A neural network inversion sliding mode control method for a marine three-phase asynchronous motor

Abstract

The application provides a neural network inversion sliding mode control method for a marine three-phase asynchronous motor, which combines the nonlinear approximation capability of an RBF neural network, good real-time performance, and the advantages of good dynamic performance and strong anti-interference of a sliding mode control, fully utilizes the back-off decoupling characteristics of a backstepping method, and designs a neural network inversion sliding mode control method for the marine three-phase asynchronous motor, so as to improve the performance of the motor control system. For the problem that the parameters cannot be determined in the modeling process of the marine three-phase asynchronous motor, a forward stability augmentation channel is designed. The backstepping method is used for decoupling control of the system, the sliding mode control solves the disturbance problem of the control system, and the RBF neural network is used for real-time estimation and compensation of the disturbance between the system coupling and the nonlinear friction force of the indirect contact surface of the control system framework.

Description

Technical Field

[0001] This invention belongs to the field of marine electrical equipment technology, specifically relating to a neural network inversion sliding mode control method for marine three-phase asynchronous motors. Background Technology

[0002] Three-phase asynchronous motors, with their advantages of light weight, simple structure, good dynamic performance, and high efficiency, are increasingly widely used in the shipbuilding industry. However, a three-phase asynchronous motor is a variable-parameter, multi-variable, strongly coupled, and nonlinear system, making effective speed control a crucial technology. Conventional speed-loop PI control suffers from high speed overshoot and poor resistance to external disturbances, failing to meet the requirements of the control system. The control effect is particularly poor when system parameters change or external loads abruptly shift. To address these issues, many researchers have proposed advanced control methods, such as PID control, adaptive control, fuzzy control, and sliding mode control.

[0003] In the control methods of marine three-phase asynchronous motors, sliding mode control is highly robust to parameter changes and unknown disturbances caused by model uncertainties, and is widely used in the field of motor control. However, when the control system is in the sliding surface, the sliding mode control method will exhibit chattering, which will adversely affect the motor control system, impacting not only the motor's lifespan but also the speed tracking accuracy.

[0004] Typically, the PID controller used in the speed loop is just a very ordinary linear PID regulator. Traditional PID control cannot meet the requirements and requires constant adjustment of PID parameters based on experience. The parameters of marine three-phase asynchronous motors are time-varying and easily affected by external disturbances, making the parameter adjustment and speed tracking performance of conventional PID speed controllers unsatisfactory. Summary of the Invention

[0005] To address the technical problems in the prior art, this invention provides a neural network inversion sliding mode control method for marine three-phase asynchronous motors, comprising the following steps:

[0006] Establish mathematical models for three-phase asynchronous motors, including mathematical models in a stationary three-phase coordinate system, mathematical models in a two-phase stationary coordinate system, and mathematical models in a two-phase synchronous rotating coordinate system;

[0007] Sliding mode adaptive control of neural networks: The RBF neural network algorithm is introduced to estimate the uncertainties in the dynamic model of marine motors;

[0008] Control system analysis and design are used to enable motor control systems to have good static and dynamic performance, including inverse decoupling control, sliding mode-based anti-interference control, and nonlinear friction and system coupling estimators.

[0009] Furthermore, the mathematical model in the stationary three-phase coordinate system has the following characteristics:

[0010] The mathematical model of a motor typically includes the following equations:

[0011] Stator voltage equation

[0012]

[0013] In the formula, u a u b u c For the three-phase winding voltage, i a i b i c R is the three-phase winding current. s ψ is the phase winding resistance. a ψ b ψ c For three-phase stator full magnetic flux linkage;

[0014] Stator flux linkage equation

[0015]

[0016] In the formula, ψ f For permanent magnet flux linkage, L a L b L c For the self-inductance of the three-phase stator windings, L ab L ba L ac L ca L bc L cb The mutual inductance of the three-phase stator windings, and L ab =L ba L ac =L ca L cb =L cb .

