Parallel control method and system for actuator of pure feedback system

Abstract

This invention proposes a parallel control method and system for actuators in pure feedback systems, relating to the technical field of parallel control. The method divides the pure feedback system containing the actuator into multiple subsystems, designs auxiliary functions, designs virtual controllers for each subsystem based on the designed auxiliary functions, and designs parallel controllers for the pure feedback system based on the virtual controllers of each subsystem. The parallel controllers are then used to perform parallel control of the actuator, which is applicable to pure feedback systems and improves the stability of pure feedback systems.

Description

Technical Field

[0001] This invention relates to the technical field of parallel control, and more specifically, to a parallel control method and system for actuators in a pure feedback system. Background Technology

[0002] An actuator is a drive device that provides linear or rotary motion. It uses some kind of driving energy and works under the action of some control signal. The actuator uses liquid, gas, electricity or other energy and converts it into driving action through motors, cylinders or other devices.

[0003] Currently, more and more factories are adopting automated control, and manual operation is being replaced by mechanical or automated equipment. People are demanding that actuators act as the interface between the control system and the mechanical movement of valves, and that actuators enhance their work safety and environmental protection performance. In some dangerous situations, automated actuator devices can reduce personnel injuries.

[0004] Modern control theory is a control theory based on the state-space method. In modern control theory, the analysis and design of control systems are mainly carried out by describing the state variables of the system, and the basic method is the time-domain method.

[0005] Modern control theory primarily addresses system problems expressed using differential or difference equations. With further development, intelligent control theory has been proposed for factory automation control. For feedback systems in automation control, intelligent control theory employs state feedback control, determining the control quantity based on the state in real-time. However, this is prone to drastic changes in the control signal, leading to poor controller stability and severely impacting the actuator's performance. To address the problems of traditional state feedback, existing technologies propose a parallel control method that determines the control quantity based on state changes. However, feedback systems include strict feedback and pure feedback systems. Existing parallel control methods are only applicable to strict feedback systems; their application to pure feedback systems cannot guarantee stability. Summary of the Invention

[0006] To address the poor control performance of existing parallel control methods when performing parallel control of actuators in pure feedback systems, this invention proposes a parallel control method and system for actuators in pure feedback systems, which is applicable to pure feedback systems and improves their stability.

[0007] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows:

[0008] A parallel control method for actuators in a pure feedback system includes:

[0009] S1. Divide the pure feedback system containing the actuator into multiple subsystems;

[0010] S2. Design auxiliary functions;

[0011] S3. Based on the designed auxiliary functions, design virtual controllers for each subsystem;

[0012] S4. Based on the virtual controllers of each subsystem, design a parallel controller for the pure feedback system and use the parallel controller to perform parallel control of the actuators.

[0013] Preferably, in step S1, the pure feedback system containing the actuator is represented as follows:

[0014]

[0015] Where x1∈R n and x2, ..., x k ∈R, x1, x2, ..., x k f1 represents the state of a pure feedback system, u∈R is the system input, and f1:R n ×R→R n and f i :R n ×R i →R, where i = 2, ..., k are nonlinear functions, and the origin of the pure feedback system is the equilibrium point. Any partial derivative in any open set D containing the origin satisfies d(t) is a bounded unknown disturbance in a pure feedback system, |d(t)|≤D, D>0, where D is a constant, and D is represented by compact set ψ. j = (x1, ..., x j );

[0016] Dividing a pure feedback system into k-1 subsystems, denoted as:

[0017]

[0018] Where ∑ i , i = 1, 2, ..., k-1 are subsystems of a pure feedback system.

[0019] Preferably, in step S2, the auxiliary function expression is designed as follows:

[0020] p(λ): =f(x1, (1-λ)γ1(x1)+λx2) (3)

[0021] Where p(λ) is the first auxiliary function used for formula derivation, λ is the intermediate variable used to assist in formula derivation, λ∈R, and γ1(x1) is the virtual controller;

[0022] Derivation and mathematical transformation based on the first auxiliary function:

[0023]

[0024] Based on formula (4):

[0025] f(x1,x2)-f(x1,γ(x1))=P(x1,x2-γ(x1))(x2-γ(x1)) (5)

[0026] in,

[0027] Based on the above derivation process, the relationships between the subsystems are determined as follows:

[0028] f i (ψ i x i+1 )=f i (ψ i γ i+1 )+P i ·(x i+1 -γ i (7)

[0029]

[0030] Among them, P i γ is the second auxiliary function used for formula derivation. i It is a virtual controller.

