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

Abstract

The application discloses a fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator faults, which adopts a fuzzy logic system to process unknown nonlinear dynamics. Through a fuzzy state observer, states that cannot be directly measured can be estimated. In addition, under 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. By using Lyapunov stability theory, it is proved that all signals in the closed-loop system remain bounded. Finally, the effectiveness and feasibility of the method are verified through simulation results.

Description

TECHNICAL FIELD

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

[0002] Permanent magnet synchronous motor (PMSM) system is widely used in intensive industrial processing due to its simple control, high power density and superior control accuracy. Compared with traditional electric synchronous motor, PMSM has the advantages of simple structure, small size, light weight and high efficiency. These advantages make PMSM widely used in fields with high requirements for control accuracy and reliability, such as aerospace, numerical control machine tools, machining centers and robots. In theoretical analysis, design and control strategies are proposed to further study new topics. Advanced control technologies such as direct torque control, adaptive control theory, robust control and sliding mode variable structure control have been successfully applied to the control of PMSM. However, with the progress of science and technology, the demand for motor systems continues to increase. The inherent complexity of PMSM, which has a multi-variable, strongly coupled nonlinear system, makes it prone to parameter fluctuations and external load damage, rendering traditional control methods insufficient to meet the ever-changing requirements.

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

[0004] First, although the existing control methods also discuss similar actuator fault problems, they require the state variables of the PMSM system to be measurable. Therefore, they cannot solve the problem of unmeasurable state.

[0005] Second, the existing neural network or fuzzy logic system fault-tolerant control scheme can only solve control problems related to actuator faults within a limited range. Therefore, they cannot solve the problem of intermittent actuator faults for PMSM systems. SUMMARY

[0006] To solve the problem that the existing permanent magnet synchronous motor method cannot solve the unmeasurable state and cannot solve the intermittent actuator fault problem for PMSM systems, the present application proposes a fault-tolerant control method for permanent magnet synchronous motor with intermittent actuator faults to realize fuzzy adaptive output feedback control for intermittent actuator faults of permanent magnet synchronous motor system with unmeasurable state.

[0007] The technical solution of the present application is as follows:

[0008] The embodiment of the application provides a fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator failure, comprising: establishing a dynamic model of a permanent magnet synchronous motor system based on components of a stator voltage, a stator current and a d-q rotating coordinate system, an armature resistance, a rotor angular velocity, an inertia magnetic flux, a rotor angle and a number of pole pairs;

[0009] Based on the simplified dynamic model of the permanent magnet synchronous motor system, a state space model of the permanent magnet synchronous motor system is formed by introducing unknown nonlinear dynamics and external disturbances with a rotor position, an angular velocity, a q-axis current and a d-axis current as state variables;

[0010] For the unknown nonlinear dynamics in the state space model, a fuzzy logic system is used for estimation, the unknown nonlinear dynamics is expressed as a combination of ideal weights, fuzzy basis vectors and approximation errors, a fuzzy logic system of nonlinear dynamics is obtained, and a fuzzy parameter estimation error is determined;

[0011] A state observer is designed to generate a state estimation value, and an observation error is defined;

[0012] An intermittent actuator failure model is established to describe the start and stop time and intensity of the actuator failure;

[0013] A tracking error is defined by coordinate transformation with a reference signal and the state estimation value as inputs, a dynamic surface error is constructed based on the tracking error through an integral term, a first-order filter is designed to generate a smooth intermediate control signal, and a filter error is defined;

[0014] The Lyapunov function is constructed in combination with the observation error, the tracking error, the dynamic surface error, the filter error and the fuzzy parameter estimation error; the virtual controller is designed by using the backstepping recursive technique based on the derivative of the Lyapunov function, and the parameter adaptive law is designed synchronously to estimate the ideal weights of the fuzzy logic system online;

[0015] The actual controller is designed according to the virtual controller in combination with the intermittent actuator failure model, and it is ensured that all error signals converge to a bounded region through the derivative analysis of the Lyapunov function; the actual controller compensates for the failure attenuation effect by using the estimation result of the parameter adaptive law, and realizes the tracking of the reference signal by the system output in the failure.

