Microwave heating temperature tracking control method and system based on piecewise discrete reaching law

Abstract

The application discloses a microwave heating temperature tracking control method and system based on a segmented discrete reaching law, and belongs to the field of microwave heating. The application establishes a sliding mode function and a discrete reaching law combined with quasi-sliding mode control according to a mathematical model of a Debye medium microwave heating process in a one-dimensional direction based on the first law of thermodynamics, and obtains a control law. The application sets the error between an expected temperature and an actual temperature as a sliding mode surface, and realizes temperature tracking control of the microwave heating process through the control law. The application can reach the sliding mode surface more quickly, can keep stable in a quasi-sliding mode band, has strong anti-interference ability, and can realize fast heating under the condition of preventing thermal runaway.

Description

Technical Field

[0001] This invention relates to a microwave heating temperature tracking control method and system based on a piecewise discrete reaching law, belonging to the field of microwave heating. Background Technology

[0002] Microwave heating, as a highly efficient and clean heating method, has been widely used in metallurgy, chemical engineering, pharmaceuticals, and food processing. However, because microwave heating is a complex system characterized by multiple variables, strong coupling, infinite dimensions, and nonlinearity, our understanding of its mechanisms is limited. Furthermore, limitations in sensor technology can lead to thermal runaway. Therefore, automatic temperature control and prevention of thermal runaway in microwave heating have been key research areas for many researchers. Traditional PID control methods are widely used in industrial process control due to their simple algorithms, good robustness, and high reliability. However, this method has certain shortcomings in practical applications. For complex nonlinear systems, changes in internal parameters or external disturbances can significantly impact normal operation. PID control cannot meet the requirements of high-performance systems, and the process requires repeated parameter tuning to select ideal parameters, increasing complexity. For microwave heating, the system's time-varying, nonlinear, and strongly coupled characteristics make it difficult to establish accurate mathematical models, resulting in unsatisfactory parameter tuning. Therefore, traditional PID control methods are insufficient for precise control of microwave heating systems. Summary of the Invention

[0003] This invention provides a microwave heating temperature tracking control method and system based on a piecewise discrete reaching law, for tracking and controlling the temperature during the microwave heating process.

[0004] The technical solution of this invention is: a microwave heating temperature tracking control method based on piecewise discrete reaching law, which obtains a mathematical model of the microwave heating process;

[0005] A sliding mode function is established based on the mathematical model of the microwave heating process;

[0006] Design an improved piecewise discrete reaching law that meets the discrete arrival condition;

[0007] By combining the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control, a discrete reaching law combined with quasi-sliding mode control is obtained.

[0008] The control law is obtained based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control.

[0009] The mathematical model of the microwave heating process includes:

[0010] Step 1: The mathematical model of the microwave heating process can be described by the following partial differential equation model:

[0011]

[0012] Boundary conditions:

[0013]

[0014]

[0015] Initial conditions:

[0016] T(z,0)=T0(z)

[0017] Where T = T (z,t) This represents the temperature at position z at time t; z = 0 indicates the leftmost part of the material, z = L indicates the rightmost part; ρ, C p κ represents the density, specific heat capacity, and thermal conductivity of the medium; h L and h R T represents the heat transfer coefficient at the medium boundary; ∞ Let T0(z) represent the ambient temperature, and Q represent the temperature at position z at time 0. av (z,t) represents the power dissipation at position z at time t;

[0018] Step 2, power dissipation Q av (z,t) is affected by microwave frequency f, relative dielectric loss ε (T), and local electric field E, and can be expressed as:

[0019] Q av (z,t)=πf×ε0ε”(T)×EE”

[0020] Where ε0 is the conductivity in vacuum; E” is the conjugate complex number of the local electric field;

[0021] Step 3: According to the Debye medium equation, the complex permittivity ε(T) as a function of temperature can be described by the following first-order equation:

[0022]

[0023] Where ε'(T) is the relative permittivity, i.e., the real part of the complex permittivity; ε'(T) is the relative permittivity loss, i.e., the imaginary part of the complex permittivity; ε ∞ ε is the relative permittivity of the radio frequency; s τ is the static relative permittivity; τ represents the time it takes for the atom to return to its original state after the electric field disappears, usually called the relaxation time; j is the imaginary part.

