Fault-tolerant control method for permanent magnet synchronous motor with intermittent actuator faults

Abstract

The invention discloses a fault-tolerant control method of a permanent magnet synchronous motor with intermittent actuator faults. A fuzzy logic system is adopted to process unknown nonlinear dynamics. Through the fuzzy state observer, the state which cannot be directly measured can be estimated. In addition, under the framework of a dynamic surface technology and a backstepping recursion technology, the invention provides a fuzzy fault-tolerant control method for a permanent magnet synchronous motor system with intermittent actuator faults. The Lyapunov stability theory is utilized to prove that all signals in a closed-loop system are kept bounded. Finally, the effectiveness and feasibility of the method are verified through a simulation result.

Description

Technical Field

[0001] The present invention relates to the field of permanent magnet synchronous motor control, in particular to a fuzzy adaptive output feedback fault-tolerant control method for a permanent magnet synchronous motor system. Background Art

[0002] Permanent magnet synchronous motor (PMSM) systems are widely used in intensive industrial processing due to their simple control, high power density, and superior control accuracy. Compared to traditional electric synchronous motors, PMSMs offer significant advantages in terms of simple structure, compact size, light weight, and high efficiency. These advantages have led to their widespread application in fields requiring extremely high control accuracy and reliability, such as aerospace, CNC machine tools, machining centers, and robotics. In theoretical analysis, design and control strategies have emerged to further explore new topics. Advanced control techniques such as direct torque control, adaptive control theory, robust control, and sliding mode variable structure control have been successfully applied to PMSM control. However, with advances in science and technology, the demands placed on motor systems continue to increase. The inherent complexity of PMSMs, with their multivariable, strongly coupled, nonlinear nature, makes them susceptible to parameter fluctuations and external load damage, rendering traditional control methods inadequate to meet these evolving requirements.

[0003] Therefore, to obtain a high-performance permanent magnet synchronous motor system, it is necessary to conduct an in-depth analysis of the permanent magnet synchronous motor model and study advanced intelligent control methods to make the system have strong environmental adaptability and anti-interference capabilities. However, the existing technology still has the following problems:

[0004] First, although existing control methods have also explored similar actuator failure issues, they all require that the state variables of the PMSM system must be measurable. Therefore, they cannot solve the problem of unmeasurable states.

[0005] Second, existing fault-tolerant control schemes for neural networks or fuzzy logic systems can only address control problems associated with actuator faults within a limited range. Therefore, they cannot address the intermittent actuator fault problem of PMSM systems. Summary of the Invention

[0006] In order to solve the problems that the existing permanent magnet synchronous motor methods are unable to solve the unmeasurable state and are unable to target the intermittent actuator faults of the PMSM system, the present invention proposes a fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator faults, so as to realize fuzzy adaptive output feedback control for intermittent actuator faults of the permanent magnet synchronous motor system with unmeasurable state.

[0007] The technical solutions of the present invention are as follows:

[0008] An embodiment of the present application provides a fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator faults, comprising: establishing a dynamic model of the permanent magnet synchronous motor system based on stator voltage, stator current, and components of a stator inductance dq rotating coordinate system, armature resistance, rotor angular velocity, inertial flux, rotor angle, and pole pair number;

[0009] Based on the simplified dynamic model of the permanent magnet synchronous motor system, the rotor position, angular velocity, q-axis current, and d-axis current are used as state variables, and unknown nonlinear dynamics and external disturbances are introduced to form a state space model of the permanent magnet synchronous motor system;

[0010] Estimating unknown nonlinear dynamics in the state-space model using a fuzzy logic system, expressing the unknown nonlinear dynamics as a combination of ideal weights, fuzzy basis vectors, and approximation errors to obtain a fuzzy logic system of the nonlinear dynamics, thereby determining fuzzy parameter estimation errors;

[0011] Design a state observer to generate state estimates and define the observation error;

[0012] Establish an intermittent actuator fault model that describes the start and end time and intensity of actuator faults;

[0013] Taking the reference signal and the state estimate as input, defining a tracking error through coordinate transformation, constructing a dynamic surface error through an integral term based on the tracking error, designing a first-order filter to generate a smooth intermediate control signal, and defining a filtering error;

[0014] Combining the observation error, tracking error, dynamic surface error, filtering error, and fuzzy parameter estimation error, a Lyapunov function is constructed; based on the derivative derivation of the Lyapunov function, a virtual controller is designed using a backstepping recursive technique, and a parameter adaptation law is simultaneously designed to online estimate the ideal weight of the fuzzy logic system;

[0015] In combination with the intermittent actuator fault model, an actual controller is designed based on the virtual controller. Through the derivative analysis of the Lyapunov function, it is ensured that all error signals converge to a bounded region. The actual controller uses the estimation results of the parameter adaptive law to compensate for the fault attenuation effect and realize the tracking of the reference signal by the system output during a fault.