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

[0017] First, the existing methods also discuss similar actuator failure problems, but they require the state variables of the PMSM system to be measurable. Therefore, they cannot solve the state unmeasurable problem involved in the present invention. The present invention makes a pioneering study on the design complexity of the intermittent actuator fault output feedback control of the PMSM system. By introducing a fuzzy logic system, the state unmeasurable problem is solved.

[0018] Second, the existing neural network or fuzzy logic system fault-tolerant control scheme can only solve the control problem related to the actuator failure within a limited range. Therefore, they cannot solve the intermittent actuator failure problem of the PMSM system designed in the present invention. The present invention proposes a fuzzy adaptive fault-tolerant control method for a permanent magnet synchronous motor (PMSM) system. This method can cope with the intermittent actuator failure problem. BRIEF DESCRIPTION OF DRAWINGS

[0019] The drawings described herein are for the purpose of explanation and are not intended to limit the scope of the present disclosure in any way. Additionally, the shapes and proportions of the components in the drawings are merely illustrative and are used to facilitate understanding of the present application, and are not specifically limited to the shapes and proportions of the components. Those skilled in the art can select various possible shapes and proportions according to specific circumstances to implement the present application under the teachings of the present application. In the drawings:

[0020] Figure 1 A flowchart of the fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator failure is provided for the embodiment.

[0021] Figure 2 A dynamic model diagram of the permanent magnet synchronous motor system is provided for the embodiment.

[0022] Figure 3 A reference signal y d and output signal y effect diagram is provided for the embodiment.

[0023] Figure 4 A curve effect diagram of x1 and is provided for the embodiment.

[0024] Figure 5 A curve effect diagram of x2 and is provided for the embodiment.

[0025] Figure 6 A curve effect diagram of x3 and is provided for the embodiment.

[0026] Figure 7 A trajectory z1, z2, z3, z4 effect diagram of the tracking error is provided for the embodiment.

[0027] Figure 8 The diagram shows the trajectory of the observation error e1, e2, e3, e4 in the embodiment.

[0028] Figure 9 The diagram shows the effect of the filtering error trajectories s1 and s2 in the embodiment.

[0029] Figure 10 These are the intermediate controller α3 and the final controller ν in the embodiment. q Renderings.

[0030] Figure 11 These are the intermediate controller α4 and the final controller ν in the embodiment. d Renderings.

[0031] Figure 12 It is the parameter adaptive law in the embodiment. Renderings.

[0032] Figure 13 It is the parameter adaptive law in the embodiment. Renderings. Detailed Implementation

[0033] 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 with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0034] This application proposes a fuzzy adaptive control method for intermittent actuator faults in permanent magnet synchronous motor (PMSM) systems with unmeasurable intermittent actuator faults. The research on PMSM systems includes designing a state observer, constructing a Lyapunov function, introducing a fuzzy logic system, and designing parameter adaptive laws and controllers based on intermittent actuator faults. State observation involves using a fuzzy logic system to estimate unknown nonlinear dynamics. Within the framework of dynamic surface techniques and backstepping recursion techniques, a fuzzy fault-tolerant control method for PMSM systems with intermittent actuator faults is proposed.

[0035] The following description, in conjunction with specific embodiments and accompanying drawings, provides further details.

[0036] The fault-tolerant control method for permanent magnet synchronous motors with intermittent actuator failures provided in this application embodiment, such as... Figure 1 As shown, it includes the following steps:

[0037] Step A, establishing the dynamic model of the permanent magnet synchronous motor system: based on the stator voltage, stator current and stator inductance d-q rotating coordinate system components, armature resistance, rotor rotation angle speed, inertia flux, rotor angle and pole pair number, the dynamic model of the permanent magnet synchronous motor system is established. 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 taken as state variables, unknown nonlinear dynamics and external disturbance are introduced, and the state space model of the permanent magnet synchronous motor system is formed.

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

[0039]

[0040] In the d-q rotating coordinate system of the permanent magnet synchronous motor, wherein 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 rotation angle speed. Φ f represents the inertia flux link, θ represents the rotor angle, and p is the pole pair number.