[0031] Preferably, in step S3, based on the auxiliary function and the relationship between the subsystems, Lyapunov functions and virtual control quantities are designed for each of the k-1 subsystems, and iterative calculations are performed based on the Lyapunov functions and virtual control quantities.

[0032] To control the subsystem ∑1, when the condition x3-γ2(ψ3)=0, design a virtual controller γ2(ψ3) for the subsystem ∑1:

[0033]

[0034] Where the constant G1 > 0, V(x1) is the strict Lyapunov function of f1(x1, γ1(x1)), γ1(x1) is a known function, and the derivative of the strict Lyapunov function of the subsystem ∑1 is:

[0035]

[0036]

[0037] When the condition x4-γ3(ψ4)=0, the virtual controller γ3(ψ4) is designed based on the derivative of the strict Lyapunov function of subsystem ∑1 with respect to subsystem ∑2:

[0038]

[0039] Where the constant G2 > 0, the derivative of the strict Lyapunov function of the subsystem ∑2 is:

[0040]

[0041] The above steps are used to iteratively calculate up to the (k-2)th subsystem ∑ k-2 , when the condition u-γ k (ψ k When u) = 0, according to the subsystem ∑ k-2 The derivative of the strict Lyapunov function for the subsystem ∑ k-1 Design a virtual controller γ k (ψ k ,u):

[0042]

[0043]

[0044] Wherein, constant G k-1 >0, subsystem ∑ k-1 The derivative of the strict Lyapunov function is:

[0045]

[0046] Through the above iterative calculations, the virtual controllers corresponding to the k-1 subsystems are obtained.

[0047] Preferably, in step S4, based on the virtual controllers corresponding to the k-1 subsystems, the parallel controller for the pure feedback system is designed as follows:

[0048]

[0049]

[0050]

[0051]

[0052] Wherein, constant G k >0.

[0053] This invention also proposes a parallel control system for actuators in a pure feedback system, comprising:

[0054] A partitioning unit is used to divide a pure feedback system into multiple subsystems.

[0055] The first design unit is used to design auxiliary functions;

[0056] The second design unit is used to design virtual controllers for each subsystem based on the designed auxiliary functions;

[0057] The third design unit is used to design parallel controllers for the pure feedback system based on the virtual controllers of each subsystem.

[0058] Preferably, the pure feedback system containing the actuator is represented as follows:

[0059]

[0060] Where x1∈R n and x2, ..., x k ∈R, x1, x2, ..., x k f1 represents the state of a pure feedback system, u∈R is the system input, and f1:R n ×R→R n and f i :R n ×R i →R, where i = 2, ..., k are nonlinear functions, and the origin of the pure feedback system is the equilibrium point. Any partial derivative in any open set D containing the origin satisfies d(t) is a bounded unknown disturbance in a pure feedback system, |d(t)|≤D, D>0, where D is a constant, and D is represented by compact set ψ. j = (x1, ..., x j ).

[0061] The partitioning unit is specifically used to divide the pure feedback system into k-1 subsystems, denoted as follows:

[0062]

[0063] Where ∑ i , i = 1, 2, ..., k-1 are subsystems of a pure feedback system.

[0064] Preferably, the auxiliary function expression designed by the first design unit is as follows:

[0065] p(λ): =f(x1, (1-λ)γ1(x1)+λx2) (3)

[0066] Where p(λ) is the first auxiliary function used for formula derivation, λ is the intermediate variable used to assist in formula derivation, λ∈R, and γ1(x1) is the virtual controller;

[0067] Derivation and mathematical transformation based on the first auxiliary function:

[0068]

[0069] Based on formula (4):

[0070] f(x1,x2)-f(x1,γ(x1))=P(x1,x2-γ(x1))(x2-γ(x1)) (5)

[0071] in,

[0072] Based on the above derivation process, the relationships between the subsystems are determined as follows:

[0073] f i (ψ i x i+1 )=f i (ψ i γ i+1 )+P i ·(x i+1 -γ i (7)

[0074]

[0075] Among them, P i γ is the second auxiliary function used for formula derivation. i It is a virtual controller.