[0016] Compared with the prior art, the fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator failure provided by the embodiment of the present application has the following beneficial technical effects:

[0017] First, while existing methods have explored similar actuator failure issues, they all require that the PMSM system's state variables be measurable. Therefore, they cannot address the unmeasurable state problem addressed by the present invention. This paper, however, conducts groundbreaking research on the design complexity of output feedback control for intermittent actuator failures in PMSM systems. By introducing a fuzzy logic system, this problem of unmeasurable state is resolved.

[0018] Second, existing neural network or fuzzy logic system fault-tolerant control schemes can only address control problems related to a limited range of actuator failures. Therefore, they cannot address the intermittent actuator failures in PMSM systems designed for this invention. However, this invention proposes a fuzzy adaptive fault-tolerant control method for permanent magnet synchronous motor (PMSM) systems. This method can address intermittent actuator failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the present application in any way. In addition, the shapes and proportional dimensions of the components in the drawings are only schematic and are used to help understand the present application. They do not specifically limit the shapes and proportional dimensions of the components of the present application. Those skilled in the art can select various possible shapes and proportional dimensions to implement the present application according to the specific circumstances under the guidance of the present application. In the drawings:

[0020] Figure 1 A schematic flow chart of a fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator failures provided in an embodiment.

[0021] Figure 2 It is a diagram of the dynamic model of the permanent magnet synchronous motor system provided in the embodiment.

[0022] Figure 3 is the reference signal y in the embodiment d And the output signal y effect diagram.

[0023] Figure 4 In the embodiment, x1 and Curve effect diagram.

[0024] Figure 5 In the embodiment, x2 and Curve effect diagram.

[0025] Figure 6 In the embodiment, x3 and Curve effect diagram.

[0026] Figure 7 3 is a diagram showing the tracking error trajectories z1, z2, z3, and z4 in the embodiment.

[0027] Figure 8 1 is an effect diagram of the trajectory e1, e2, e3, and e4 of the observation error in the embodiment.

[0028] Figure 9 s1 and s2 are the effect diagrams of the filtering error trajectories in the embodiment.

[0029] Figure 10 is the intermediate controller α3 and the final controller ν in the embodiment q Effect picture.

[0030] Figure 11 is the intermediate controller α4 and the final controller ν in the embodiment d Effect picture.

[0031] Figure 12 is the parameter adaptive law in the embodiment Effect picture.

[0032] Figure 13 is the parameter adaptive law in the embodiment Effect picture. DETAILED DESCRIPTION

[0033] In order to enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0034] This application is aimed at a fuzzy adaptive control method for intermittent actuator faults in an unmeasurable permanent magnet synchronous motor system. The research on the permanent magnet synchronous motor system includes designing a state observer, constructing a Lyapunov function, introducing a fuzzy logic system, and causing intermittent actuator faults to design parameter adaptive laws and controllers. State observation involves a fuzzy logic system to estimate unknown nonlinear dynamics. Within the framework of dynamic surface technology and backstepping recursive technology, a fuzzy fault-tolerant control method for a permanent magnet synchronous motor system with intermittent actuator faults is proposed.

[0035] The following is further described with reference to specific embodiments and drawings.

[0036] The embodiment of the present application provides a fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator failure, such as Figure 1 As shown, the following steps are included:

[0037] Step A: Establish a dynamic model of the permanent magnet synchronous motor system: A dynamic model of the permanent magnet synchronous motor system is established based on the stator voltage, stator current, and components of the stator inductance in the dq rotating coordinate system, the armature resistance, the rotor angular velocity, the inertial flux, the rotor angle, and the number of pole pairs. Based on the simplified dynamic model of the permanent magnet synchronous motor system, the rotor position, angular velocity, q-axis current, and d-axis current are used as state variables, and unknown nonlinear dynamics and external disturbances are introduced to form a state-space model of the permanent magnet synchronous motor system.

