Discrete fault-tolerant control method for permanent magnet synchronous motor with command filtering considering voltage fluctuation

Abstract

The present invention discloses a method for discrete fault-tolerant control of command filtering of a permanent magnet synchronous motor considering voltage fluctuation. The method comprises the following steps: step 1. establishing a discrete mathematical model of a synchronous motor system; step 2. considering voltage failure faults and voltage deviation faults to obtain a voltage fluctuation fault model; designing a new command filtering discrete fault-tolerant controller for a synchronous motor based on a neural network; step 3. selecting a Lyapunov function for derivation to prove that the control system designed by the controller in step 2 is Lyapunov stable. In view of the fact that permanent magnet synchronous motors are prone to voltage fluctuations, which may cause safety accidents and accuracy requirements, the present invention overcomes the computational complexity and causal contradiction problems existing in the backstepping control algorithm through a new command filtering technology; at the same time, the controller is designed in combination with the neural network adaptive technology to address the input voltage fluctuation problem, thereby eliminating the influence of voltage fluctuations on the system. The method of the present invention realizes fast and stable speed tracking control of the motor.

Description

Technical Field

[0001] The invention belongs to the technical field of speed tracking control of permanent magnet synchronous motors, and specifically discloses a command filtering discrete fault-tolerant control method for permanent magnet synchronous motors taking voltage fluctuation into consideration. Background Art

[0002] With the rapid development of information technology, automation technology and microelectronics technology, industrial and agricultural production and people's daily life have become more automated and intelligent. As a power equipment that is widely used in production and life and plays a huge role, the motor has attracted widespread attention and has developed rapidly due to its advantages such as low price, high reliability and good control accuracy. Permanent magnet synchronous motor has the advantages of high power efficiency, reliable operation and convenient maintenance, and has played a huge role in industrial and agricultural production. Permanent magnets generate the magnetic field of permanent magnet synchronous motors, thereby avoiding the excitation loss caused by the magnetic field generated by the excitation current, making the motor loss low, reducing production costs and improving the operating efficiency of the motor; permanent magnet synchronous motors have a large power factor, and the power factor is close to 1 when the motor is fully loaded, and it is independent of the level. The motor current is small and the copper consumption is small, which improves the reliability of the motor operation, so it is widely used in various fields. In industrial and agricultural production, a large number of production machinery require continuous single-direction operation at a roughly constant speed, such as fans, pumps, compressors, ordinary machine tools, etc. Permanent magnet synchronous motors have been widely used due to their low cost, simple and reliable structure, and convenient maintenance.

[0003] However, due to the highly nonlinear and multivariable characteristics of the mathematical model of the permanent magnet synchronous motor, and the operation of the permanent magnet synchronous motor is sensitive to factors such as parameter changes and external load disturbances, it is a challenging task to achieve effective control of the permanent magnet synchronous motor. In recent years, nonlinear control methods have made rapid progress, such as backstepping control, sliding mode control, adaptive control and some other advanced control methods. However, most of these technologies consider the continuous system of the permanent magnet synchronous motor, and there are few control algorithms for its discrete system. Since most actual engineering systems use discrete control technology, such as the field of digital computer control, and discrete control algorithms are superior to continuous algorithms in terms of feasibility and stability. Therefore, it is of great practical significance to construct a control method for the discrete system of the permanent magnet synchronous motor. On the other hand, when the permanent magnet synchronous motor starts, the voltage suddenly rises, exceeding the range that the equipment can bear, causing the performance of the control system to decline, resulting in equipment damage and even causing serious harm to personal safety, and the voltage needs to be constrained. Therefore, it is of practical significance to consider voltage fluctuations in the position control process of the permanent magnet synchronous motor. Summary of the invention

[0004] The purpose of the present invention is to propose a permanent magnet synchronous motor command filtering discrete fault-tolerant control method considering voltage fluctuations. The method takes into account the voltage fluctuation problem that is prone to occur in the operation of the permanent magnet synchronous motor discrete system, thereby realizing fast and stable speed tracking control of the motor.