[0017] Furthermore, the mathematical model in the two-phase stationary coordinate system has the following characteristics:

[0018] Based on the principle of equal-phase amplitude transformation, the Clarke transform expression is obtained as follows:

[0019]

[0020] i a +i b +i b =0, substituting it into the equation, we get:

[0021]

[0022] The corresponding Clarke inverse transform is:

[0023]

[0024] The voltage equation is:

[0025]

[0026] The flux linkage equation is:

[0027]

[0028] In the formula, U α U β Let i be the voltage across the αβ axis. α i β For the α and β axis currents, Ψ α Ψ β Let L be the voltage across the α and β axes, and ω be the voltage across the α and β axes. e ω is the electric angular velocity of the rotor.

[0029] Furthermore, the mathematical model under the two-phase synchronous rotating coordinate system includes:

[0030] The Park transform expression is as follows:

[0031]

[0032] The expression for the inverse Park transform is as follows:

[0033]

[0034] In the formula, P 2s / 2r Let P be the Park transformation matrix. 2r / 2s This is the inverse transformation matrix of Park;

[0035] Stator voltage equation:

[0036]

[0037] Stator flux linkage equation:

[0038] ψ d =L d i d +ψ f

[0039] ψ d =L q i q

[0040] Where u d u q These are the dq-axis components of the stator; i d iq These are the dq-axis components of the stator current; Rs is the stator winding resistance; ψ d ψ q ω is the axial component of the stator flux linkage; r It is the rotor's electrical angular velocity; L d L q These are the axial inductance components; ψ f Represents permanent magnet flux linkage;

[0041] The electromagnetic torque equation is:

[0042] T e =nP n [ψ d i q -ψ q i d ]P n i q [ψ f +(L d -L q )i d ]

[0043] The equation of motion for the machine is:

[0044]

[0045] In the formula, J is the moment of inertia, B is the coefficient of friction, and T is the coefficient of friction. e For electromagnetic torque, T L This indicates the load torque of the motor.

[0046] Furthermore, sliding mode adaptive control of neural networks includes radial basis function neural network design:

[0047] The radial basis function neural network estimates the actual output of the marine motor model as fNN∈n, and the ideal output as f*NN∈n, as shown in the following equation:

[0048]

[0049] f NN =w T δ(x)

[0050] In the formula: f is the actual output of the neural network; w is the optimal weight of the neural network. * The estimation of δ; δ is the basis function of the neural network; L is the number of nodes in the hidden layer of the neural network;

[0051] The Gaussian function expression is:

[0052]

[0053] i = 1, 2, ..., n; j = 1, 2, ..., L

[0054]

[0055] c i =[c i1 ,c i2 ,…,c iL ] T

[0056] b i =[b i1 ,b i2 ,…,b iL ]

[0057] In the formula: x i c is the input vector of the i-th neural network; i b is the center matrix of the i-th neural network; i Let be the basis width vector of the i-th neural network;

[0058] Unknown nonlinear functions of motor control systems:

[0059]

[0060] In the formula: f1 is an unknown nonlinear function; M(q) is a positive definite inertia matrix; This refers to the angular velocity of the motor. This refers to the angular acceleration of the motor. For centrifugal force and Coriolis force; G(q) is the gravity term vector; τ d For interference; Let be the angular acceleration of the desired trajectory.

[0061] Furthermore, sliding mode control requires high accuracy in the mathematical model, and the unknown nonlinear function of the motor control system contains modeling errors and interference from unknown factors. RBF approximation of the nonlinear function has lower requirements for the accuracy of the mathematical model and can control the motor even without an accurate model.

[0062] Neural networks suffer from approximation errors. When the number of intermediate layer nodes is small, it can affect the performance of the control system. To make fNN infinitely approximate f*NN, the adaptive compensation update law and the design weight update law are as follows:

[0063]

[0064] In the formula: δ is the basis function of the neural network.

[0065] Furthermore, inversion decoupling control includes:

[0066] Assume the desired attitude signal is x d =[x dx x dy xdz ] T Define the tracking angle error:

[0067]

[0068] In the formula: z1 is the tracking angle error; x1 is the system's inertial angle; x2 is the system's inertial angular velocity; x d The desired attitude signal;

[0069] Designing Lyapunov functions using inversion control methods:

[0070]

[0071] In the formula: L1 is the Lyapunov function for design; z1 is the tracking angle error for definition;

[0072] Differentiating L1, we get:

[0073]

[0074] In the formula: L1 is the Lyapunov function for design; z1 is the tracking angle error; x2 is the inertial angular velocity of the system; x d The desired attitude signal;

