An improved adaptive backstepping control method for MPCVD reactor

Abstract

An improved adaptive backstepping control method for an MPCVD reactor, which relates to the technical field of MPCVD reactor process control. Aiming at the problem of non-parametric uncertainty in the process control modeling of MPCVD synthetic diamond in the prior art, which further leads to the problem that the system output cannot track the given target signal within a small error range, this application first proposes a direct adaptive law to estimate this uncertainty for dealing with the non-parametric uncertainty of the system; uses the equivalent transformation of the system to solve the problem brought by the unknown direction function; realizes the design of the feedback controller u i , so that the system output y i (t) can track the given target signal within a small error range #imgabs0#

Description

Technical Field

[0001] The invention relates to the technical field of MPCVD reactor process control, in particular to an improved adaptive backstepping control method for an MPCVD reactor. Background Art

[0002] Diamond is the hardest and most thermally conductive bulk material on earth, but its cost and size are huge obstacles to its widespread application. Microwave Plasma Chemical Vapor Deposition is the mainstream method for artificially synthesizing large-sized diamonds. The MPCVD reactor system includes three different types of control systems, namely, temperature control system, pressure control system, and gas flow control system. Temperature, pressure, and gas flow have an important influence on the chemical vapor phase reaction in the reactor. Therefore, it is very important to achieve good control performance of the three different control systems in the MPCVD reactor. At present, the most commonly used control method in the MPCVD reactor system is still PID control. Although PID control can solve the control problem of the MPCVD reactor system through parameter tuning. It requires too much experience to handle the parameter tuning of the controller. Compared with traditional PID control, the model-based control scheme can obtain better control performance under theoretical guidance. However, there is a non-parametric uncertainty problem in the control modeling of the MPCVD synthetic diamond process, which leads to the inability of the system output to track the given target signal within a small error range. Summary of the invention

[0003] The purpose of the present invention is to propose an improved adaptive backstepping control method for an MPCVD reactor in view of the non-parametric uncertainty problem in the control modeling of the MPCVD synthetic diamond process in the prior art, which leads to the problem that the system output cannot track a given target signal within a small error range.

[0004] The technical solution adopted by the present invention to solve the above technical problems is:

[0005] An improved adaptive backstepping control method for an MPCVD reactor comprises the following steps:

[0006] Step 1: Establish a one-dimensional state space model of a non-parametric uncertain strict feedback system with unknown control direction for process control of an MPCVD reactor; the one-dimensional state space model is expressed as:

[0007]

[0008]

[0009]

[0010] Where T represents the temperature of the MPCVD reaction substrate, represents the derivative of the MPCVD reaction substrate temperature with respect to time, P represents the reaction chamber pressure of the MPCVD reaction substrate, It represents the derivative of the reaction chamber pressure of the MPCVD reaction substrate with respect to time, Q = [Q1, Q2] T , Q1 and Q2 represent the CH4 gas flow rate and H2 gas flow rate of the MPCVD reaction substrate, respectively. and K, m, C, T0, k represent the derivative of the CH4 gas flow rate of the MPCVD reaction substrate with respect to time and the derivative of the H2 gas flow rate with respect to time, respectively. w and R t denote the temperature attenuation coefficient, the mass of the heater resistor, the specific heat capacity of the reaction substrate, the initial temperature of the reaction substrate, the cooling coefficient and the heater resistor, respectively; k1, C1, ρ1 and ΔT1 denote the heat exchange coefficient, specific heat, density and temperature difference of CH4; k2, C2, ρ2 and ΔT2 denote the heat exchange coefficient, specific heat, density and temperature difference of H2; k o , C o , o , ΔT o Represents the heat exchange coefficient, specific heat, density and temperature difference of air, R, V, k p , T r , k d They represent the gas constant, the volume of the reactor, the voltage coefficient of the vacuum pump, the reaction temperature and the temperature coefficient, respectively. v , C v , k v , k f Respectively represent the equivalent resistance, equivalent capacitance, amplification factor and proportionality factor of the valve drive circuit, and the unknown equation is the unknown nonlinearity of the system, u t 、u w 、u p , Respectively represent the heater voltage, water pump voltage, vacuum pump voltage and electronic valve voltage, and Indicates CH4 electronic valve voltage and H2 electronic valve voltage;

[0011] Step 2: Based on the one-dimensional state space model, define the extended state variable s i =u i , a state space model of a two-dimensional nonlinear system for process control of an MPCVD reactor with extended state variables is established, and then the error variable z is defined based on the state space model of the two-dimensional nonlinear system. 1,i 、z 2,i, i=1,2,3,4;

[0012] Step 3: Use the error variable z in step 2 1,i 、z 2,i Design the Lyapunov function V;

[0013] Step 4: Using the Lyapunov function V in step 3, take the first-order derivative with respect to time and obtain

[0014] Step 5: Introduce the command filter, and then according to the first-order derivative of the Lyapunov function in step 4 And use the backstepping method to get the controller input u i .