[0024] The establishment of the sliding mode function based on the mathematical model of the microwave heating process includes:

[0025] Let r(k) be the desired temperature of the microwave-heated material at time k, and let dr(k) be the rate of change. Let R = [r(k); dr(k)] and R1 = [r(k+1); dr(k+1)]. We then use linear extrapolation to predict r(k+1) and dr(k+1), i.e.:

[0026] r(k+1) = 2r(k) - r(k-1)

[0027] dr(k+1) = 2dr(k) - dr(k-1)

[0028] The discrete-time state equation of a microwave heating system can be expressed as:

[0029] x(k+1)=A*x(k)+B*u(k)+D(k)

[0030] In the formula: x(k+1) represents the state variable of the system at time (k+1), A and B both represent matrices, u(k) represents the input of the system; D(k) contains unknown heat conduction losses and disturbances. Let e(k) = Rx(k), then the sliding mode function s(k) can be set as:

[0031] s(k)=C e *e(k)=C e (Rx(k))

[0032] Where: C e = [c,1] is the error coefficient matrix, where c is a constant, then:

[0033] s(k+1)=C e (R1-x(k+1))

[0034] =C e *R1-C e *A*x(k)-C e *B*u(k)-C e *D(k)°

[0035] The improved piecewise discrete convergence law is as follows:

[0036]

[0037] In the formula: k1>0, k2>0, k3>0, r1, r2, r3 are nonlinear functions. The nonlinear function divides the reaching law into two parts, Δ t It is the sampling time;

[0038]

[0039]

[0040]

[0041] In the formula: n represents a variable;

[0042] Hyperbolic tangent function tanh(n·x):

[0043]

[0044] In the formula: e is a natural constant.

[0045] The discrete arrival condition is:

[0046]

[0047] When |s(k)|>1, the sampling time Δ t The value satisfies 2-Δ t k2-Δ t k3 > 0:

[0048]

[0049]

[0050] When |s(k)|≤1, the sampling time Δ t The value satisfies 2-Δ t k1-Δ t k2-Δ t k3 > 0:

[0051]

[0052]

[0053] The method of combining the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control to obtain a discrete reaching law combined with quasi-sliding mode control includes:

[0054] By replacing the sign function sgn(s(k)) in the piecewise discrete reaching law with the saturation function sat(s(k)), a discrete reaching law combined with quasi-sliding mode control is obtained; where the saturation function is:

[0055]

[0056] Where γ represents the quasi-sliding mode bandwidth and s(k) represents the sliding mode function.

[0057] The control law obtained based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control is as follows:

[0058]

[0059] In the formula: u(k) represents the system input, C e Let A and B be matrices representing error coefficients, D(k) contain unknown heat conduction losses and disturbances, s(k) represent the sliding mode function, R1 represent the matrix consisting of the expected temperature and rate of change of the microwave-heated material at time k+1, x(k) represent the state variables of the system at time k, and Δ t The sampling time is represented by k1>0,k2>0,k3>0,r1,r2,r3 are nonlinear functions, and sat(s(k)) represents the saturation function.

[0060] According to another aspect of the present invention, a microwave heating temperature tracking control system based on a piecewise discrete reaching law is provided, comprising:

[0061] The first acquisition module is used to obtain the mathematical model of the microwave heating process;

[0062] A module is established to create a sliding mode function based on a mathematical model of the microwave heating process;

[0063] The design module is used to design improved piecewise discrete reaching laws that meet discrete arrival conditions;

[0064] The second acquisition module is used to combine the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control to obtain the discrete reaching law combined with quasi-sliding mode control.

[0065] The third acquisition module is used to obtain the control law based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control.

[0066] According to another aspect of the present invention, a processor is provided for running a program, wherein the program executes the microwave heating temperature tracking control method based on piecewise discrete reaching law as described above.

[0067] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium including a stored program, wherein when the program is executed, the device on which the computer-readable storage medium is located executes the microwave heating temperature tracking control method based on the piecewise discrete reaching law described above.

[0068] The beneficial effects of this invention are as follows: Based on the mathematical model of the microwave heating process of Debye medium in one dimension based on the first law of thermodynamics, this invention establishes a sliding mode function and a discrete approaching law combined with quasi-sliding mode control, thus obtaining a control law; by setting the error between the desired temperature and the actual temperature as the sliding mode surface, this invention achieves temperature tracking control of the microwave heating process through this control law, and this invention can reach the sliding mode surface faster, maintain stability within the quasi-sliding mode band, has strong anti-interference ability, and can achieve rapid heating under the condition of preventing thermal runaway. Attached Figure Description

[0069] Figure 1 This is the overall flowchart of the present invention;

[0070] Figure 2 This is the design flowchart for the piecewise discrete reaching law;

[0071] Figure 3 This is a flowchart illustrating the implementation steps of this invention in a microwave heating system. Detailed Implementation

[0072] The invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited to the description.