[0076] Preferably, the second design unit is specifically used to design Lyapunov functions and virtual control quantities for k-1 subsystems respectively, based on the auxiliary function and the relationship between the subsystems, and to perform iterative calculations based on the Lyapunov functions and virtual control quantities.

[0077] To control the subsystem ∑1, when the condition x3-γ2(ψ3)=0, design a virtual controller γ2(ψ3) for the subsystem ∑1:

[0078]

[0079] Where the constant G1 > 0, V(x1) is the strict Lyapunov function of f1(x1, γ1(x1)), γ1(x1) is a known function, and the derivative of the strict Lyapunov function of the subsystem ∑1 is:

[0080]

[0081]

[0082] When the condition x4-γ3(ψ4)=0, the virtual controller γ3(ψ4) is designed based on the derivative of the strict Lyapunov function of subsystem ∑1 with respect to subsystem ∑2:

[0083]

[0084] Where the constant G2 > 0, the derivative of the strict Lyapunov function of the subsystem ∑2 is:

[0085]

[0086] The above steps are used to iteratively calculate up to the (k-2)th subsystem ∑ k-2 , when the condition u-γ k (ψ k When u) = 0, according to the subsystem ∑ k-2 The derivative of the strict Lyapunov function for the subsystem ∑ k-1 Design a virtual controller γ k (ψ k ,u):

[0087]

[0088]

[0089] Wherein, constant G k-1 >0, subsystem ∑ k-1 The derivative of the strict Lyapunov function is:

[0090]

[0091] Through the above iterative calculations, the virtual controllers corresponding to the k-1 subsystems are obtained.

[0092] Preferably, the second design unit is specifically used to design a parallel controller for the pure feedback system based on the virtual controllers corresponding to k-1 subsystems, as follows:

[0093]

[0094]

[0095]

[0096]

[0097] Wherein, constant G k >0.

[0098] The parallel control system for actuators in a pure feedback system proposed in this invention is used to execute the parallel control method for actuators in a pure feedback system proposed in this invention.

[0099] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0100] This invention proposes a parallel control method and system for actuators in pure feedback systems. A parallel controller is designed for the actuators of the pure feedback system, and the parallel controller is used to perform parallel control of the actuators in the pure feedback system, thereby improving the stability of the pure feedback system. Attached Figure Description

[0101] Figure 1 A flowchart illustrating the parallel control method for actuators in a pure feedback system proposed in this invention;

[0102] Figure 2 This diagram illustrates the structure of the parallel controller proposed in this invention.

[0103] Figure 3 A schematic diagram illustrating an example of the parallel control process for a helicopter hovering system proposed in this invention;

[0104] Figure 4 This diagram illustrates the parallel control system for actuators in a pure feedback system proposed in this invention. Detailed Implementation

[0105] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0106] To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions;

[0107] It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0108] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0109] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0110] Example 1

[0111] Considering the poor control performance of existing parallel control methods when performing parallel control of actuators in pure feedback systems, this embodiment proposes a parallel control method and system for actuators in pure feedback systems. This method is applicable to pure feedback systems and improves their stability. A flowchart of the method is shown below. Figure 1 As shown, it includes the following steps:

[0112] S1. Divide the pure feedback system containing the actuator into multiple subsystems;

[0113] In this step, the pure feedback system containing the actuator is represented as follows:

[0114]

[0115] Where x1∈R n and x2, ..., x k ∈R, x1, x2, ..., x k f1 represents the state of a pure feedback system, u∈R is the system input, and f1:R n ×R→R n and f i :R n ×R i →R, where i = 2, ..., k are nonlinear functions, and the origin of the pure feedback system is the equilibrium point. Any partial derivative in any open set D containing the origin satisfies d(t) is a bounded unknown disturbance in a pure feedback system, |d(t)|≤D, D>0, where D is a constant, and D is represented by compact set ψ. j = (x1, ..., x j );

[0116] Dividing a pure feedback system into k-1 subsystems, denoted as:

[0117]

[0118] Where ∑ i , i = 1, 2, ..., k-1 are subsystems of a pure feedback system.