[0015] Furthermore, the state space model of the two-dimensional nonlinear system in step 2 is expressed as:

[0016]

[0017]

[0018] ψ1=-K(T-T0) / mC+k1C1ρ1ΔT1Q1+k2C2ρ2ΔT2Q2-k o C o ρ o ΔT o

[0019] ψ2=R(T r -k d T)(Q1+Q2) / V

[0020] ψ3=-Q1 / (R v C v )

[0021] ψ4=-Q2 / (R v C v )

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] u2=u p

[0028]

[0029]

[0030] in, Indicates i The first derivative of The state variable x represents the process control of the MPCVD reactor i The first derivative of , s i Indicates extended state variable, b1 = 1, b2 = -R(T r -k d T)k p / V,b3=b4=k v k f / (R v C v ), ψ i Indicates the substitution symbol, represents the unknown nonlinear function of the system, represents the first-order derivative of the controller.

[0031] Furthermore, the error variable z 1,i 、z 2,i It is expressed as:

[0032]

[0033] z 2,i =s i -α i

[0034] Among them, α i Represents a virtual control function, Indicates the target signal.

[0035] Furthermore, the Lyapunov function V is expressed as:

[0036]

[0037] Furthermore, the It is expressed as:

[0038]

[0039] in The target signal The first derivative of Represents the first-order derivative of the virtual control function α1.

[0040] Furthermore, the controller inputs u i It is expressed as:

[0041]

[0042] Among them, dτ represents the integral variable, k 2,i >0 indicates design parameters, represents the output of the command filter, g i represents the equivalent control direction function, and t is the time.

[0043] Furthermore, the output of the command filter It is expressed as:

[0044]

[0045] Among them, η 2,i >0 indicates filter parameters, w 2,i Indicates the filter status.

[0046] Furthermore, the specific steps of step five are:

[0047] Step 51: Rewrite the first-order derivative of the Lyapunov function in step 4 using the equivalent control direction function

[0048]

[0049] in, Represents α i The first derivative of ;

[0050] Step 52: Define the unknown terms that need to be approximated by the adaptive law Right now:

[0051]

[0052] Among them, φ i Unknown to the system

[0053] Step 53: Based on the first-order derivative of the Lyapunov function Using backstepping and adaptive law, design virtual control function

[0054] Among them, k 1,i >0 indicates design parameters, Represents φ i estimates;

[0055] Step 54: Use the adaptive law to approximate the unknown term φ i , Design Update Law for:

[0056]

[0057] Among them, γ i is a normal number, Represents the output of the command filter:

[0058]

[0059] Among them, η 1,i >0 indicates filter parameters, w 1,i represents the filter estimate, i.e. the first-order derivative of the Lyapunov function

[0060]

[0061] Step 5: Design control signal u i :

[0062]

[0063] The beneficial effects of the present invention are:

[0064] This application aims to process the non-parametric uncertainty of the system. Firstly, a direct adaptive law is proposed to estimate this uncertainty. The problem caused by the unknown direction function is solved by using the equivalent transformation of the system. The feedback controller u is designed. i , so that the system outputs y i (t) Ability to track a given target signal within a small error range BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is the temperature response curve of the system;

[0066] Figure 2 It is the pressure response curve of the system;

[0067] Figure 3 It is the CH4 gas flow response curve;

[0068] Figure 4 It is the H2 gas flow response curve;

[0069] Figure 5 This is the voltage input curve diagram for the control system. DETAILED DESCRIPTION

[0070] It should be particularly noted that, in the absence of conflict, the various embodiments disclosed in this application can be combined with each other.