[0075] Pick z2 is the control variable of the virtual control term, that is:

[0076]

[0077] Differentiating L2, we get:

[0078]

[0079] Design the system control law so that

[0080] In the formula: A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M δ is the system control law; z1 is the basis function of the neural network; z2 is the tracking angle error; z2 is the control quantity of the virtual control term; d t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d The desired attitude signal;

[0081]

[0082] In the formula: A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M δ is the system control law; z1 is the basis function of the neural network; z2 is the tracking angle error; z2 is the control quantity of the virtual control term; dt The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d C represents the desired attitude signal. ′ It is a 3×3 positive definite diagonal matrix;

[0083] Control rate T M Substitution We can obtain:

[0084]

[0085] In the formula: C is a 3×3 positive definite diagonal matrix; C ′ It is a 3×3 positive definite diagonal matrix; z1 is the defined tracking angle error; z2 is the control quantity of the virtual control term.

[0086] As t→∞, z1→0 and z2→0. Based on the tracking angle error, we have:

[0087] x1→x d and

[0088] Furthermore, sliding mode-based anti-interference control includes:

[0089] Define the sliding surface as:

[0090] σ=Kz1+z2

[0091] In the formula: σ is the defined sliding surface; K is a 3×3 positive definite diagonal matrix; z1 is the defined tracking angle error; z2 is the control quantity of the virtual control term;

[0092] Substituting the Lyapunov function into the sliding surface formula yields:

[0093]

[0094] In the formula: σ is the defined sliding surface; K and C are 3×3 positive definite diagonal matrices; z1 is the defined tracking angle error;

[0095] if but Redesign the Lyapunov function for inversion control:

[0096]

[0097] In the formula: L1 and L2 are Lyapunov functions; σ is the defined sliding surface;

[0098] Differentiating L2, we get:

[0099]

[0100] Differentiating σ and substituting the stator flux linkage equation, we get:

[0101]

[0102] In order to make The tracking angle error control rate is updated as follows:

[0103]

[0104] In the formula: ф and ψ are 3×3 diagonal matrices. A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M δ is the system control law; z1 is the basis function of the neural network; z2 is the tracking angle error; z2 is the control quantity of the virtual control term; d t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d This represents the desired attitude signal.

[0105] Furthermore, the nonlinear friction and system coupling estimator specifically includes: establishing an adaptive law to approximate the nonlinear friction force δ using an RBF network structure. The RBF network algorithm is as follows:

[0106]

[0107] In the formula: δ is the nonlinear frictional force; j = 1, 2, ..., 7, x is the network input; h(x) represents the ideal weights for the network. 7×1 For the network Gaussian function output; ε 3×1 For network approximation error; c j Let b be the coordinates of the center point of the basis function of the j-th neuron in the hidden layer of the network. j Let $\mathbf{j}$ be the propagation range of the basis function of the $j$-th neuron in the hidden layer of the network.

[0108] The network input is the motor angular velocity x = [ωp] x ,ωp y ,ωp z ] T The network output will then be:

[0109]

[0110] In the formula: For network output; h(x) represents the ideal weights for the network. 7×1 For the output of the Gaussian function of the network;

[0111] Pick The error of the estimator is:

[0112]

[0113] In the formula: ε represents the ideal weights of the network; h(x) is the Gaussian function output of the network; ε is the network approximation error;

[0114] The update law of RBFNN is:

[0115]

[0116] In the formula: B 3×3 Г 3×3 These are positive definite diagonal matrices; h(x) 7×1 For the output of the Gaussian function of the network;

[0117] After applying the disturbance estimator, the control tracking angle error is updated as follows:

[0118]

[0119] In the formula: ф and ψ are 3×3 diagonal matrices; A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M σ is the system control law; z1 is the defined sliding surface; z2 is the defined tracking angle error; d is the control quantity of the virtual control term. t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d This represents the desired attitude signal.