[0005] In order to achieve the above object, the present invention adopts the following technical scheme:

[0006] The method for discrete fault-tolerant control of permanent magnet synchronous motor command filtering considering voltage fluctuation comprises the following steps:

[0007] Step 1. Establish a discrete mathematical model of the synchronous motor system;

[0008] Step 2. Considering voltage failure fault and voltage deviation fault, a voltage fluctuation fault model is obtained; a new command filter discrete fault-tolerant controller for synchronous motor is designed based on neural network to realize fault-tolerant control of permanent magnet synchronous motor;

[0009] Step 3. Select the Lyapunov function for derivation, and then prove the Lyapunov stability of the control system of the new command filter discrete fault-tolerant controller for synchronous motors designed based on neural networks in step 2.

[0010] The present invention has the following advantages:

[0011] 1. The method of the present invention is aimed at discrete-time systems. Compared with the control method of continuous-time systems, it has higher stability and feasibility and is widely used in the computer field.

[0012] 2. The application of the new command filter controller in the permanent magnet synchronous motor discrete system simplifies the complexity of the controller design, overcomes the problems of "causal contradiction" and "computational complexity", and achieves good control effect.

[0013] 3. Combined with engineering practice, the influence of voltage fluctuation failure that may occur in the permanent magnet synchronous motor system on the system is considered, and the controller is designed for the input voltage fluctuation problem by combining neural network adaptive technology to realize fault-tolerant control of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is an overall schematic diagram of the system overall controller and the system composite controlled object in an embodiment of the present invention.

[0015] Figure 2 It is a tracking response curve diagram of the speed of the permanent magnet synchronous motor after adopting the control method of the present invention.

[0016] Figure 3 The figure is a curve diagram of the q-axis voltage response of the permanent magnet synchronous motor after the control method of the present invention is adopted.

[0017] Figure 4 The figure is a curve diagram of the voltage response of the d-axis of the permanent magnet synchronous motor after the control method of the present invention is adopted.

[0018] Figure 5 The figure is a q-axis current response curve diagram of a permanent magnet synchronous motor after adopting the control method of the present invention.

[0019] Figure 6 It is a d-axis current response curve diagram of a permanent magnet synchronous motor after adopting the control method of the present invention. DETAILED DESCRIPTION

[0020] At present, the backstepping method has been widely used in permanent magnet synchronous motor control systems and has achieved good control effects. However, the traditional backstepping method is prone to "computational complexity" problems when repeatedly taking differences in virtual control variables.

[0021] Therefore, introducing command filtering technology in the process of controller design can effectively solve the above problems.

[0022] In addition, for some high-order systems with high nonlinearity and parameter uncertainty, the nonlinear terms will make the controller design very complicated, which is not conducive to the online control of computer control systems. Related studies have proposed approximate theories such as fuzzy logic systems (FLS) or neural networks (NN) to simplify the system and make the controller design simpler.

[0023] The basic concept of the present invention is: for a discrete mathematical model of a permanent magnet synchronous motor taking voltage fluctuation into consideration, a novel command filtering fault-tolerant control method is proposed to achieve tracking control of the desired speed of the system.

[0024] The novel instruction filtering fault-tolerant control method generally includes the following steps:

[0025] Firstly, a discrete model of permanent magnet synchronous motor system considering input voltage fluctuation is established.

[0026] Secondly, a new command filtering control method is used to deal with the problems of "causal contradiction" and "computational complexity" in the backstepping method, and the neural network adaptive technology is combined to design a controller for the input voltage fluctuation problem.

[0027] Finally, the Lyapunov stability theory is used to verify that the closed-loop system is semi-globally uniformly ultimately bounded.