[0071] Specific implementation method 1: refer to Figure 1 Specifically describing this embodiment, an improved adaptive backstepping control method for an MPCVD reactor described in this embodiment comprises the following steps:

[0072] Step 1: Establish a one-dimensional state space model of a non-parametric uncertain strict feedback system with unknown control direction for process control of an MPCVD reactor; the one-dimensional state space model is expressed as:

[0073]

[0074]

[0075]

[0076] Where T represents the temperature of the MPCVD reaction substrate, represents the derivative of the MPCVD reaction substrate temperature with respect to time, P represents the reaction chamber pressure of the MPCVD reaction substrate, It represents the derivative of the reaction chamber pressure of the MPCVD reaction substrate with respect to time, Q = [Q1, Q2] T , Q1 and Q2 represent the CH4 gas flow rate and H2 gas flow rate of the MPCVD reaction substrate, respectively. and K, m, C, T0, k represent the derivative of the CH4 gas flow rate of the MPCVD reaction substrate with respect to time and the derivative of the H2 gas flow rate with respect to time, respectively. w and R t denote the temperature attenuation coefficient, the mass of the heater resistor, the specific heat capacity of the reaction substrate, the initial temperature of the reaction substrate, the cooling coefficient and the heater resistor, respectively; k1, C1, ρ1 and ΔT1 denote the heat exchange coefficient, specific heat, density and temperature difference of CH4; k2, C2, ρ2 and ΔT2 denote the heat exchange coefficient, specific heat, density and temperature difference of H2; k o , C o , o , ΔT o Represents the heat exchange coefficient, specific heat, density and temperature difference of air, R, V, k p 、T r , k d They represent the gas constant, the volume of the reactor, the voltage coefficient of the vacuum pump, the reaction temperature and the temperature coefficient, respectively. v , C v , k v , k f Respectively represent the equivalent resistance, equivalent capacitance, amplification factor and proportionality factor of the valve drive circuit, and the unknown equation is the unknown nonlinearity of the system, u t 、u w 、u p , Respectively represent the heater voltage, water pump voltage, vacuum pump voltage and electronic valve voltage, and Indicates CH4 electronic valve voltage and H2 electronic valve voltage;

[0077] Step 2: Based on the one-dimensional state space model, define the extended state variable s i =u i , a state space model of a two-dimensional nonlinear system for process control of an MPCVD reactor with extended state variables is established, and then the error variable z is defined based on the state space model of the two-dimensional nonlinear system. 1,i 、z 2,i , i=1,2,3,4;

[0078] Step 3: Use the error variable z in step 2 1,i 、z 2,i Design the Lyapunov function V;

[0079] Step 4: Using the Lyapunov function V in step 3, take the first-order derivative with respect to time and obtain

[0080] Step 5: Introduce the command filter, and then according to the first-order derivative of the Lyapunov function in step 4 And use the backstepping method to get the controller input u i .

[0081] In step 1, the state variable x of the MPCVD reactor process control is i , output signal y i and control signal u i , a one-dimensional state space model of a nonparametric uncertain strict feedback system with unknown control direction for MPCVD reactor process control is established, so that the output of the system tracks the target signal and the system output y i (t) Ability to track a given system target signal within a small error range The specific process is:

[0082] The one-dimensional state space model of a nonparametric uncertain strict feedback system with unknown control direction for MPCVD reactor process control is established as:

[0083]

[0084] Where T[℃], P[Pa] and Q=[Q1,Q2] T [m 3 / s] are the temperature of the MPCVD reaction substrate, the reaction chamber pressure, the CH4 gas flow rate and the H2 gas flow rate, respectively.

[0085] Coefficient K, m [kg], C [J / (kg·℃)], T0 [℃], k w and R t[Ω] represents the temperature attenuation coefficient, the mass of the heater resistor, the specific heat capacity of the reaction substrate, the initial temperature of the reaction substrate, the cooling coefficient, and the heater resistor, respectively.

[0086] k1,C1,ρ1,ΔT1,k2,C2,ρ2,ΔT2 and k o ,C o ,ρ o ,ΔT o They represent the heat exchange coefficient, specific heat, density and temperature difference of CH4, H2 and air respectively.

[0087] Coefficient R,V,k p , T r [℃],k d They represent the gas constant, the volume of the reactor, the voltage coefficient of the vacuum pump, the reaction temperature and the temperature coefficient respectively.

[0088] Coefficient R v , C v , k v , k f They represent the equivalent resistance, equivalent capacitance, amplification factor and proportionality factor of the valve drive circuit respectively.

[0089] Unknown equation is the unknown nonlinearity of the system, u t ,u w ,u p , They represent heater voltage, water pump voltage, vacuum pump voltage and electronic valve voltage respectively.