[0120] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0121] This invention addresses the complex nonlinear system of marine three-phase asynchronous motors, reducing the impact of unknown external disturbances; it facilitates real-time estimation and compensation of disturbances between nonlinear frictional forces and system couplings within the control system framework; and it ensures system stability. Attached Figure Description

[0122] Figure 1 This is the NNBSMC control flowchart of the present invention. Detailed Implementation

[0123] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0124] This application proposes a neural network inversion sliding mode control method for marine three-phase asynchronous motors, which specifically includes:

[0125] 1. Mathematical Model of Three-Phase Asynchronous Motor

[0126] 1.1 Mathematical Model in a Stationary Three-Phase Coordinate System

[0127] The mathematical model of a motor typically includes the following equations, including the stator voltage equations:

[0128]

[0129] In the formula, u a u b u c For the three-phase winding voltage, i a i b i c R is the three-phase winding current. s ψ is the phase winding resistance. a ψ b ψ c This is a three-phase stator with full magnetic flux linkage.

[0130] Stator flux linkage equation:

[0131]

[0132] In the formula, ψ f For permanent magnet flux linkage, L a L b L c For the self-inductance of the three-phase stator windings, L ab L ba L ac L ca L bc L cb The mutual inductance of the three-phase stator windings, and L ab =L ba L ac =L ca L cb =L cb .

[0133] 1.2 Mathematical Model in Two-Phase Stationary Coordinate System

[0134] Based on the principle of equal-phase amplitude transformation, the Clarke transform expression is obtained as follows:

[0135]

[0136] i a +i b +i b =0, substituting it into the equation, we get:

[0137]

[0138] The corresponding Clarke inverse transform is:

[0139]

[0140] The voltage equation is:

[0141]

[0142] The flux linkage equation is:

[0143]

[0144] In the formula, U α U β Let i be the voltage across the αβ axis. α i β Let Ψ be the α-axis and β-axis currents. α Ψ β Let L be the voltage across the α and β axes, and ω be the voltage across the α and β axes. e ω is the electric angular velocity of the rotor.

[0145] 1.3 Mathematical Model in Two-Phase Synchronous Rotating Coordinate System

[0146] The Park transform expression is as follows:

[0147]

[0148] The expression for the inverse Park transform is as follows:

[0149]

[0150] In the formula, P 2s / 2r Let P be the Park transformation matrix. 2r / 2s Park inverse transformation matrix.

[0151] Stator voltage equation:

[0152]

[0153] Stator flux linkage equation:

[0154]

[0155] Where u d u q These are the dq-axis components of the stator; i d i q These are the dq-axis components of the stator current; Rs is the stator winding resistance; ψ d ψ q ω is the axial component of the stator flux linkage; r It is the rotor's electrical angular velocity; L d L q These are the axial inductance components; ψ f Represents permanent magnet flux linkage.

[0156] The electromagnetic torque equation is:

[0157] Te =nP n [ψ d i q -ψ q i d ]P n i q [ψ f +(L d -L q )i d (12)

[0158] The equation of motion for the machine is:

[0159]

[0160] In the formula, J is the moment of inertia, B is the coefficient of friction, and T is the coefficient of friction. e For electromagnetic torque, T L This indicates the load torque of the motor.

[0161] 2. Sliding Mode Adaptive Control of Neural Networks

[0162] 2.1 Radial Basis Function (RBF) Neural Network Design

[0163] The purpose of introducing the RBF neural network algorithm into the control system in this invention is to estimate the uncertainties in the dynamic model of the marine motor.

[0164] The RBF neural network estimates the actual output of the marine motor model as fNN∈n, and the ideal output as f*NN∈n, as shown in the following formula:

[0165]

[0166] f NN =w T δ(x) (15)

[0167] In the formula: f is the actual output of the neural network; w is the optimal weight of the neural network. * The estimate is given by δ, where δ is the basis function of the neural network and L is the number of nodes in the hidden layer of the neural network.

[0168] The Gaussian function expression is:

[0169]

[0170] i = 1, 2, ..., n; j = 1, 2, ..., L

[0171]

[0172] c i =[c i1 ,c i2 ,…,ciL ] T (18)

[0173] b i =[b i1 ,b i2 ,…,b iL (19)

[0174] In the formula: x i c is the input vector of the i-th neural network; i b is the center matrix of the i-th neural network; i Let be the base width vector of the i-th neural network.