[0028] Figure 1 Schematic diagram of a composite controlled object composed of a permanent magnet synchronous motor command filter discrete controller, a coordinate transformation unit and an SVPWM inverter considering voltage fluctuations in an embodiment of the present invention. * represents the preset rotor position, Θ represents the actual rotor position, ωr represents the rotor angular velocity, u d and u q represents the d-axis and q-axis voltages, and represents the voltage in the two-phase rotating coordinate system, U, V and W represent the three-phase AC voltage, i A 、i B and i C Indicates three-phase alternating current.

[0029] Figure 1 The components involved include a permanent magnet synchronous motor command filter discrete controller 1 considering voltage fluctuations, a coordinate transformation unit 2, an SVPWM inverter 3, a speed detection unit 4 and a current detection unit 5. The speed detection unit 4 and the current detection unit 5 are mainly used to detect the current value of the speed-related variable of the permanent magnet synchronous motor discrete system, and the voltage control is performed by the permanent magnet synchronous motor command filter discrete controller 1 considering voltage fluctuations through the actual measured current and speed variables as inputs, and finally converted into the position tracking control of the three-phase electric control permanent magnet synchronous motor.

[0030] In order to design a more effective controller, it is necessary to establish a discrete system model of permanent magnet synchronous motor.

[0031] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0032] The method for discrete fault-tolerant control of permanent magnet synchronous motor command filtering considering voltage fluctuation comprises the following steps:

[0033] Step 1. Establish a dynamic mathematical model of the permanent magnet synchronous motor discrete system.

[0034] In the synchronous rotating coordinate system, the dynamic mathematical model of the permanent magnet synchronous motor discrete system is expressed as:

[0035]

[0036] Where k is the number of steps of the permanent magnet synchronous motor discrete system.

[0037] ω(k) and ω(k+1) represent the angular velocities of the permanent magnet synchronous motor discrete system at the kth step and k+1th step, respectively.

[0038] i d (k), i d (k+1) represents the d-axis current of the permanent magnet synchronous motor discrete system at the kth step and k+1th step respectively.

[0039] i q (k), i q(k+1) represents the q-axis current of the permanent magnet synchronous motor discrete system at the kth step and k+1th step respectively.

[0040] u d (k) represents the nonlinear input of the k-th step d-axis of the permanent magnet synchronous motor discrete system.

[0041] u q (k) represents the k-th step q-axis saturated nonlinear input of the permanent magnet synchronous motor discrete system.

[0042] i d and i q Represent the d-axis and q-axis currents, u d and u q represent the d-axis and q-axis voltages respectively.

[0043] L d and L q represent the d-axis and q-axis stator side inductances respectively.

[0044] B represents the friction factor; Δ t represents the sampling time of the system, ω represents the rotor angular velocity of the permanent magnet synchronous motor, T L represents the load torque, J represents the moment of inertia, and p represents the number of magnetic pole pairs.

[0045] φ and R s They represent the magnetic flux generated by the permanent magnet and the stator equivalent resistance respectively.

[0046] In order to simplify the above permanent magnet synchronous motor discrete system dynamic mathematical model, namely formula (1), new variables are defined as follows:

[0047]

[0048] Refer to two types of voltage fluctuation fault models. The first is the voltage failure fault model, which is defined as:

[0049] u s (k) = (1-ρ)u(k);

[0050] Where ρ represents the loss rate of input voltage effectiveness, 0<ρ<1, u(k) represents the control signal to be designed, that is, the actuator input signal, u s (k) represents the actuator output signal.

[0051] The second is the voltage deviation fault model, which is defined as:

[0052] u s (k) = u(k) + l;

[0053] Here, l represents the unknown but bounded deviation.

[0054] The voltage fluctuation model of the permanent magnet synchronous motor system is given as:

[0055]

[0056] Among them, u qs (k) represents the actuator q-axis nonlinear output, u ds (k) represents the actuator d-axis nonlinear output; ρ q represents the loss rate of the actuator q-axis output voltage effectiveness, ρ d Indicates the loss rate of effectiveness of the actuator d-axis output voltage.

[0057] u q (k) represents the actuator q-axis nonlinear input, u d (k) represents the actuator d-axis nonlinear input.