[0119] S2. Design auxiliary functions;

[0120] In step S2, the auxiliary function expression is as follows:

[0121] p(λ): =f(x1, (1-λ)γ1(x1)+λx2) (3)

[0122] Where p(λ) is the first auxiliary function used for formula derivation, λ is the intermediate variable used to assist in formula derivation, λ∈R, and γ1(x1) is the virtual controller;

[0123] Derivation and mathematical transformation based on the first auxiliary function:

[0124]

[0125] Based on formula (4):

[0126] f(x1,x2)-f(x1,γ(x1))=P(x1,x2-γ(x1))(x2-γ(x1)) (5)

[0127] in,

[0128] Based on the above derivation process, the relationships between the subsystems are determined as follows:

[0129] f i (ψ i x i+1 )=f i (ψ i γ i+1 )+P i ·(x i+1 -γ i (7)

[0130]

[0131] Among them, P i γ is the second auxiliary function used for formula derivation. i It is a virtual controller.

[0132] S3. Based on the designed auxiliary functions, design virtual controllers for each subsystem;

[0133] In step S3, based on the auxiliary function and the relationship between the subsystems, Lyapunov functions and virtual control quantities are designed for each of the k-1 subsystems, and iterative calculations are performed based on the Lyapunov functions and virtual control quantities.

[0134] To control the subsystem ∑1, when the condition x3-γ2(ψ3)=0, design a virtual controller γ2(ψ3) for the subsystem ∑1:

[0135]

[0136] Where the constant G1 > 0, V(x1) is the strict Lyapunov function of f1(x1, γ1(x1)), γ1(x1) is a known function, and the derivative of the strict Lyapunov function of the subsystem ∑1 is:

[0137]

[0138]

[0139] When the condition x4-γ3(ψ4)=0, the virtual controller γ3(ψ4) is designed based on the derivative of the strict Lyapunov function of subsystem ∑1 with respect to subsystem ∑2:

[0140]

[0141] Where the constant G2 > 0, the derivative of the strict Lyapunov function of the subsystem ∑2 is:

[0142]

[0143] The above steps are used to iteratively calculate up to the (k-2)th subsystem ∑ k-2 , when the condition u-γ k (ψ k When u) = 0, according to the subsystem ∑ k-2 The derivative of the strict Lyapunov function for the subsystem ∑ k-1 Design a virtual controller γ k (ψ k ,u):

[0144]

[0145]

[0146] Wherein, constant G k-1 >0, subsystem ∑ k-1 The derivative of the strict Lyapunov function is:

[0147]

[0148] Through the above iterative calculations, the virtual controllers corresponding to the k-1 subsystems are obtained.

[0149] S4. Based on the virtual controllers of each subsystem, design a parallel controller for the pure feedback system and use the parallel controller to perform parallel control of the actuators.

[0150] In step S4, based on the virtual controllers corresponding to the k-1 subsystems, the parallel controller for the pure feedback system is designed as follows:

[0151]

[0152]

[0153]

[0154]

[0155] Wherein, constant G k >0.

[0156] See Figure 2 In the structure of a parallel controller, x represents the state of the pure feedback system. For the dynamics of a pure feedback system, u is the control input of the pure feedback system. For the parallel controller, d represents the disturbance. The dynamics of the pure feedback system are affected by the state of the pure feedback system and the control input. The dynamics of the pure feedback system are obtained through equation calculation, and then input into the integral module to obtain the state of the pure feedback system at that moment. The cycle continues. The equation calculation for the parallel controller is the same as above, and the details will not be elaborated here.