[0175] Unknown nonlinear functions of motor control systems:

[0176]

[0177] In the formula: f1 is an unknown nonlinear function; M(q) is a positive definite inertia matrix; This refers to the angular velocity of the motor. This refers to the angular acceleration of the motor. For centrifugal force and Coriolis force; G(q) is the gravity term vector; τ d For interference; Let be the angular acceleration of the desired trajectory.

[0178] Sliding mode control requires high accuracy of the mathematical model, and formula (20) contains modeling errors and interference from unknown factors. RBF approximation of nonlinear functions requires lower accuracy of the mathematical model and can control the motor even without an accurate model.

[0179] Neural networks suffer from approximation errors. When the number of intermediate layer nodes is small, it can affect the performance of the control system. To make fNN infinitely approximate f*NN, the adaptive compensation update law and the design weight update law are as follows:

[0180]

[0181] In the formula: δ is the basis function of the neural network.

[0182] 3 Control System Analysis and Design

[0183] While RBF neural networks meet the real-time requirements of control systems, establishing accurate mathematical models is challenging, and neural networks suffer from approximation errors. Therefore, a forward stabilization channel is designed to improve system robustness. This invention designs a neural network backstepping sliding mode controller (NNBSMC) based on RBF neural networks, enabling the motor control system to possess excellent static and dynamic performance. The controller principle is as follows: Figure 1 As shown.

[0184] 3.1 Inversion Decoupling Control

[0185] Assume the desired attitude signal is x d =[x dx x dy x dz ] T Define tracking angle error

[0186]

[0187] In the formula: z1 is the tracking angle error; x1 is the system's inertial angle; x2 is the system's inertial angular velocity; x f This represents the desired attitude signal.

[0188] Designing Lyapunov functions using inversion control methods:

[0189]

[0190] In the formula: L1 is the Lyapunov function for design; z1 is the tracking angle error for definition.

[0191] Differentiating L1, we get:

[0192]

[0193] In the formula: L1 is the Lyapunov function for design; z1 is the tracking angle error; x2 is the inertial angular velocity of the system; x d This represents the desired attitude signal.

[0194] Pick z2 is the control variable of the virtual control term, i.e.

[0195]

[0196] In the formula: z2 is the control quantity of the virtual control term; x2 is the inertial angular velocity; x d z1 represents the desired attitude signal; z1 represents the defined tracking angle error; and C is a 3×3 positive definite diagonal matrix.

[0197] If z2 = 2, then Therefore, further system design is needed. Design Lyapunov functions:

[0198]

[0199] Differentiating L2 yields

[0200]

[0201] Design the system control law so that

[0202] In the formula: A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M δ is the system control law; z1 is the basis function of the neural network; z2 is the tracking angle error; z2 is the control quantity of the virtual control term; d t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d This represents the desired attitude signal.

[0203]

[0204] In the formula: A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M δ is the system control law; z1 is the basis function of the neural network; z2 is the tracking angle error; z2 is the control quantity of the virtual control term; d t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d C represents the desired attitude signal. ′ It is a 3×3 positive definite diagonal matrix.

[0205] Substituting the control rate (30) into equation (29), we get

[0206]

[0207] In the formula: C is a 3×3 positive definite diagonal matrix; C ′ It is a 3×3 positive definite diagonal matrix; z1 is the defined tracking angle error; z2 is the control quantity of the virtual control term.

[0208] As t→∞, z1→0 and z2→0. According to equation (23), we have x1→x d and

[0209] 3.2 Anti-interference control based on sliding mode

[0210] Individual inversion control is susceptible to external disturbances and has poor robustness. To improve robustness, a sliding surface is introduced. The sliding surface is defined as:

[0211] σ=Kz1+z2 (32)

[0212] In the formula: σ is the defined sliding surface; K is a 3×3 positive definite diagonal matrix; z1 is the defined tracking angle error; z2 is the control quantity of the virtual control term.

[0213] Substituting equation (24) into equation (32) yields

[0214]

[0215] In the formula: σ is the defined sliding surface; K and C are 3×3 positive definite diagonal matrices; z1 is the defined tracking angle error.

[0216] if but Redesign the Lyapunov function in step 2 of the inversion control:

[0217]

[0218] In the formula: L1 and L2 are Lyapunov functions; σ is the defined sliding surface.

[0219] Differentiating L2 yields

[0220]

[0221] Differentiating σ and substituting equation (11) into it, we get

[0222]

[0223] In order to make Based on equation (23), the control law is updated to...