[0058] l q Indicates the deviation of the actuator q-axis output voltage, l d Indicates the deviation of the actuator d-axis output voltage.

[0059] The discrete model of the permanent magnet synchronous motor considering voltage fluctuation is:

[0060]

[0061] Step 2. Based on the command filtering technology and the principle of backstepping, a command filtering discrete fault-tolerant controller for permanent magnet synchronous motors considering voltage fluctuations is designed. The dynamic mathematical model of the permanent magnet synchronous motor discrete system is simplified into two independent subsystems, namely, the state variables x1(k), x2(k) and the q-axis nonlinear input u qs (k) as the input signal of the subsystem and the state variable x3(k) and the d-axis nonlinear input u ds (k) Subsystem composed of input signals.

[0062] Assume that f(Z) is in a compact set Ω Z is a continuous function, there exists a radial basis function neural network W T S(Z) makes:

[0063] f(Z)=W T S(Z)+τ.

[0064] Where τ is the approximation error and satisfies |τ|≤ε, and ε is an arbitrarily small positive constant; is the input vector, q is the neural network input dimension, R q is a real vector set, Ω z represents a compact set.

[0065] W∈R his the weight vector, the number of neural network nodes h is a positive integer, and h>1, R h is a set of real vectors; S(Z)=[s1(Z),...,s h (Z)] T ∈R h is the basis function vector; s c (Z) is a Gaussian function, expressed as:

[0066]

[0067] Where c = 1, ..., h, μ c is the Gaussian function s c (Z) The center of the receptive field, η c is the Gaussian function s c (Z) width.

[0068] The command filter is defined as shown in the following formula (3):

[0069]

[0070] Among them, the system error e1(k) is the filter input, is the filter output, ω c represents a positive parameter of the design.

[0071] The system errors e1(k), e2(k), and e3(k) are defined as:

[0072]

[0073] Among them, x 1d (k) is the given desired signal, and the virtual control function α1(k) is the input signal of the command filter.

[0074] In each step of the discrete control method, a Lyapunov function is selected to construct a virtual control function. The specific process is as follows:

[0075] Step 2.1. Define the error

[0076] According to the error variable e1(k)=x1(k)-x 1d (k) obtain:

[0077]

[0078] Select the Lyapunov function Differentiating V1(k) gives ΔV1(k), which is:

[0079]

[0080] Where N is a positive number; the virtual control function α1(k) is constructed as:

[0081]

[0082] According to the virtual control function α1(k) and formula (4), using Young's inequality, we can get:

[0083]

[0084] Step 2.2. According to the error variable e2(k)=x2(k)-α1(k), we get:

[0085] e2(k+1)=f2(k)+a4Δ t [(1-ρ q ) q (k)+l q ];

[0086] Where, f2(k)=(1+a1Δ t )x2(k)+a2Δ t x1(k)+a3Δ t x1(k)x3(k)-α1(k+1).

[0087] Select the Lyapunov function Then, by differentiating V2(k), we can obtain ΔV2(k), that is:

[0088]

[0089] According to the RBF neural network approximation theorem, for any value d2>0, the RBF neural network is designed

[0090] make

[0091] Where Z2(k)=[x1(k),x2(k),x3(k)] T , τ2 is the approximation error, and satisfies |τ2|≤d2.

[0092] Select the control law and adaptive law as:

[0093]

[0094]

[0095] Among them, γ2 and δ2 are bounded positive constants; Represents the weight vector The norm of is the estimated value of η2, is the estimation error.

[0096] Substituting formula (7) into formula (6), we can obtain the following equation using Young's inequality:

[0097]

[0098] Step 2.3. Based on the error variable e3(k)=x3(k), we get: e3(k+1)=f3(k)+b3Δ t [(1-ρ d ) d (k)+l d ].

[0099] Where, f3(k)=(1+b1Δ t )x3(k)+b2Δ t x1(k)x2(k).

