined time.

[0110] Furthermore, in the above technical solution, the uncertain dynamic system is:

[0111]

[0112] in, is the derivative corresponding to c; t is the time variable, x∈R n is the system state variable, d∈R m is an unknown but bounded disturbance; f: R + ×R n ×R m →R n is a nonlinear function; is a dimensionless system state variable.

[0113] Furthermore, in the above technical solution, the radially unbounded Lyapunov function is:

[0114]

[0115] Where V(x) is a radially unbounded Lyapunov function; is the derivative of the radially unbounded Lyapunov function; T c >0 is a predefined constant, η∈(0,1) and 0<∈<∞ are system parameters; α is a constant;

[0116] The residual of the solution of the uncertain dynamical system is:

[0117]

[0118] Among them, 0<μ<1; T pc To adjust the time,

[0119] Furthermore, in the above technical solution, the formula of the sliding mode control law of the predefined time sliding mode controller is:

[0120]

[0121] Where u is the sliding mode control law of the predefined time sliding mode controller, is another Lyapunov function, T c2 is the predefined time of the arrival phase; f d =Dtanh(sD / ω), ω is a constant greater than zero, D is the upper limit of disturbance; β2, α2 and η2 are system parameters.

[0122] Furthermore, in the above technical solution, the specific steps of stability analysis of the predefined time sliding mode controller are:

[0123] Verify the predefined time stability of the arrival phase and the sliding phase respectively;

[0124] The verification process of the predefined time stability in the arrival stage is to drive the tracking error of the continuous stirred tank reactor model onto the defined sliding surface within the predefined time using the control law of the designed predefined time sliding mode controller stability;

[0125] The verification process of the predefined time stability of the sliding stage is to make the sliding mode motion of the designed predefined time sliding mode controller converge to zero within the predefined time for the tracking error of the continuous stirred tank reactor model and keep it stable afterwards, that is, to ensure the predefined time stability of the sliding stage.

[0126] Furthermore, in the above technical solution, the specific process of verifying the stability of the predefined time in the sliding phase includes:

[0127] The sliding surface function satisfies s=0,

[0128]

[0129] Define the error Lyapunov function:

[0130]

[0131] The derivative is:

[0132]

[0133] The error e obtained by solving will be c1 reaches 0 within 1 second; among them, is the derivative of the error e;

[0134] The specific process of verifying the predefined time stability of the arrival stage includes:

[0135] The Lyapunov function of the sliding surface is defined as:

[0136]

[0137] The derivative is:

[0138]

[0139] Substituting the formula of the sliding mode control law of the predefined time sliding mode controller into the formula, we can obtain:

[0140]

[0141]

[0142] in, is the derivative of s; is the derivative of Ψ;

[0143] According to the inequality 0≤|z|-ztanh(z / ∈)<ζ∈, where z∈R,∈>0, ζ satisfies ζ=e -ζ-1 , i.e. ζ=0.2785;

[0144] so,

[0145]

[0146] Here, σ = ζω is bounded, so s can be in a predefined time T c2 Converges to 0 internally;

[0147] According to the validation process of the predefined time stability of the sliding phase and the reaching phase, the continuous stirred tank reactor model is c1 +T c2 reaches equilibrium within a certain period of time.

[0148] Example:

[0149] Design the model parameters of the continuous stirred reactor: B = 8, Da = 0.078, γ = 20, β = 0.3, x_2c = 0. The system has multiple steady-state equilibrium points, select one of the steady-state equilibrium points (x_1, x_2) = (0.4472, 2.7517); specify the predefined time T c1 =3s, T c2 =1s. When there is no interference, d1 and d2 are set to zero, and the upper limit of disturbance D = 0; when there is interference, set the disturbance amount d_1 = 0.1, d_2 = 0.037sin (0.1t), and the upper limit of disturbance D = 5.

[0150] Figure 3 and Figure 4 The response curves of the finite-time sliding mode control and the predefined-time sliding mode control are compared. It can be seen from the figure that the control performance of the predefined-time sliding mode control is significantly better than that of the finite-time control; therefore, the predefined-time sliding mode control has a better convergence speed than the finite-time sliding mode control, and the control effect is better than that of the finite-time control as a whole.

[0151] Figure 5 This is the input curve of the predefined time sliding mode control without interference. It can be seen from the figure that there is no oscillation in the control input and the control effect is good.

[0152] Figure 6 and Figure 7 The concentration and temperature response curves of the predefined time sliding mode control when there is no interference; it can be seen from the figure that the response is smooth and the state trajectory always remains near the desired operating point. The temperature is stable within the predetermined time of 4s.

[0153] Figure 8 and Fig. 9 This is the state response curve of the predefined time sliding mode control when interference is added to the system. It can be seen from the figure that after the interference is added, the system can still reach stability within the predefined time (4s), but the temperature curve will vibrate slightly before 2s, and the state trajectory always remains near the desired operating point. This shows that the predefined time sliding mode controller has a certain performance robustness to unknown interference, and its convergence speed will not be affected.

[0154] Fig.10 The control input curve of the predefined time sliding mode control when a disturbance is added to the system. It can be seen that in order to maintain high control accuracy, the control input needs to be switched at a high frequency, a phenomenon called "chattering". Chattering may wear out actuators, such as control valves.