[0224]

[0225] In the formula: ф and ψ are 3×3 diagonal matrices. A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M δ is the system control law; z1 is the basis function of the neural network; z2 is the tracking angle error; z2 is the control quantity of the virtual control term; d t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d This represents the desired attitude signal.

[0226] 3.3 Nonlinear Friction and System Coupling Estimator

[0227] Sliding mode anti-interference control has both advantages and disadvantages. It has good dynamic performance, but the system output exhibits chattering. In the control law (24), the friction force is unknown. Due to mutual interference between the various subsystems, the control system is coupled, making it difficult to construct an accurate model. Because the relationship between angular velocity and friction force is not linear, the system output will exhibit chattering. Eliminating chattering can improve system performance. Neural networks have strong environmental adaptability and good nonlinear approximation performance. A neural network is selected as the disturbance estimator, and combined with a sliding mode anti-interference controller, the goal of reducing system chattering is achieved.

[0228] RBF networks are a type of local approximation network. They use a Gaussian function as the action function, resulting in fast learning speed, good real-time performance, good convergence, and less susceptibility to getting trapped in local optima.

[0229] This design uses an RBF network structure to establish an adaptive law to approximate the nonlinear friction force δ. The RBF network algorithm is as follows:

[0230]

[0231] In the formula: δ is the nonlinear frictional force; j = 1, 2, ..., 7, x is the network input; Let h(x) be the ideal weights for the network. 7×1 For the network Gaussian function output; ε 3×1 For network approximation error; c j Let b be the coordinates of the center point of the basis function of the j-th neuron in the hidden layer of the network. j Let be the propagation range of the basis function of the j-th neuron in the hidden layer of the network.

[0232] The network input is the motor angular velocity x = [ωp] x ,ωp y ,ωp z ] T The network output is

[0233]

[0234] In the formula: For network output; Let h(x) be the ideal weights for the network. 7×1 This is the output of the Gaussian function for the network.

[0235] Pick The error of the estimator is then...

[0236]

[0237] In the formula: ε represents the ideal weights of the network; h(x) is the Gaussian function output of the network; and ε is the network approximation error.

[0238] The update law of RBFNN is

[0239]

[0240] In the formula: B 3×3 Г 3×3 These are positive definite diagonal matrices; h(x) 7×1 This is the output of the Gaussian function for the network.

[0241] After applying the disturbance estimator, the control law (36) is updated to

[0242]

[0243] In the formula: ф and ψ are 3×3 diagonal matrices; A and B are system parameters, respectively; C is a 3×3 positive definite diagonal matrix; T M σ is the system control law; z1 is the defined sliding surface; z2 is the defined tracking angle error; d is the control quantity of the virtual control term. t The external disturbance is unknown; x2 is the inertial angular velocity of the system; x d This represents the desired attitude signal.

[0244] This design combines the advantages of RBF neural network's nonlinear approximation capability and good real-time performance with sliding mode control's good dynamic performance and strong anti-interference ability. It makes full use of the backstepping decoupling characteristics of the backstepping method and designs a neural network inversion sliding mode control method for marine three-phase asynchronous motors to improve the performance of the motor control system.

[0245] To address the issue of undetermined parameters during the modeling of marine three-phase asynchronous motors, a forward stabilization channel was designed. Backstepping was employed for decoupling control of the system, sliding mode control resolved disturbances in the control system, and the RBF neural network was used to estimate and compensate for disturbances arising from system coupling and nonlinear friction at the contact surfaces between the control system frames in real time.

[0246] In summary, these are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent changes and modifications made in accordance with the scope of the present invention and the contents of the specification are within the scope of the present invention.