[0090] Taking x1 = T, x2 = P, x3 = Q1, x4 = Q2, the one-dimensional state space model of the non-parametric uncertain strict feedback system with unknown control direction for the MPCVD reactor process control is established as follows:

[0091]

[0092] Where b1 = 1, b2 = -R(T r -k d T)k p / V,b3=b4=k v k f / (R v C v ),

[0093] ψ1=-K(T-T0) / mC+k1C1ρ1ΔT1Q1+k2C2ρ2ΔT2Q2-k o C o ρ o ΔT o ,

[0094] ψ2=R(T r -k d T)(Q1+Q2) / V,

[0095] ψ3=-Q1 / (R v C v ), ψ4=-Q2 / (R v C v );

[0096]

[0097] in The controller design goal is to minimize the error of the system output tracking the target temperature, pressure, and gas flow.

[0098] where x i represents the state variables of system (1), is the unknown nonlinear function of the system, b2,...,b4 are the unknown control direction functions of the system, For x i The first derivative of (t), t is time, u i (t) is the controller, y i Output for the system.

[0099] Uncertainty Uncertainty; nonlinearity is nonlinear; strict feedback is Only and x i About not involving u i (t).

[0100] "Having unknown control direction function" means that b2, ..., b4 are unknown, and such a system is more difficult to design.

[0101] The control objective is to design a feedback controller u i (t), so that the system outputs y i Capable of tracking a given system target signal within a small error range

[0102] When the state variables x1,…x4 are bounded, is bounded, The first-order derivative of each with respect to time is bounded;

[0103] Said Respectively represent

[0104] The target signal is continuous and bounded, the target signal The first-order derivative with respect to time is continuous and bounded, and the target signal The second-order derivative with respect to time is continuous and bounded.

[0105] In step 2, the extended state variable s is defined i =u i , a two-dimensional nonlinear system state space model for MPCVD reactor process control with extended state variables, defining the error variable z 1,i , z 2,i ; The specific process is:

[0106] 1) Define the extended state variable s i =u i ,

[0107] 2) Establish a two-dimensional nonlinear system state space model with extended state variables:

[0108]

[0109] in For i The first derivative of ;

[0110] 3) Define the error variable z 2,i =s i -α i

[0111] where α i Represents a virtual control function.

[0112] In step 3, the error variables z1 and z2 in step 2 are used to design the Lyapunov function V; the specific process is:

[0113] Use the error variables z1 and z2 in step 2 to design the Lyapunov function V

[0114]

[0115] In step 4, the first-order derivative of the Lyapunov function V in step 3 is calculated with respect to time.

[0116]

[0117] Use the Lyapunov function V in step 3 to find the first-order derivative with respect to time

[0118] in is the target signal y d The first derivative of Represents the first-order derivative of the virtual control function α1.

[0119] The adaptive law based on the command filter is introduced in step 5, according to the first-order derivative of the Lyapunov function in step 4 Using the backstepping method, the virtual control function α is designed i , adaptive update law and controller input u i ; The specific process is:

[0120] 1) Rewrite the first-order derivative of the Lyapunov function in step 4 using the equivalent control direction function

[0121]

[0122] Among them, g i is the equivalent control direction function;

[0123] 2) Define the unknown terms that need to be approximated by the adaptive law Right now:

[0124]

[0125] 3) According to the first-order derivative of the Lyapunov function in step 5 Using backstepping and adaptive law, design virtual control function

[0126] where k 1,i >0 is the design parameter, Represents φ i Estimates.

[0127] 4) Use the adaptive law to approximate the unknown term φ i , Design Update Law for:

[0128]

[0129] where γ i is a normal number, Represents the output of the following command filter:

[0130]

[0131] Among them, η 1,i >0 is the filter parameter, i.e. the first-order derivative of the Lyapunov function

[0132]

[0133] 5) Design control signal u:

[0134]

[0135] Among them, τ is the integration variable, k 2,i >0 is the design parameter, is the output of the following command filter:

[0136]

[0137] Formula (11) is a tracking controller based on improved adaptive backstepping control.