[0041] In order to simplify the model of the permanent magnet synchronous motor system, the following is used:

[0042]

[0043] Wherein, 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] Wherein f3(x)=b3x2+b1x3+b2x2x4,f4(x)=c1x4+c2x2x3,(x=[x1,x2,x3,x4] T ). y is the output, d l (t) represents unknown external disturbance, and there is satisfies where l=1,2,3,4. uq , 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 the unknown nonlinear dynamics in the state space model, estimate it by using fuzzy logic system, express the unknown nonlinear dynamics as a combination of ideal weight, fuzzy basis vector and approximation error, get the fuzzy logic system of nonlinear dynamics, and determine the fuzzy parameter estimation error.

[0048] The nonlinear dynamics f i (x) is unknown, in order 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 bounded by an unknown positive constant , and requires

[0051] Permanent magnet synchronous motor system approximated by fuzzy logic system

[0052]

[0053] Step C, introduce state observer: design state observer to generate state estimation value, and define observation error.

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

[0055]

[0056] Where represents the estimated state variable is the estimated value of the output signal, is the estimated value of .

[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] 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 , k i is an intermediate value, i = 2, 3, 4.

[0062] Step D, introduce intermittent actuator fault: establish an intermittent actuator fault model describing the start and end time and strength of the actuator fault.

[0063] The embodiments described herein describe 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 e [t j,s , t j,s+1 ), s e z + (10)

[0066] wherein β j,s and are unknown constants, u f,jm (t) is a bounded signal. t e [t j,s , t j,s+1 ) for s e z + , z + denotes the set of positive integers, t j,s and t j,s+1 represent the start time and end time of the occurrence of the actuator fault, respectively. v j (t) is the input signal of the actuator.

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

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

[0069]

[0070] where y d represents the reference signal to be tracked by the system output y, z1 is the tracking error, z i is the dynamic surface error, s i-1 represents the filtering error, a 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 a function of z1, z2, z3, z4, s1, s2, w1, w2, . Since for any given parameter Υ i > 0, the set exists a constant such that

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

[0076] v0 = e T Le (14)

[0077] where L is a positive definite matrix.

[0078]

[0079] Step G, designing virtual controller and parameter adaptive law: based on the derivative of the Lyapunov function, the virtual controller is designed using the backstepping recursive technique, and the parameter adaptive law is designed synchronously to estimate the ideal weight of the fuzzy logic system online.

[0080] The virtual controller is constructed as follows in the embodiment:

[0081]

[0082] where c i (i = 1, 2, 3, 4) is a design parameter.

[0083] The parameter adaptive law is constructed as:

[0084]

[0085]

[0086] wherein are design parameters.

[0087] Step H, designing the final controller and the parameter adaptive law: combining the intermittent actuator fault model, the actual controller is designed according to 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 compensates the fault attenuation effect by using the estimation result of the parameter adaptive law, and the tracking of the reference signal by the system output is realized when the fault occurs.

[0088] In the embodiment, the final controller v d is designed as follows: q and the parameter adaptive law is designed as follows:

[0089]

[0090] wherein v q is the voltage control quantity of the q-axis in the d-q rotating coordinate system, v d is the voltage control quantity of the d-axis in the d-q rotating coordinate system, and are design parameters.

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

[0092] Figures 3-13 are simulation results, wherein Figure 3 is the tracking effect of the reference signal y d and the output signal y, Figures 4-6 is the curve of the state x i and , Figure 7 is the state tracking error z i of the permanent magnet synchronous motor system, Figure 8 is the state observation error e i of the permanent magnet synchronous motor system, Figure 9 is the filter error s1, s2,Figures 10-11 intermediate controllers a3, a4 and final controller v q , v d . Figures 12-13 respectively represent parameter adaptive law From the simulation results above, it can be seen that the effectiveness and feasibility of the fuzzy adaptive output feedback fault-tolerant control method for the intermittent actuator fault of the permanent magnet synchronous motor system.