[0038] The dynamics of a permanent magnet synchronous motor system is described by the following equations:

[0039]

[0040] In the dq rotating coordinate system of the permanent magnet synchronous motor, u d represents the d-axis component of the stator voltage in the rotating coordinate system, u q represents the q-axis component of the stator voltage in the rotating coordinate system; R s represents the armature resistance; i d represents the d-axis component of the stator current in the rotating coordinate system, i q represents the q-axis component of the stator current in the rotating coordinate system; L d Represents the d-axis component of the stator inductance in the rotating coordinate system, L q represents the q-axis component of the stator inductance in the rotating coordinate system; ω represents the rotor angular velocity. f represents the inertial flux link, θ represents the rotor angle, and p is the number of pole pairs.

[0041] In order to simplify the permanent magnet synchronous motor system model, it is as follows:

[0042]

[0043] Among them, x1 represents the rotor position, x2 represents the angular velocity, x3 represents the q-axis current, and x4 represents the d-axis current.

[0044] The state space expression of the permanent magnet synchronous motor system is:

[0045]

[0046] in f3(x)=b3x2+b1x3+b2x2x4, f4(x)=c1x4+c2x2x3, (x=[x1,x2,x3,x4] T ). y is the output, d l (t) represents an unknown external disturbance, which exists satisfy Where l=1,2,3,4.q ,u d The input voltage of the system, y represents the output of the control system, x represents the state vector of the system, and x=[x1,x2,x3,x4] T .f i (x) represents the unknown nonlinear dynamics of the system and satisfies f i (x(0)) = 0. Where i = 2, 3, 4.

[0047] Step B, introduce fuzzy logic system: for unknown nonlinear dynamics in the state space model, use fuzzy logic system to estimate, express the unknown nonlinear dynamics as a combination of ideal weights, fuzzy basis vectors and approximation errors, obtain the fuzzy logic system of nonlinear dynamics, and thus determine the fuzzy parameter estimation error.

[0048] Nonlinear dynamicsf i (x) is unknown. To overcome the influence of unknown nonlinear dynamics on controller design, we design the FLSs nonlinear function approximator based on the estimated value of the system state as follows:

[0049]

[0050] is the ideal weight, φ i (·) is the fuzzy basis vector with x as input, ε i is the approximation error, which is caused by an unknown positive constant For the boundary, requirements

[0051] Permanent Magnet Synchronous Motor System Approximated by Fuzzy Logic System

[0052]

[0053] Step C: Introduce the state observer: Design the state observer to generate state estimates and define the observation error.

[0054] The model of the permanent magnet synchronous motor system after the state observer is introduced is as follows

[0055]

[0056] in Represents the estimated state variable is the estimated value of the output signal, for estimated value.

[0057] The state observer error is defined as

[0058]

[0059] The observation error of the permanent magnet synchronous motor system is obtained as

[0060]

[0061] in: B1=(0,0,0,0) T ,B2=(0,1,0,0) T ,B3=(0,0,1,0) T , B4=(0,0,0,1) T ,ε=(0,ε1,ε2,ε2) T , d=(d1,d2,d3,d4) T , k i is the middle value, i=2,3,4.

[0062] Step D: Introduce intermittent actuator faults: Establish an intermittent actuator fault model that describes the start and end time and intensity of the actuator fault.

[0063] The embodiment of this article describes an intermittent fault model as follows:

[0064] u j (t) = β j (t)ν j (t)+u f,jm (t) (9)

[0065] β j (t) = β j,s ,t∈[t j,s ,t j,s+1 ),s∈z + (10)

[0066] in β j,s and is an unknown constant, u f,jm (t) is a bounded signal. t∈[t j,s ,t j,s+1 ) for s∈z + , z + represents a set of positive integers, t j,s and t j,s+1 Respectively represent the start time and end time of the actuator failure. j (t) is the input signal of the actuator.

[0067] Step E: Introduce dynamic surface technology: take the reference signal and state estimation value as input, define the tracking error through coordinate transformation, construct the dynamic surface error through the integral term based on the tracking error, design a first-order filter to generate a smooth intermediate control signal, and define the filtering error.

[0068] In the embodiment, the corresponding coordinate transformation is designed by introducing a filter as follows:

[0069]

[0070] where y d Indicates that the system output y is the reference signal to be tracked, z1 is the tracking error, and z i is the dynamic surface error, s i-1 represents the filtering error, α i-1 is the intermediate control signal, w i-1 is the filtered intermediate signal, satisfying the following first-order filter:

[0071]

[0072] where i = 2, 3, r i-1 is a design constant.