[0138] The desired virtual control function

[0139] It will be demonstrated below that the process control method tracking controller (11) based on the improved adaptive backstepping control of the MPCVD reactor can make the system tracking error converge to a smaller neighborhood near the origin. The proof process is as follows:

[0140] For i=1,2,3,4, we can get

[0141]

[0142] When x∈Ω x It is not difficult to conclude is bounded, so we have:

[0143]

[0144] where ξ 1,i represents the estimation error, Yes 1,i Substituting (14) into (8) yields

[0145]

[0146] Select the Lyapunov function Available

[0147]

[0148] in express The upper bound of

[0149]

[0150] The parameter γ i Designed so that

[0151] Virtual control function α i The derivative of

[0152]

[0153] From the above, we know that α i and is also bounded, and there exists a constant Make We take Available

[0154]

[0155] in Available

[0156]

[0157] where η 2,i Designed so that Substituting (17) and (20) into (10), we can obtain

[0158]

[0159] in

[0160] The following can be obtained

[0161]

[0162] where k 1,i , k 2,i It is designed so that (b3 / a3)≤V2(0)≤ρ, so

[0163]

[0164] Among them, (b3 / a3)≤τ≤ρ, in addition, the following set can be obtained

[0165]

[0166] So far, equation (23) shows that the system tracking error converges to a smaller neighborhood near the origin, and the proof is complete.

[0167] The following examples are used to verify the beneficial effects of the present invention:

[0168] Embodiment 1:

[0169] For the system (Formula 2), the nonparametric uncertainty equations of the system are

[0170] Take the initial value x(0) = [25,1200,0,0] T

[0171] The MPCVD reaction system parameters are: K = 0.5, C = 1, m = 1, T0 = 25, C1 = 2.2, C2 = 14, C o =8, ρ1=0.716, ρ2=0.089, ρ o =0.5, R t =10, k w =20,k1=0.01,k2=0.01,k o =0.01, ΔT1 = ΔT2 = 1500, ΔT o =1200, R=8.314, V=1, k p =0.001, T r =1500, k d =0.01, R v =50, C v =20, k v =0.05, k f =0.1.

[0172] The parameters of the improved adaptive backstepping controller are: g1 = 1, k 1,1 =4, k 2,1 =2,η 1,1 =η 2,1 =50, γ1=50, g2=-10, k 1,2 =2, k 2,2 =22,η 1,2 =η 2,2 =50,γ2=50,g3=10 -6 , k 1,3 =4, k 2,3 =2,η 1,3 =η 2,3 =20,γ3=50,g4=10 -6 , k 1,4 =4, k 2,4 =2,η 1,4 =η 2,4 =20, γ4=50, initial value is: x 2,1 (0) = x 2,2 (0) = x 2,3 (0) = x 2,4 (0)=0, u1(0)=u2(0)=u3(0)=u4(0)=0, w 1,1 (0) = -1075, w 1,2 (0) = 200, w 1,3 (0) = 0, w 1,4 (0) = 0, w 2,1 (0) = 4300, w 2,2 (0) = 40, w 2,3 (0) = 6.7, w2,4 (0)=1.3, φ1(0)=φ2(0)=φ3(0)=φ4(0)=0.

[0173] Figure 1 is a temperature response curve diagram of the system of the present invention; Figure 2 is a pressure response curve diagram of the system of the present invention; Figure 3 It is a CH4 gas flow response curve diagram of the present invention; Figure 4 It is the H2 gas flow response curve diagram of the present invention; Figure 5 This is a curve diagram of voltage input of the control system under the present invention.

[0174] Conclusion: Figure 1 It can be seen that the control signal u designed based on the improved adaptive backstepping control method for MPCVD reactor process control can make the system tracking error converge to a small area near the origin.

[0175] It should be noted that the specific implementation is only an explanation and description of the technical solution of the present invention, and cannot be used to limit the scope of protection of the rights. Any partial changes made according to the claims and description of the present invention should still fall within the scope of protection of the present invention.