[0155] Specifically, the principle of the present invention is: establish a continuous stirred reactor model; define a given temperature x 2dThe error e between the actual position and the actual position is used to construct the sliding surface; on the basis of the sliding surface, the control law is designed in combination with the predefined time stability theory and the Lyapunov stability theory to obtain the predefined time sliding mode controller; the coolant temperature output by the predefined time sliding mode controller is applied to the continuous stirred reactor; the effectiveness and feasibility of the verification steps are analyzed in the absence of interference and with interference, and the finite time sliding mode control and the predefined time sliding mode control are compared and analyzed.

[0156] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A predefined time sliding mode control method for a continuous stirred tank reactor, characterized in that: The steps include: S10: Establish a continuous stirred tank reactor model; S20: Define a given temperature x 2d The error e between the actual position and the sliding surface is constructed; S30: Based on the sliding surface, a control law is designed in combination with a predefined time stability theory and a Lyapunov stability theory to obtain a predefined time sliding mode controller, wherein the predefined time sliding mode controller is used to control the continuous stirred tank reactor model to converge and stabilize within a predefined time; S40: applying the coolant temperature output by the predefined time sliding mode controller to the continuous stirred reactor; S50: verifying the effectiveness and feasibility of the steps S10-S40, respectively analyzing the conditions without interference and with interference, and comparing and analyzing the finite time sliding mode control and the predefined time sliding mode control; The function of the sliding surface is: s=x2+Ψ; Among them, s is the sliding surface; x2 is the temperature variable; α1, β1 and η1 are constants, where α1, β1>0, 0<η1<1; is the Lyapunov function; T c1 is the predefined time of the sliding phase; The specific steps of designing a control law based on the sliding surface and combining the predefined time stability theory and the Lyapunov stability theory to obtain a predefined time sliding mode controller include: The first step is to establish an uncertain dynamic system; The second step is to introduce a radially unbounded Lyapunov function to determine the trajectory of the uncertain dynamical system; The third step is to obtain a formula of a sliding mode control law of the predefined time sliding mode controller according to the function of the sliding mode surface; The fourth step is to analyze the stability of the predefined time sliding mode controller.

2. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 1, characterized in that: The specific steps of establishing the continuous stirred reactor model include: According to the principles of energy conservation and mass conservation, the kinetic model of the continuous stirred reactor was established, and the kinetic model was normalized and dimensionless to obtain a simplified CSTR mathematical model. The CSTR mathematical model is: Among them, x1 is the system concentration variable; x2 is the temperature variable; are the derivatives corresponding to x1 and x2 respectively; u is the coolant temperature, representing the control input; d1 and d2 are the system disturbances; γ, β, D a , B and x 2c is the system parameter; The kinetic model of the given continuous stirred tank reactor is described by function:

3. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 2, characterized in that: The given temperature x 2d The error e between the actual position is: e=x2-x 2d ; Among them, x 2d is the expected temperature value.

4. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 3, characterized in that: The uncertain dynamic system is: in, is the derivative corresponding to x; t is the time variable, x∈R n is the system state variable, d∈R m is an unknown but bounded disturbance; f: R + ×R n ×R m →R n is a nonlinear function.

5. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 4, characterized in that: The radially unbounded Lyapunov function is: Where V(x) is a radially unbounded Lyapunov function; is the derivative of the radially unbounded Lyapunov function; T c >0 is a predefined constant, η∈(0,1) and 0<∈<∞ are system parameters; α is a constant; The residual of the solution of the uncertain dynamical system is: Among them, 0<μ<1; T pc To adjust the time, 6. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 5, characterized in that: The formula of the sliding mode control law of the predefined time sliding mode controller is: Where u is the sliding mode control law of the predefined time sliding mode controller, is another Lyapunov function, T c2 is the predefined time of the arrival phase; f d =Dtanh(sD / ω), ω is a constant greater than zero, D is the upper limit of disturbance; β2, α2 and η2 are system parameters.

7. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 6, characterized in that: The specific steps of analyzing the stability of the predefined time sliding mode controller are: Verify the predefined time stability of the arrival phase and the sliding phase respectively; The verification process of the predefined time stability of the arrival stage is to drive the tracking error of the continuous stirred tank reactor model onto the defined sliding mode surface within the predefined time by using the control law of the stability of the predefined time sliding mode controller designed; The verification process of the predefined time stability of the sliding stage is to make the sliding mode motion of the designed predefined time sliding mode controller make the tracking error of the continuous stirred tank reactor model converge to zero within the predefined time and remain stable thereafter, that is, to ensure the predefined time stability of the sliding stage.

8. A predefined time sliding mode control method for a continuous stirred tank reactor according to claim 7, characterized in that: The specific process of verifying the predefined time stability of the sliding stage includes: The sliding surface function satisfies s=0, Define the error Lyapunov function: The derivative is: The error e obtained by solving will be at the predefined time T c1 reaches 0 within 1 second; among them, is the derivative of the error e; The specific process of verifying the predefined time stability of the arrival stage includes: The Lyapunov function of the sliding surface is defined as: The derivative is: Substituting the formula of the sliding mode control law of the predefined time sliding mode controller into the formula, we can obtain: in, is the derivative of s; is the derivative of Ψ; D is the upper limit of disturbance; According to the inequality 0≤|z|-ztanh(z / ∈)<ζ∈, where z∈R,∈>0, ζ satisfies ζ=e -ζ-1 , i.e. ζ=0.2785; so, Here, σ = ζω is bounded, so s can be in a predefined time T c2 Converges to 0 internally; According to the validation process of the predefined time stability of the sliding phase and the reaching phase, the continuous stirred tank reactor model is c1 +T c2 reaches equilibrium within a certain period of time.

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