[0073]

[0074] where Λ i-1 Represents z1,z2,z3,z4,s1,s2,w1,w2, A function of . Since for any set parameter Υ i >0, collection Existence constant Make

[0075] Step F, constructing the Lyapunov function: Combining the observation error, tracking error, dynamic surface error, filtering error, and fuzzy parameter estimation error, construct the Lyapunov function as follows:

[0076] v0=e T Le (14)

[0077] where L is a positive definite matrix.

[0078]

[0079] Step G, designing a virtual controller and parameter adaptation law: Based on the derivative derivation of the Lyapunov function, a backstepping recursive technique is used to design a virtual controller, and a parameter adaptation law is simultaneously designed to online estimate the ideal weights of the fuzzy logic system.

[0080] The overall structure of the virtual controller in the embodiment is:

[0081]

[0082] where c i (i=1,2,3,4) are design parameters.

[0083] The constructed parameter adaptive law is:

[0084]

[0085]

[0086] in is the design parameter.

[0087] Step H, design the final controller and parameter adaptation law: Combined with the intermittent actuator fault model, the actual controller is designed based on the virtual controller. Through the derivative analysis of the Lyapunov function, it is ensured that all error signals converge to the bounded region. The actual controller uses the estimation results of the parameter adaptation law to compensate for the fault attenuation effect and realize the tracking of the reference signal by the system output during the fault.

[0088] In the embodiment, the final controller v is designed d ,v q and parameter adaptation law As shown below:

[0089]

[0090] Among them, v q is the voltage control quantity of the q axis in the dq rotating coordinate system, v d is the voltage control quantity of the d-axis in the dq rotating coordinate system, and is the design parameter.

[0091] The dynamic model of the permanent magnet synchronous motor system involved in the present invention is shown in FIG. Figure 2 As shown. The unknown nonlinear dynamics are approximated by fuzzy logic system, the unmeasurable state is estimated by state observer, and the intermittent actuator failure problem is considered based on adaptive backstepping recursive technology. The goal of this invention is to make the output signal y track the reference signal y d , proving that all signals in the closed-loop system remain bounded.

[0092] Figure 3-13 is the simulation result, where Figure 3 is the reference signal y d and the output signal y tracking effect, Figure 4-6 is state x i and The curve, Figure 7 is the permanent magnet synchronous motor system state tracking error z i , Figure 8 is the permanent magnet synchronous motor system state observation error e i , Figure 9 is the filtering error s1,s2, Figure 10-11 are the intermediate controllers α3, α4 and the final controller ν q , ν d . Figure 12-13 They represent the parameter adaptation law The above simulation results show the effectiveness and feasibility of the fuzzy adaptive output feedback fault-tolerant control method for intermittent actuator faults in permanent magnet synchronous motor systems.

[0093] This application uses a fuzzy logic system to handle unknown nonlinear dynamics. Through the fuzzy logic system's state observer, it is possible to estimate states that cannot be directly measured. Furthermore, within the framework of dynamic surface technology and backstepping recursion, a fuzzy fault-tolerant control method for a permanent magnet synchronous motor system with intermittent actuator failures is proposed. Using Lyapunov stability theory, it is demonstrated that all signals in the closed-loop system remain bounded. Finally, simulation results verify the effectiveness and feasibility of this method.

[0094] The above is a detailed introduction to the fault-tolerant control method of a permanent magnet synchronous motor with intermittent actuator failure provided by the present application. This article uses specific examples to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the concept of the present application and should not be understood as limiting the scope of protection of the present application.