[0073] Example 1: As Figure 1-3 As shown, a microwave heating temperature tracking control method based on a piecewise discrete reaching law includes:

[0074] Obtain a mathematical model of the microwave heating process;

[0075] A sliding mode function is established based on the mathematical model of the microwave heating process;

[0076] Design an improved piecewise discrete reaching law that meets the discrete arrival condition;

[0077] By combining the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control, a discrete reaching law combined with quasi-sliding mode control is obtained.

[0078] Based on the sliding mode function and the discrete approach law combined with quasi-sliding mode control, the control law is obtained to complete microwave heating temperature tracking;

[0079] Optionally, the mathematical model of the microwave heating process is a mathematical model of the Debye medium microwave heating process in one dimension based on the first law of thermodynamics, used to describe the changing trend of the system state during microwave heating, including:

[0080] Step 1: The mathematical model of the microwave heating process can be described by the following partial differential equation model:

[0081]

[0082] Boundary conditions:

[0083]

[0084]

[0085] Initial conditions:

[0086] T(z,0)=T0(z)

[0087] Where T = T (z,t) This represents the temperature at position z at time t; z = 0 indicates the leftmost part of the material, z = L indicates the rightmost part; ρ, C p κ represents the density, specific heat capacity, and thermal conductivity of the medium; h L and h R T represents the heat transfer coefficient at the medium boundary; ∞ Let T0(z) represent the ambient temperature, and Q represent the temperature at position z at time 0. av (z,t) represents the power dissipation at position z at time t;

[0088] Step 2, power dissipation Q av (z,t) is affected by microwave frequency f, relative dielectric loss ε (T), and local electric field E, and can be expressed as:

[0089] Q av =πf×ε0ε(T)×EE”

[0090] Where, ε0=8.854×10 -14 rad / cm is the conductivity in vacuum; E” is the conjugate complex number of the local electric field;

[0091] Step 3: According to the Debye medium equation, the complex permittivity ε(T) as a function of temperature can be described by the following first-order equation:

[0092]

[0093] Where ε'(T) is the relative permittivity, i.e., the real part of the complex permittivity; ε'(T) is the relative permittivity loss, i.e., the imaginary part of the complex permittivity; ε ∞ ε is the relative permittivity of the radio frequency; s τ is the static relative permittivity; τ represents the time it takes for the atom to return to its original state after the electric field disappears, usually called the relaxation time; j is the imaginary part.

[0094] Optionally, establishing the sliding mode function based on the mathematical model of the microwave heating process includes:

[0095] Let r(k) be the desired temperature of the microwave-heated material at time k, and let dr(k) be the rate of change. Let R = [r(k); dr(k)] and R1 = [r(k+1); dr(k+1)]. We then use linear extrapolation to predict r(k+1) and dr(k+1), i.e.:

[0096] r(k+1) = 2r(k) - r(k-1)

[0097] dr(k+1) = 2dr(k) - dr(k-1)

[0098] The discrete-time state equation of a microwave heating system can be expressed as:

[0099] x(k+1)=A*x(k)+B*u(k)+D(k)

[0100] In the formula: x(k+1) represents the state variable of the system at time (k+1), A and B both represent matrices, u(k) represents the input of the system; D(k) contains unknown heat conduction losses and disturbances. Let e(k) = Rx(k), then the sliding mode function s(k) can be set as:

[0101] s(k)=C e *e(k)=C e (Rx(k))

[0102] Where: C e = [c,1] is the error coefficient matrix, where c is a constant, then:

[0103] s(k+1)=C e (R1-x(k+1))

[0104] =C e *R1-C e *A*x(k)-C e *B*u(k)-C e *D(k)°

[0105] Optionally, the improved piecewise discrete reaching law is:

[0106]

[0107] In the formula: k1>0, k2>0, k3>0, r1, r2, r3 are nonlinear functions. The nonlinear function divides the reaching law into two parts, Δ t It is the sampling time;

[0108]

[0109]

[0110]

[0111] in: n represents a variable;

[0112] Hyperbolic tangent function tanh(n·x):

[0113]

[0114] e is a natural constant, approximately equal to 2.718281828.