[0100] Select the Lyapunov function:

[0101] Where A>0, taking the difference of V3(k) we get ΔV3(k), that is:

[0102]

[0103] According to the RBF neural network approximation theorem, for any value d3>0, the RBF neural network is designed

[0104] make

[0105] Where Z3(k)=[x1(k),x2(k),x3(k)] T , τ3 is the approximation error, and satisfies |τ3|≤d3.

[0106] Select the control law and adaptive law as:

[0107]

[0108]

[0109] Among them, γ3 and δ3 are bounded positive constants; Represents the weight vector The norm of is the estimated value of η3, is the estimation error.

[0110] Substituting formula (11) into formula (10), we can obtain the following equation using Young's inequality:

[0111]

[0112] Substituting formula (5) and formula (9) into formula (13), we get:

[0113]

[0114] Step 3. Perform stability analysis on the discrete fault-tolerant controller for permanent magnet synchronous motor command filtering considering voltage fluctuations.

[0115] definition Then ε1(k)=C(k)-C(k+1).

[0116] Select the Lyapunov function:

[0117]

[0118] Then the first-order difference equation of V(k) is:

[0119]

[0120] according to have to:

[0121]

[0122] Using Young's inequality and ||S j (Z j (k))|| 2 ≤m j ,j=2,3, we get:

[0123]

[0124] Among them, m j represents any positive constant, j = 2, 3; Substituting formula (18) into formula (17), we get:

[0125]

[0126]

[0127] Define λ(k)=e1(k)-e1(k+1), and we get C(k+1)=(1-Δ t ω c )C(k)+λ(k), and then we get:

[0128]

[0129] Select parameter Δ t and ω c So that:

[0130] From formula (21), we know that

[0131] Substituting formulas (19), (20), and (21) into formula (16), we obtain:

[0132]

[0133] in:

[0134]

[0135]

[0136]

[0137]

[0138] Select the design parameter Δ t ,ω c , A, N, γ2, γ3, δ2, δ3, such that:

[0139]

[0140] From formula (22), we know that when the error formula and holds, and we further obtain ΔV(k)≤0, and then we know that for Established.

[0141] Therefore, the system error e1(k) converges to a sufficiently small neighborhood of the origin, and the closed-loop system is semi-globally consistent and ultimately bounded.

[0142] The present invention aims to solve the problem of voltage fluctuation in permanent magnet synchronous motors, which may easily lead to safety accidents and accuracy requirements. The present invention overcomes the computational complexity and causal contradiction problems in backstepping control through command filtering technology. At the same time, the controller is designed in combination with neural network adaptive technology to solve the problem of input voltage fluctuation, thereby eliminating the influence of voltage fluctuation on the system.

[0143] In order to verify the effectiveness of the proposed control method, a permanent magnet synchronous motor servo system is experimentally verified.

[0144] The LINKS-PMSM1.0 AC servo experimental platform is used to simulate input voltage fluctuation faults to verify the effectiveness of the designed fault-tolerant instruction filtering control method and analyze it. The platform consists of a synchronous motor, a servo drive and a simulation host.

[0145] The rated speed of the permanent magnet synchronous motor is 1000r / min, the rated torque is 15N / m, the rated power is 1.5kW, and the rated current is 7.3A. The control method is written in Matlab of the simulation host and runs on the synchronous motor after compilation.

[0146] The experimental sampling time is set to Δ t =0.0002s.

[0147] Given load torque:

[0148] Reference speed:

[0149] Input voltage failure fault:

[0150] Input voltage deviation fault:

[0151] During the experiment, the RBF neural network was designed It contains 11 nodes, the centers are evenly distributed in the interval [-10, 10] and the width is 2. The fault-tolerant command filter controller parameters are:

[0152] ω c =0.8, γ2=0.02, γ3=0.005, δ2=0.000006, δ3=0.000006.