[0157] In this embodiment, a parallel controller is designed for the actuators of the pure feedback system. The parallel controller is used to perform parallel control of the actuators of the pure feedback system, thereby improving the stability of the pure feedback system.

[0158] Example 2

[0159] Please see Figure 3 This embodiment, based on Embodiment 1, uses a helicopter hovering system as a specific example of the actuator, combined with, for example... Figure 1 , Figure 2 , Figure 3 The diagram shown illustrates the parallel control process of a helicopter hovering system:

[0160] The dynamic equations of the helicopter hovering system are:

[0161]

[0162]

[0163]

[0164]

[0165] Where ξ = (x, y, z) are the position coordinates of the helicopter, v is the velocity of the helicopter, m is the mass of the helicopter, u is the force of the rigid body motion, and ω = (ω 1 ω 2 ω 3 There are three control torques. Let be the direction frame, g be the gravitational acceleration, mge3 be the constant gravitational force, R be the orthogonal rotation matrix, sk(Ω) be the antisymmetric matrix, Ω be the angular velocity of the helicopter, r be the measured non-directional distance, (-l1, 0, -l3) be the offset between the tail rotor hub and the center of mass, I be the constant inertia matrix, and Q2 and Q3 be the rotational counter-torques of the rotor hub.

[0166] The dynamic equations of the helicopter hovering system are transformed into a simplified pure feedback form:

[0167] Helicopter hovering system module one is:

[0168]

[0169]

[0170] in, The control input for Module 1 is the force u of the rigid body motion, and the state of the pure feedback system is the helicopter's position ξ and velocity ν. ξ , let f 11 (ξ,ν ξ )=ν ξ ,

[0171] Helicopter hovering system module two is:

[0172]

[0173]

[0174] Among them, the control input of module two is the control torque. The state of a pure feedback system is given by an orthogonal rotation matrix R and the angular velocity Ω of the helicopter, let f 21 (R, Ω) = Rsk(Ω),

[0175] Module 1 contains the translational dynamics equations, and Module 2 contains the rotational dynamics equations. At this point, the helicopter hovering system is a second-order pure feedback system with two pure feedback systems, and K = 2.

[0176] It is understandable that in practical applications, the order of a pure feedback system can be other than two, and no specific limit is set here.

[0177] This embodiment represents the helicopter hovering system in a pure feedback manner, transforming the helicopter hovering system into a pure feedback system. A parallel controller is designed for the actuators of the transformed pure feedback system, and the parallel controller is used to perform parallel control of the actuators of the pure feedback system, thereby improving the stability of the pure feedback system.

[0178] Example 3

[0179] Please see Figure 4 This embodiment describes the parallel control system for actuators in a pure feedback system according to the present invention. The parallel control system for actuators in this embodiment includes:

[0180] The partitioning unit 401 is used to divide the pure feedback system into multiple subsystems;

[0181] The first design unit 402 is used to design auxiliary functions;

[0182] The second design unit 403 is used to design virtual controllers for each subsystem based on the designed auxiliary functions;

[0183] The third design unit 404 is used to design a parallel controller for the pure feedback system based on the virtual controllers of each subsystem.

[0184] Specifically, the pure feedback system in which the implementing agency is located is represented as follows:

[0185]

[0186] Where x1∈R n and x2, ..., x k ∈R, x1, x2, ..., x k f1 represents the state of a pure feedback system, u∈R is the system input, and f1:R n ×R→R n and f i :R n ×R i →R, where i = 2, ..., k are nonlinear functions, and the origin of the pure feedback system is the equilibrium point. Any partial derivative in any open set D containing the origin satisfies d(t) is a bounded unknown disturbance in a pure feedback system, |d(t)|≤D, D>0, where D is a constant, and D is represented by compact set ψ. j = (x1, ..., x j ).

[0187] Specifically, the partitioning unit 401 is used to divide the pure feedback system into k-1 subsystems, denoted as follows:

[0188]

[0189] Where ∑ i , i = 1, 2, ..., k-1 are subsystems of a pure feedback system.