Claims

1. An improved adaptive backstepping control method for an MPCVD reactor, characterized in that The following steps are involved: Step 1: Establish a one-dimensional state space model of a non-parametric uncertain strict feedback system with unknown control direction for process control of an MPCVD reactor; the one-dimensional state space model is expressed as: Where T represents the temperature of the MPCVD reaction substrate, represents the derivative of the MPCVD reaction substrate temperature with respect to time, P represents the reaction chamber pressure of the MPCVD reaction substrate, It represents the derivative of the reaction chamber pressure of the MPCVD reaction substrate with respect to time, Q = [Q1, Q2] T , Q1 and Q2 represent the CH4 gas flow rate and H2 gas flow rate of the MPCVD reaction substrate, respectively. and K, m, C, T0, k represent the derivative of the CH4 gas flow rate of the MPCVD reaction substrate with respect to time and the derivative of the H2 gas flow rate with respect to time, respectively. w and R t denote the temperature attenuation coefficient, the mass of the heater resistor, the specific heat capacity of the reaction substrate, the initial temperature of the reaction substrate, the cooling coefficient and the heater resistor, respectively; k1, C1, ρ1 and ΔT1 denote the heat exchange coefficient, specific heat, density and temperature difference of CH4; k2, C2, ρ2 and ΔT2 denote the heat exchange coefficient, specific heat, density and temperature difference of H2; k o , C o , o , ΔT o Represents the heat exchange coefficient, specific heat, density and temperature difference of air, R, V, k p , T r , k d They represent the gas constant, the volume of the reactor, the voltage coefficient of the vacuum pump, the reaction temperature and the temperature coefficient, respectively. v , C v , k v , k f Respectively represent the equivalent resistance, equivalent capacitance, amplification factor and proportionality factor of the valve drive circuit, and the unknown equation is the unknown nonlinearity of the system, u t 、u w 、u p , They represent the heater voltage, water pump voltage, vacuum pump voltage and electronic valve voltage respectively. and Indicates CH4 electronic valve voltage and H2 electronic valve voltage; Step 2: Based on the one-dimensional state space model, define the extended state variable s i =u i , a state space model of a two-dimensional nonlinear system for process control of an MPCVD reactor with extended state variables is established, and then the error variable z is defined based on the state space model of the two-dimensional nonlinear system. 1,i 、z 2,i , i=1,2,3,4; Step 3: Use the error variable z in step 2 1,i 、z 2,i Design the Lyapunov function V; Step 4: Using the Lyapunov function V in step 3, take the first-order derivative with respect to time and obtain Step 5: Introduce the command filter, and then according to the first-order derivative of the Lyapunov function in step 4 And use the backstepping method to get the controller input u i ; The specific steps of step five are: Step 51: Rewrite the first-order derivative of the Lyapunov function in step 4 using the equivalent control direction function in, Represents α i The first derivative of ; Step 52: Define the unknown terms that need to be approximated by the adaptive law Right now: Among them, φ i Unknown to the system Step 53: Based on the first-order derivative of the Lyapunov function Using backstepping and adaptive law, design virtual control function Among them, k 1,i >0 indicates design parameters, Represents φ i estimates; Step 54: Use the adaptive law to approximate the unknown term φ i , Design Update Law for: Among them, γ i is a normal number, Represents the output of the command filter: Among them, η 1,i >0 indicates filter parameters, w 1,i represents the filter estimate, i.e. the first-order derivative of the Lyapunov function Step 55: Design control signal u i : Among them, s i Indicates the extended state variable, g i represents the equivalent control direction function, b1 = 1, b2 = -R(T r -k d T)k p / V, b3=b4=k v k f / (R v C v ), α i Represents a virtual control function, represents the first-order derivative of the virtual control function α1, ψ i Indicates the substitution symbol, represents the unknown nonlinear function of the system, represents the first-order derivative of the controller, The target signal The first derivative of represents the target signal, dτ represents the integral variable, k 2,i >0 indicates design parameters, represents the output of the command filter, represents the first-order derivative of the controller, t is the time; The output of the command filter It is expressed as: Among them, η 2,i >0 indicates filter parameters, w 2,i Indicates the filter status.

2. The improved adaptive backstepping control method for an MPCVD reactor according to claim 1, characterized in that The state space model of the two-dimensional nonlinear system in step 2 is expressed as: ψ1=-K(T-T0) / mC+k1C1ρ1ΔT1Q1+k2C2ρ2ΔT2Q2-k o C o r o ΔT o ψ2=R(T r -k d T)(Q1+Q2) / V ψ3=-Q1 / (R v C v ) ψ4−Q2 / (R v C v ) u2=u p u3=u q1 u4=u q2 in, Indicates i The first derivative of The state variable x represents the process control of the MPCVD reactor i The first derivative of , s i Indicates extended state variable, b1 = 1, b2 = -R(T r -k d T)k p / V,b3=b4=k v k f / (R v C v ), ψ i Indicates the substitution symbol, represents the unknown nonlinear function of the system, represents the first-order derivative of the controller.

3. The improved adaptive backstepping control method for an MPCVD reactor according to claim 2, characterized in that The error variable z 1,i 、z 2,i It is expressed as: z 1,i =x i -y di z 2,i =s i -α i Among them, α i Represents the virtual control function, y di Indicates the target signal.

4. The improved adaptive backstepping control method for an MPCVD reactor according to claim 3, characterized in that The Lyapunov function V is expressed as:

5. The improved adaptive backstepping control method for an MPCVD reactor according to claim 4, characterized in that Said It is expressed as: in The target signal The first derivative of Represents the first-order derivative of the virtual control function α1.

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