[0115] Optionally, the discrete arrival condition is:

[0116]

[0117] When |s(k)|>1, the sampling time Δ t The value satisfies 2-Δ t k2-Δ t k3 > 0:

[0118]

[0119]

[0120] When |s(k)|≤1, the sampling time Δ t The value satisfies 2-Δ t k1-Δ t k2-Δ t k3 > 0:

[0121]

[0122]

[0123] If the discrete reaching law satisfies the discrete arrival condition according to the above equation, it indicates that the reaching law mode has good quality. Since discrete systems cannot completely reach the sliding surface, it is necessary to combine it with quasi-sliding mode control.

[0124] Optionally, the step of combining the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control to obtain a discrete reaching law combined with quasi-sliding mode control includes:

[0125] Replacing the sign function sgn(s(k)) in the piecewise discrete reaching law with the saturation function sat(s(k)) yields a discrete reaching law combined with quasi-sliding mode control, which can reduce chattering; the saturation function is:

[0126]

[0127] Wherein, γ represents the quasi-sliding mode band width;

[0128] Optionally, the control law obtained based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control is as follows:

[0129] That is, based on The control law is obtained by combining the discrete reaching law with quasi-sliding mode control:

[0130] In the formula: u(k) represents the system input, C e Let A and B be matrices representing error coefficients, D(k) contain unknown heat conduction losses and disturbances, s(k) represent the sliding mode function, R1 represent the matrix consisting of the expected temperature and rate of change of the microwave-heated material at time k+1, x(k) represent the state variables of the system at time k, and Δ t The sampling time is represented by k1>0,k2>0,k3>0,r1,r2,r3 are nonlinear functions, and sat(s(k)) represents the saturation function.

[0131] like Figure 3 As shown, the control law of this invention is applied to a microwave heating system, dividing the entire microwave heating process into two stages. Before the predetermined desired maximum temperature T1 (i.e., far from the sliding mode surface), the power is high and the temperature rise is rapid. Near temperature T1 (i.e., within the quasi-sliding mode bandwidth), the temperature rise rate slows down, and the temperature change remains within the critical temperature for thermal runaway. The problem of suppressing thermal runaway during microwave heating is essentially an output tracking problem for a system simultaneously exhibiting input saturation, internal uncertainty, and external disturbance characteristics. Therefore, this invention can effectively achieve microwave heating temperature tracking control and suppress the occurrence of thermal runaway.

[0132] Example 2: A microwave heating temperature tracking control system based on a piecewise discrete reaching law, comprising:

[0133] The first acquisition module is used to obtain the mathematical model of the microwave heating process;

[0134] A module is established to create a sliding mode function based on a mathematical model of the microwave heating process;

[0135] The design module is used to design improved piecewise discrete reaching laws that meet discrete arrival conditions;

[0136] The second acquisition module is used to combine the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control to obtain the discrete reaching law combined with quasi-sliding mode control.

[0137] The third acquisition module is used to obtain the control law based on the sliding mode function and the discrete approach law combined with quasi-sliding mode control, and to complete the microwave heating temperature tracking.

[0138] It should be noted that the above-mentioned modules can be implemented by software or hardware. For example, for the latter, it can be implemented in the following ways: the above-mentioned modules can be located in the same processor; and / or, the above-mentioned modules can be located in different processors in any combination. The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein.

[0139] According to another aspect of the present invention, a processor is provided for running a program, wherein the program executes the microwave heating temperature tracking control method based on piecewise discrete reaching law as described above.

[0140] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium including a stored program, wherein when the program is executed, the device on which the computer-readable storage medium is located executes the microwave heating temperature tracking control method based on the piecewise discrete reaching law described above.