[0190] Specifically, the auxiliary function expression designed by the first design unit 402 is as follows:

[0191] p(λ): =f(x1, (1-λ)γ1(x1)+λx2) (3)

[0192] Where p(λ) is the first auxiliary function used for formula derivation, λ is the intermediate variable used to assist in formula derivation, λ∈R, and γ1(x1) is the virtual controller;

[0193] Derivation and mathematical transformation based on the first auxiliary function:

[0194]

[0195] Based on formula (4):

[0196] f(x1,x2)-f(x1,γ(x1))=P(x1,x2-γ(x1))(x2-γ(x1)) (5)

[0197] in,

[0198] Based on the above derivation process, the relationships between the subsystems are determined as follows:

[0199] f i (ψ i x i+1 )=f i (ψ i γ i+1 )+P i ·(x i+1 -γ i (7)

[0200]

[0201] Among them, P i γ is the second auxiliary function used for formula derivation. i It is a virtual controller.

[0202] Specifically, the second design unit 403 is used to design Lyapunov functions and virtual control quantities for k-1 subsystems respectively, based on the auxiliary function and the relationship between the subsystems, and to perform iterative calculations based on the Lyapunov functions and virtual control quantities.

[0203] To control the subsystem ∑1, when the condition x3-γ2(ψ3)=0, design a virtual controller γ2(ψ3) for the subsystem ∑1:

[0204]

[0205] Where the constant G1 > 0, V(x1) is the strict Lyapunov function of f1(x1, γ1(x1)), γ1(x1) is a known function, and the derivative of the strict Lyapunov function of the subsystem ∑1 is:

[0206]

[0207]

[0208] When the condition x4-γ3(ψ4)=0, the virtual controller γ3(ψ4) is designed based on the derivative of the strict Lyapunov function of subsystem ∑1 with respect to subsystem ∑2:

[0209]

[0210] Where the constant G2 > 0, the derivative of the strict Lyapunov function of the subsystem ∑2 is:

[0211]

[0212] The above steps are used to iteratively calculate up to the (k-2)th subsystem ∑ k-2 , when the condition u-γ k (ψ k When u) = 0, according to the subsystem ∑ k-2 The derivative of the strict Lyapunov function for the subsystem ∑ k-1 Design a virtual controller γ k (ψ k ,u):

[0213]

[0214]

[0215] Wherein, constant G k-1 >0, subsystem ∑ k-1 The derivative of the strict Lyapunov function is:

[0216]

[0217] Through the above iterative calculations, the virtual controllers corresponding to the k-1 subsystems are obtained.

[0218] Specifically, the third design unit 404 is used to design a parallel controller for the pure feedback system based on the virtual controllers corresponding to k-1 subsystems, as follows:

[0219]

[0220]

[0221]

[0222]

[0223] Wherein, constant G k >0.

[0224] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A parallel control method for actuators of a pure feedback system, characterized by, The method comprises the following steps: S1. dividing a pure feedback system in which an actuator is located into multiple subsystems; In step S1, the pure feedback system in which the actuator is located is represented as follows: （1） where and , , represents the state of the pure feedback system, is the input of the system, and are nonlinear functions, , the origin of the pure feedback system is an equilibrium point , any partial derivative in any open set containing the origin satisfies , is a bounded unknown disturbance in the pure feedback system, , , D is a constant; The pure feedback system is divided into k-1 subsystems, represented as （2） wherein subsystem that is a pure feedback system ; S2. designing an auxiliary function; S3. designing a virtual controller for each subsystem based on the designed auxiliary function; S4. designing a parallel controller for the pure feedback system according to the virtual controllers of the subsystems, and performing parallel control of the actuator by using the parallel controller.

2. The parallel control method of an actuator for a pure feedback system according to claim 1, wherein In step S2, the auxiliary function is designed as follows: （3） wherein is a first auxiliary function for formula derivation, is an intermediate variable for assisting formula derivation, , is a virtual controller; According to the first auxiliary function, deduction and mathematical transformation are performed as follows: （4） According to formula (4), it is deduced that （5） wherein (6) According to the above deduction process, the relationship between the subsystems is determined as follows: （7） （8） wherein, is a second auxiliary function for formula derivation, is a virtual controller.