Claims

1. A neural network inversion sliding mode control method for a marine three-phase asynchronous motor, characterized in that, The method comprises the following steps: A mathematical model of a three-phase asynchronous motor is established, including a mathematical model in a stationary three-phase coordinate system, a mathematical model in a two-phase stationary coordinate system, and a mathematical model in a two-phase synchronous rotating coordinate system; Sliding mode adaptive control of a neural network, in which a RBF neural network algorithm is introduced to estimate an uncertain part of a marine motor dynamics model; Control system analysis and design, which is used to make the motor control system have good static and dynamic performance, including backstepping decoupling control, sliding mode anti-interference control, and a nonlinear friction and system coupling estimator; The sliding mode anti-interference control comprises the following steps: A sliding mode surface is defined as follows: σ=Kz1+z2 In the formula, σ is the defined sliding mode surface, K is a 3*3 positive diagonal matrix, z1 is a defined tracking angle error, and z2 is a control quantity of a virtual control item. The Lyapunov function is substituted into the sliding mode surface formula to obtain: In the formula, σ is the defined sliding mode surface, K and C are 3*3 positive diagonal matrices, and z1 is the defined tracking angle error. If then Redesigning the Lyapunov function for inversion control: In the formula, L1 and L2 are Lyapunov functions, and σ is the defined sliding mode surface. The L2 is differentiated to obtain: The σ is differentiated, and the stator flux linkage equation is substituted into the formula to obtain: To this end The tracking angle error control rate is updated based on: wherein: φ, ψ are 3x3 diagonal matrices. A and B are system parameters; C is a 3x3 positive definite diagonal matrix; T M is the system control rate; δ is the base function of the neural network; z1 is the definition of the tracking angle error; z2 is the virtual control item control quantity; d t is the unknown external disturbance; x2 is the inertial angular velocity of the system; x d is the desired attitude signal; The nonlinear friction and system coupling estimator specifically comprises the following steps: an RBF network structure is used to establish an adaptive law to approximate the nonlinear friction force δ, and the RBF network algorithm is as follows: where δ is the nonlinear frictional force; j = 1, 2, ··· · · 7, x is the network input; is the ideal weight of the network; h(x) 7×1 is the Gaussian basis function output of the network; ε 3×1 is the approximation error of the network; c j is the coordinate of the center point of the jth neuron basis function in the hidden layer of the network, b j is the propagation range of the jth neuron basis function in the hidden layer of the network; The network input is the motor angular velocity The network output is then: where: is the network output; is the network ideal weight; h(x) 7×1 is the network Gaussian kernel output; Take The error of the estimator is then: where: is the network ideal weight; h(x) is the network Gaussian basis function output; and ε is the network approximation error. The RBFNN update law is as follows: where B 3×3 , G 3×3 are positive definite diagonal matrices; h(x) 7×1 is the network Gaussian kernel output; After the disturbance estimator is applied, the control tracking angle error is updated as follows: wherein: φ, ψ are 3 × 3 diagonal matrices; A and B are system parameters; C is a 3 × 3 positive definite diagonal matrix; T M is the system control rate; σ is the definition of the sliding mode surface; z1 is the definition of the tracking angle error; z2 is the virtual control item control quantity; d t is the unknown external disturbance; x2 is the inertial angular velocity of the system; x d is the desired attitude signal.

2. The method of claim 1, wherein, The mathematical model in the stationary three-phase coordinate system comprises the following characteristics: The mathematical model of a general motor comprises the following equations: A stator voltage equation where u a , u b , u c are the three-phase winding voltages, i a , i b , i c are the three-phase winding currents, R s are the phase winding resistances, ψ a , ψ b , ψ c are the three-phase stator total flux linkages; A stator flux linkage equation where ψ f is the permanent magnet flux linkage, L a , L b , L c is the self-inductance of the stator three-phase winding, L ab , L ba , L ac , L ca , L bc , L cb is the mutual inductance of the three-phase stator winding, and L ab = L ba , L ac = L ca , L cb = L cb .

3. The method of claim 2, wherein, The mathematical model in the two-phase stationary coordinate system comprises the following characteristics: According to the equal-phase-amplitude transformation principle, the Clarke transformation expression is as follows: i a +i b +i b = 0, which is substituted into the equation gives: The corresponding Clarke inverse transformation is as follows: The voltage equation is as follows: The flux linkage equation is as follows: where U α , U β is the αβ-axis voltage, i α , i β is the α, β-axis current, Ψ α , Ψ β is the α, β-axis voltage, L is the α, β-axis voltage, and ω e is the electrical angular velocity of the rotor rotation.