[0093] The fuzzy logic system is used in the application to process unknown nonlinear dynamics, and the state observer of the fuzzy logic system can estimate the states that cannot be directly measured. In addition, under the framework of dynamic surface technology and backstepping recursive technology, a fuzzy fault-tolerant control method for the permanent magnet synchronous motor system with intermittent actuator faults is proposed. Using Lyapunov stability theory, it is proved that all signals in the closed-loop system are bounded. Finally, the effectiveness and feasibility of the method are verified by simulation results.

[0094] The fault-tolerant control method for the permanent magnet synchronous motor with intermittent actuator faults provided by the application is described in detail above, and specific examples are applied in this paper to explain the principles and implementation modes of the application. The above description of the examples is only used to help understand the concept of the application and should not be understood as limiting the scope of protection of the application.

Claims

1. A fault-tolerant control method for a permanent magnet synchronous motor with intermittent actuator faults, characterized in that, include: A dynamic model of a permanent magnet synchronous motor system is established based on the components of stator voltage, stator current, and stator inductance dq in the rotating coordinate system, armature resistance, rotor angular velocity, flux linkage, rotor angle, and number of pole pairs. Based on the simplified dynamic model of the permanent magnet synchronous motor system, with rotor position, angular velocity, q-axis current and d-axis current as state variables, unknown nonlinear dynamics and external disturbances are introduced to form a state-space model of the permanent magnet synchronous motor system. For the unknown nonlinear dynamics in the state-space model, a fuzzy logic system is used for estimation. The unknown nonlinear dynamics are expressed as a combination of ideal weights, fuzzy basis vectors and approximation errors, resulting in a fuzzy logic system for nonlinear dynamics, thereby determining the fuzzy parameter estimation error. 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 times and intensity of actuator failure; Using the reference signal and the state estimate as input, the tracking error is defined by coordinate transformation. Based on the tracking error, a dynamic surface error is constructed by an integral term. A first-order filter is designed to generate a smooth intermediate control signal, and the filtering error is defined. By 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 backstepping recursion, and a parameter adaptive law is designed simultaneously to estimate the ideal weights of the fuzzy logic system online. Based on the intermittent actuator fault model, an actual controller is designed according to 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 adaptive law to compensate for the fault attenuation effect and realize the system output tracking the reference signal during a fault.

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

3. The fault-tolerant control method according to claim 1, characterized in that, 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 i represents the d-axis component of the stator current in the rotating coordinate system. q L represents the q-axis component of the stator current in a rotating coordinate system. d L represents the d-axis component of the stator inductance in a rotating coordinate system. q ω represents the q-axis component of the stator inductance in the rotating coordinate system; 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; p is the number of pole pairs; R s Φ represents armature resistance. f Indicates flux linkage; f3(x) = b3x² + b1x³ + b2x²x⁴, f4(x) = c1x⁴ + c2x²x³, y is the output, d l This indicates an unknown external disturbance, which exists. satisfy Where l = 1, 2, 3, 4, u d u represents the d-axis component of the stator voltage in a rotating coordinate system. q y 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 system's state vector, 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 3, characterized in that, The expression for the nonlinear dynamic fuzzy logic system is as follows: in It is the ideal weight, φ i (·) is the fuzzy basis vector with x as input, ε i It is the approximation error, which is determined by an unknown positive constant. As a boundary, requirements 5. The fault-tolerant control method according to claim 4, characterized in that, The expression for the state observer is as follows: in, Represents the estimated state variables This is an estimate of the output signal. for The estimated value, k i The intermediate values ​​are i = 2, 3, 4; The error of the state observer is defined as follows: The observation error of the permanent magnet synchronous motor system is: Where: 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 fault model expression for the intermittent actuator is as follows: u j (t)=β j (t)v j (t)+u f，jm (t) b j (t)=β j，s ,t∈[t j,s ,t j，s+1 ),s∈z + ; in, β j,s and It is an unknown constant, u f,jm (t) is a bounded signal, t∈[t] j,s ,t j,s+1 For s∈z + , z + Let t represent the set of positive integers. j,s and t j,s+1 v represents the start and end times of the actuator failure, respectively. j (t) is the input signal of the intermittent actuator.

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