Claims

1. A fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator failure, characterized in that: include: A dynamic model of the permanent magnet synchronous motor system is established based on the stator voltage, stator current, components of the stator inductance dq rotating coordinate system, armature resistance, rotor angular velocity, inertial flux, rotor angle, and pole pair number; Based on the simplified dynamic model of the permanent magnet synchronous motor system, the rotor position, angular velocity, q-axis current, and d-axis current are used as state variables, and unknown nonlinear dynamics and external disturbances are introduced to form a state space model of the permanent magnet synchronous motor system; Estimating unknown nonlinear dynamics in the state-space model using a fuzzy logic system, expressing the unknown nonlinear dynamics as a combination of ideal weights, fuzzy basis vectors, and approximation errors to obtain a fuzzy logic system of the nonlinear dynamics, thereby determining fuzzy parameter estimation errors; Design a state observer to generate state estimates and define the observation error; Establish an intermittent actuator fault model that describes the start and end time and intensity of actuator faults; Taking the reference signal and the state estimate as input, defining a tracking error through coordinate transformation, constructing a dynamic surface error through an integral term based on the tracking error, designing a first-order filter to generate a smooth intermediate control signal, and defining a filtering error; Constructing a Lyapunov function by combining the observation error, tracking error, dynamic surface error, filtering error and fuzzy parameter estimation error; Based on the derivative derivation of the Lyapunov function, a backstepping recursive technique is used to design a virtual controller, and a parameter adaptation law is simultaneously designed to estimate the ideal weight of the fuzzy logic system online; In combination with the intermittent actuator fault model, an actual controller is designed based on the virtual controller. Through the derivative analysis of the Lyapunov function, it is ensured that all error signals converge to a bounded region. The actual controller uses the estimation results of the parameter adaptive law to compensate for the fault attenuation effect and realize the tracking of the reference signal by the system output during a fault.

2. The fault-tolerant control method according to claim 1, wherein: The dynamic model of the permanent magnet synchronous motor system is expressed as follows: Among them, u d represents the d-axis component of the stator voltage in the rotating coordinate system, u q represents the q-axis component of the stator voltage in the rotating coordinate system; R s represents the armature resistance; i d represents the d-axis component of the stator current in the rotating coordinate system, i q represents the q-axis component of the stator current in the rotating coordinate system; L d Represents the d-axis component of the stator inductance in the rotating coordinate system, L q represents the q-axis component of the stator inductance in the rotating coordinate system; ω represents the rotor angular velocity, Φ f represents the inertial flux link, θ represents the rotor angle, and p is the number of pole pairs.

3. The fault-tolerant control method according to claim 1, wherein: The state space model expression of the permanent magnet synchronous motor system is: x1=θ,x2=ω,x3=i q ,x4=i d Among them, i d represents the d-axis component of the stator current in the rotating coordinate system, i q represents the q-axis component of the stator current in the rotating coordinate system; L d Represents the d-axis component of the stator inductance in the rotating coordinate system, L q represents the q-axis component of the stator inductance in the rotating coordinate system; ω represents the rotor angular velocity, x1 represents the rotor position, x2 represents the angular velocity, x3 represents the q-axis current, x4 represents the d-axis current, θ represents the rotor angle, and p is the number of pole pairs; f3(x)=b3x2+b1x3+b2x2x4, f4(x)=c1x4+c2x2x3, (x=[x1,x2,x3,x4] T ), y is the output, d l (t) represents an unknown external disturbance, which exists satisfy Where l=1,2,3,4,u d represents the d-axis component of the stator voltage in the rotating coordinate system, u q represents the q-axis component of the stator voltage in the rotating coordinate system; y represents the output of the control system, x represents the state vector of the system, and x=[x1,x2,x3,x4] T , f i (x) represents the unknown nonlinear dynamics of the system and satisfies f i (x(0))=0, where i=2,3,4.

4. The fault-tolerant control method according to claim 2, wherein: The expression of the nonlinear dynamic fuzzy logic system is as follows: in is the ideal weight, φ i (·) is the fuzzy basis vector with x as input, ε i is the approximation error, which is caused by an unknown positive constant For the boundary, requirements 5. The fault-tolerant control method according to claim 4, characterized in that: The expression of the state observer is as follows: in, Represents the estimated state variable is the estimated value of the output signal, for The estimated value of k i is the middle value, i=2,3,4; The error of the state observer is defined as: The observation error of the permanent magnet synchronous motor system is: Wherein: B1 = (0, 0, 0, 0) T , B2 = (0, 1, 0, 0) T , B3 = (0, 0, 1, 0) T , B4 = (0, 0, 0, 1) T , ε = (0, ε1, ε2, ε2) T , d = (d1, d2, d3, d4) T , 6. The fault-tolerant control method according to claim 4, characterized in that: The intermittent actuator fault model expression is: u j (t)=β j (t)v j (t)+u f，jm (t) b j (t)=β j,s ∈[t j，s ,t j,s+1 ),s∈z + ; in, β j,s and is an unknown constant, u f,jm (t) is a bounded signal, t∈[t j,s ,t j,s+1 ) for s∈z + , z + represents a set of positive integers, t j,s and t j,s+1 They represent the start time and end time of the actuator failure, ν j (t) is the input signal of the intermittent actuator.

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