[0153] like Figures 2 to 6 The experimental results are shown, where: Figure 2 It can be seen that the actual speed quickly reaches the set value after the motor starts. When the load torque and the expected speed are changed at the same time at 10s, the actual speed can still effectively track the set value. When the input voltage fluctuation fault is simulated at 20s, the actual speed drops significantly and then recovers to the state before the fault in a short time, indicating that the designed fault-tolerant controller has strong robustness. Figure 3 and Figure 4 It can be seen that after the motor is started, the q-axis and d-axis voltages remain stable and within a reasonable range. Figure 5 and Figure 6 It can be seen that after the motor is started, the q-axis and d-axis currents remain stable and within a reasonable range. The above experimental results show that the method of the present invention can effectively reduce the adverse effects of voltage fluctuations, with small speed tracking errors and good tracking effects. The experimental signals clearly show that the method of the present invention can quickly and stably track the reference signal under voltage fluctuations, thereby ensuring fast and smooth operation of the motor.

[0154] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A discrete fault-tolerant control method for permanent magnet synchronous motor command filtering considering voltage fluctuations, characterized in that: The steps include: Step 1. Establish a dynamic mathematical model of the permanent magnet synchronous motor discrete system; In the synchronous rotating coordinate system, the dynamic mathematical model of the permanent magnet synchronous motor discrete system is expressed as: Where k is the number of steps of the permanent magnet synchronous motor discrete system; ω(k) and ω(k+1) represent the angular velocities of the k-th and k+1-th steps of the permanent magnet synchronous motor discrete system, respectively; i d (k), i d (k+1) represents the d-axis current of the kth step and k+1th step of the permanent magnet synchronous motor discrete system respectively; i q (k), i q (k+1) represents the q-axis current of the k-th step and k+1-th step of the permanent magnet synchronous motor discrete system respectively; u d (k) represents the nonlinear input of the k-th step d-axis of the permanent magnet synchronous motor discrete system; u q (k) represents the k-th step q-axis saturation nonlinear input of the permanent magnet synchronous motor discrete system; i d and i q Represent the d-axis and q-axis currents, u d and u q denote the d-axis and q-axis voltages respectively; L d and L q denote the d-axis and q-axis stator side inductances respectively; B represents the friction factor, Δ t represents the sampling time of the system, ω represents the rotor angular velocity of the permanent magnet synchronous motor, T L represents the load torque, J represents the moment of inertia, and p represents the number of magnetic pole pairs; φ and R s They represent the flux generated by the permanent magnet and the stator equivalent resistance respectively; In order to simplify the above permanent magnet synchronous motor discrete system dynamic mathematical model, namely formula (1), new variables are defined as follows: The first is the voltage failure fault model, which is defined as: in s (k)=(1-ρ)u(k); Where ρ represents the loss rate of input voltage effectiveness, 0<ρ<1, u(k) represents the control signal to be designed, that is, the actuator input signal, u s (k) represents the actuator output signal; The second is the voltage deviation fault model, which is defined as: in s (k)=u(k)+l; Among them, l represents the unknown but bounded deviation; The voltage fluctuation model of the permanent magnet synchronous motor system is given as: Among them, u qs (k) represents the actuator q-axis nonlinear output, u ds (k) represents the actuator d-axis nonlinear output; ρ q represents the loss rate of the actuator q-axis output voltage effectiveness, ρ d Indicates the loss rate of the actuator d-axis output voltage effectiveness; u q (k) represents the actuator q-axis nonlinear input, u d (k) represents the actuator d-axis nonlinear input; l q Indicates the deviation of the actuator q-axis output voltage, l d Indicates the deviation of the actuator d-axis output voltage; The discrete model of the permanent magnet synchronous motor considering voltage fluctuation is: Step 2. Design a command filter discrete fault-tolerant controller for permanent magnet synchronous motor considering voltage fluctuations based on command filtering technology and backstepping principle; the dynamic mathematical model of the permanent magnet synchronous motor discrete system is simplified into two independent subsystems, namely, the state variables x1(k), x2(k) and the q-axis nonlinear input u qs (k) as the input signal of the subsystem and the state variable x3(k) and the d-axis nonlinear input u ds (k) a subsystem consisting of input signals; Assume that f(Z) is in a compact set Ω Z is a continuous function, there exists a radial basis function neural network W T S(Z) makes: f(Z)=W T S(Z)+τ; Where τ is the approximation error and satisfies |τ|≤ε, and ε is an arbitrarily small positive constant; is the input vector, q is the neural network input dimension, R q is a real vector set, Ω z represents a compact set; W∈R h is the weight vector, the number of neural network nodes h is a positive integer, and h>1, R h is a set of real vectors; S(Z)=[s1(Z),...,s h (Z)] T ∈R h is the basis function vector; s c (Z) is a Gaussian function, expressed as: Where c = 1, ..., h, μ c is the Gaussian function s c (Z) The center of the receptive field, η c is the Gaussian function s c (Z) width; The command filter is defined as shown in the following formula (3): Among them, the system error e1(k) is the filter input, is the filter output, ω c represents a positive parameter of the design; The system errors e1(k), e2(k), and e3(k) are defined as: Among them, x 1d (k) is the given desired signal, and the virtual control function α1(k) is the input signal of the command filter; In each step of the discrete control method, a Lyapunov function is selected to construct a virtual control function. The specific process is as follows: Step 2.