4. The method of claim 3, wherein, The mathematical model in the two-phase synchronous rotating coordinate system comprises the following: The Park transformation expression is as follows: The Park inverse transformation expression is as follows: where P 2s / 2r is the Park transformation matrix, P 2r / 2s is the inverse Park transformation matrix; A stator voltage equation A stator flux linkage equation ψ d = L d i d + ψ f Ψ d = L q i q where u d , u q are the d-q axis components of the stator voltage; i d , i q are the d-q axis components of the stator current; Rs is the stator winding resistance; ψ d , ψ q are the axis components of the stator flux linkage; ω r is the rotor electrical angular velocity; L d , L q are the axis inductance components; ψ f represents the permanent magnet flux linkage; An electromagnetic torque equation is as follows: T e = nP n [ψ d i q - ψ q i d ]P n i q [ψ f + (L d - L q ) i d ] A mechanical motion equation is as follows: where J is the moment of inertia, B is the friction coefficient, T e is the electromagnetic torque, T L represents the load torque of the motor.

5. The method of claim 4, wherein, The sliding mode adaptive control of the neural network comprises radial basis neural network design: The radial basis neural network estimates the actual output fNN of the marine motor model, and the ideal output f*NN is as shown in the following formula: f NN = w T δ(x) where: f is the actual output of the neural network; w is the optimal weight of the neural network * estimate; δ is the base function of the neural network; L is the number of nodes of the hidden layer of the neural network; The Gaussian basis function expression is as follows: i=1, 2, …, n; j=1, 2, …, L c i = [c i1 ,c i2 ,…,c iL ] T b i = [b i1 ,b i2 ,…,b iL ] where: x i is the input vector for the i-th neural network; c i is the center matrix for the i-th neural network; b i is the base width vector for the i-th neural network; An unknown nonlinear function of the motor control system: where: f1is an unknown nonlinear function; M(q) is a positive definite inertia matrix; is the motor angular velocity; is the motor angular acceleration; is the centrifugal and Coriolis forces; G(q) is the gravity term vector; τ d is the disturbance; is the desired trajectory angular acceleration.

6. The method of claim 5, wherein: The sliding mode control has a high requirement for the accuracy of the mathematical model, the unknown nonlinear function of the motor control system contains modeling errors and unknown factor interference, the RBF approximation of the nonlinear function has a low requirement for the accuracy of the mathematical model, and the motor can be controlled without an accurate model, There is an approximation error of the neural network, and when the number of intermediate layer nodes is small, the performance of the control system is affected, in order to make fNN infinitely approximate f*NN, the adaptive compensation update law and the weight value update law are as shown in the following formula: In the formula, δ is a basis function of the neural network.

7. The method of claim 6, wherein, The backstepping decoupling control comprises the following steps: Assume desired attitude signal is x d = [x dx x dy x dz ] T , define tracking angle error: where: z1 is a tracking angle error; x1 is an inertial angle of the system; x2 is an inertial angular velocity of the system; x d is a desired attitude signal; A Lyapunov function is designed by using the backstepping control method: In the formula, L1 is the designed Lyapunov function, and z1 is the defined tracking angle error. Differentiating L1 gives where: L1 is a design Lyapunov function; z1 is a definition tracking angle error; x2 is a system's inertial angular velocity; x d is a desired attitude signal; Take z2 is the control quantity of the virtual control item, namely: Differentiating L2 gives The system control law is designed such that where A and B are system parameters; C is a 3x3 positive definite diagonal matrix; T M is the system control rate; δ is the base function of the neural network; z1 is the definition of the tracking angle error; z2 is the virtual control item control variable; d t is the unknown external disturbance; x2 is the inertial angular velocity of the system; x d is the desired attitude signal; wherein: A and B are system parameters; C is a 3x3 positive definite diagonal matrix; T M is the system control rate; δ is the base function of the neural network; z1 is the definition of the tracking angle error; z2 is the virtual control item control quantity; d t is the unknown external disturbance; x2 is the inertial angular velocity of the system; x d is the expected attitude signal; C ′ is a 3x3 positive definite diagonal matrix; The control rate T M is substituted is obtained: where: C is a 3x3 positive definite diagonal matrix; C ′ is a 3x3 positive definite diagonal matrix; z1 is a defined tracking angle error; z2 is a control quantity of a virtual control item; When t→∞, z1→0 and z2→0, according to the tracking angle error, then x1→x d and

Images