[0141] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A microwave heating temperature tracking control method based on a piecewise discrete reaching law, characterized in that: include: Obtain a mathematical model of the microwave heating process; A sliding mode function is established based on the mathematical model of the microwave heating process; Design an improved piecewise discrete reaching law that meets the discrete arrival condition; By combining the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control, a discrete reaching law combined with quasi-sliding mode control is obtained. The control law is obtained based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control; The mathematical model of the microwave heating process includes: Step 1: The mathematical model of the microwave heating process can be described by the following partial differential equation model: Boundary conditions: Initial conditions: in, This represents the temperature at position z at time t; z=0 indicates the leftmost part of the material, and z=L indicates the rightmost part. , and The density, specific heat capacity, and thermal conductivity of the medium are indicated. and This represents the heat transfer coefficient at the boundary of the medium; For ambient temperature, This represents the temperature at position z at time 0. Let be the power dissipated at position z at time t; Step 2, power dissipation Subject to microwave frequency f and relative dielectric loss The influence of the local electric field E can be expressed as: in, It is the conductivity in a vacuum; It is the conjugate complex number of the local electric field; Step 3: According to the Debye medium equation, the complex permittivity varies with temperature. It can be described by the following first-order equation: in, It is the relative permittivity, that is, the real part of the complex permittivity; It is the relative permittivity, i.e., the imaginary part of the complex permittivity; The relative permittivity of the radio frequency; It is the static relative permittivity; The time it takes for an atom to return to its original state after the electric field disappears is called the relaxation time; j is the imaginary part.

2. The microwave heating temperature tracking control method based on piecewise discrete reaching law according to claim 1, characterized in that: The establishment of the sliding mode function based on the mathematical model of the microwave heating process includes: Let r(k) be the desired temperature of the material heated by microwave at time k, and let dr(k) be the rate of change. Let R = [r(k); dr(k)]. We use linear extrapolation to predict r(k+1) and dr(k+1), that is: The discrete-time state equation of the microwave heating system is expressed as: In the formula: x(k+1) represents the state variable of the system at time (k+1), A and B both represent matrices, u(k) represents the input of the system; D(k) contains unknown heat conduction losses and disturbances. Let e(k) = Rx(k), then the sliding mode function s(k) can be set as: in: Let c be the error coefficient matrix, and c be a constant. Then: 。 3. The microwave heating temperature tracking control method based on piecewise discrete reaching law according to claim 1, characterized in that: The improved piecewise discrete convergence law is as follows: In the formula: It is a nonlinear function, and the nonlinear function divides the reaching law into two parts. It is the sampling time; In the formula: , where n represents a variable; Hyperbolic tangent function tanh(n·x): In the formula: e is a natural constant.

4. The microwave heating temperature tracking control method based on piecewise discrete reaching law according to claim 3, characterized in that: The discrete arrival condition is: when At that time, sampling time The value satisfies : when At that time, sampling time The value satisfies : 。 5. The microwave heating temperature tracking control method based on piecewise discrete reaching law according to claim 1, characterized in that: The method of combining the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control to obtain a discrete reaching law combined with quasi-sliding mode control includes: The sign function in the piecewise discrete reaching law Replacing the saturation function sat(s(k)), we obtain the discrete reaching law combined with quasi-sliding mode control; where the saturation function is: in, Let s(k) represent the quasi-sliding mode bandwidth, and s(k) represent the sliding mode function.

6. The microwave heating temperature tracking control method based on piecewise discrete reaching law according to claim 1, characterized in that: The control law obtained based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control is as follows: In the formula: u(k) represents the system input, Let A and B be the error coefficient matrix, where D(k) contains unknown heat conduction losses and disturbances, and s(k) represent the sliding mode function. Let x(k) be a matrix representing the expected temperature and rate of change of the microwave-heated material at time k+1, and let x(k) represent the state variables of the system at time k. Indicates the sampling time. It is a nonlinear function, and sat(s(k)) represents the saturation function.

7. A microwave heating temperature tracking control system based on a piecewise discrete reaching law that performs the method of claim 1, characterized in that: include: The first acquisition module is used to obtain the mathematical model of the microwave heating process; A module is established to create a sliding mode function based on a mathematical model of the microwave heating process; The design module is used to design improved piecewise discrete reaching laws that meet discrete arrival conditions; The second acquisition module is used to combine the improved piecewise discrete reaching law that meets the discrete arrival condition with quasi-sliding mode control to obtain the discrete reaching law combined with quasi-sliding mode control. The third acquisition module is used to obtain the control law based on the sliding mode function and the discrete reaching law combined with quasi-sliding mode control.

8. A processor, characterized in that: The processor is used to run a program, wherein the program executes the microwave heating temperature tracking control method based on the piecewise discrete reaching law as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program that, when the program is executed, controls the device containing the computer-readable storage medium to perform the microwave heating temperature tracking control method based on the piecewise discrete reaching law as described in any one of claims 1 to 6.

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