3. The parallel control method of an actuator for a pure feedback system according to claim 2, wherein In step S3, According to the auxiliary function and the relationship between the subsystems, Lyapunov functions and virtual control amounts are designed for the k-1 subsystems respectively, and iterative calculation is performed according to the Lyapunov functions and the virtual control amounts: The subsystem is controlled when the condition is met, the subsystem is designed to control the virtual controller : （9） where the constant , is a strict Lyapunov function, is a known function, the derivative of the strict Lyapunov function of the subsystem is （10） （11） When the condition is true, a virtual controller is designed for the subsystem based on the derivative of the strict Lyapunov function of the subsystem :​ （12） where the constant , subsystem derivative of the strict lyapunov function is: （13） Iterative computation is performed according to the above steps to the k-2th subsystem When the condition is satisfied, the derivative of the strict Lyapunov function of the subsystem is used to design the virtual controller for the subsystem :​ （14） （15） where the constant , the derivative of the strict Lyapunov function of the subsystem is （16） Through the above iterative calculation, the virtual controllers corresponding to the k-1 subsystems are obtained.

4. The parallel control method of an actuator for a pure feedback system according to claim 3, wherein In step S4, Based on the virtual controllers corresponding to the k-1 subsystems, a parallel controller for the pure feedback system is designed as follows: （17） （18） （19） （20） wherein the constant .

5. A parallel control system for actuators of a pure feedback system, characterized in that, The method comprises the following steps: A dividing unit is configured to divide a pure feedback system into multiple subsystems; The pure feedback system in which the actuator is located is represented as follows: （1） where and , , represents the state of the pure feedback system, is the input of the system, and are nonlinear functions, , the origin of the pure feedback system is an equilibrium point , any partial derivative in any open set containing the origin satisfies , is a bounded unknown disturbance in the pure feedback system, , , D is a constant; The pure feedback system is divided into k-1 subsystems, represented as （2） wherein subsystem that is a pure feedback system, ; A first designing unit is configured to design an auxiliary function; A second designing unit is configured to design a virtual controller for each subsystem based on the designed auxiliary function; A third designing unit is configured to design a parallel controller for the pure feedback system according to the virtual controllers of the subsystems.

6. The parallel control system for a pure feedback system oriented actuator according to claim 5, wherein The auxiliary function designed by the first designing unit is expressed as follows: （3） wherein is a first auxiliary function for formula derivation, is an intermediate variable for assisting formula derivation, , is a virtual controller; According to the first auxiliary function, deduction and mathematical transformation are performed as follows: （4） According to formula (4), it is deduced that （5） wherein (6) According to the above deduction process, the relationship between the subsystems is determined as follows: （7） （8） wherein, is a second auxiliary function for formula derivation, is a virtual controller.

7. The parallel control system for a pure feedback system oriented actuator according to claim 6, wherein The second designing unit is specifically configured to design Lyapunov functions and virtual control amounts for the k-1 subsystems respectively according to the auxiliary function and the relationship between the subsystems, and perform iterative calculation according to the Lyapunov functions and the virtual control amounts: To subsystem Control is performed when the condition To subsystem Design virtual controller : （9） where the constant , is a strict Lyapunov function, is a known function, the derivative of the strict Lyapunov function of the subsystem is （10） （11） When the condition is true, a virtual controller is designed for the subsystem based on the derivative of the strict Lyapunov function of the subsystem :​ （12） where the constant , subsystem derivative of the strict lyapunov function is: （13） Iterative computation is performed according to the above steps to the k-2th subsystem When the condition is satisfied, the derivative of the strict Lyapunov function of the subsystem is used to design the virtual controller for the subsystem : （14） （15） where the constant , subsystem derivative of the strict lyapunov function is: （16） Through the above iterative calculation, the virtual controllers corresponding to the k-1 subsystems are obtained.

8. The parallel control system for a pure feedback system oriented actuator according to claim 7, wherein The third designing unit is specifically configured to design a parallel controller for the pure feedback system based on the virtual controllers corresponding to the k-1 subsystems as follows: （17） （18） （19） （20） wherein the constant .

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