1. Define the error According to the error variable e1(k)=x1(k)-x 1d (k) obtain: Select the Lyapunov function Differentiating V1(k) gives ΔV1(k), which is: Where N is a positive number; the virtual control function α1(k) is constructed as: According to the virtual control function α1(k) and formula (4), using Young's inequality, we can get: Step 2.

2. According to the error variable e2(k)=x2(k)-α1(k), we get: e2(k+1)=f2(k)+a4Δ t [(1-ρ q )u q (k)+l q ]; where, f2(k) = (1 + a1Δ t )x2(k) + a2Δ t x1(k) + a3Δ t x1(k)x3(k) - α1(k + 1); Select the Lyapunov function Then, by differentiating V2(k), we can obtain ΔV2(k), that is: According to the RBF neural network approximation theorem, for any value d2>0, the RBF neural network is designed Where Z2(k)=[x1(k),x2(k),x3(k)] Τ , τ2 is the approximation error, and satisfies |τ2|≤d2; Select the control law and adaptive law as: Among them, γ2 and δ2 are bounded positive constants; Represents the weight vector The norm of is the estimated value of η2, is the estimation error; Substituting formula (7) into formula (6), we can obtain the following equation using Young's inequality: Step 2.

3. Based on the error variable e3(k)=x3(k), we get: e3(k+1)=f3(k)+b3Δ t [(1-ρ d ) d (k)+l d ]; Where, f3(k)=(1+b1Δ t )x3(k)+b2Δ t x1(k)x2(k); Select the Lyapunov function: Where A>0, taking the difference of V3(k) we get ΔV3(k), that is: According to the RBF neural network approximation theorem, for any value d3>0, the RBF neural network is designed make Where Z3(k)=[x1(k),x2(k),x3(k)] Τ , τ3 is the approximation error, and satisfies |τ3|≤d3; Select the control law and adaptive law as: Among them, γ3 and δ3 are bounded positive constants; Represents the weight vector The norm of is the estimated value of η3, is the estimation error; Substituting formula (11) into formula (10), we can obtain the following equation using Young's inequality: Substituting formula (5) and formula (9) into formula (13), we get: Step 3. Perform stability analysis on the discrete fault-tolerant controller for permanent magnet synchronous motor command filtering considering voltage fluctuations.

2. The method for discrete fault-tolerant control of permanent magnet synchronous motor command filtering considering voltage fluctuation according to claim 1 is characterized in that: In step 3, the stability analysis process is as follows: definition Then ε1(k)=C(k)-C(k+1); Select the Lyapunov function: Then the first-order difference equation of V(k) is: according to have to: Using Young's inequality and have to: Among them, m j represents any positive constant, j = 2, 3; Substituting formula (18) into formula (17), we get: Define λ(k)=e1(k)-e1(k+1), and we get C(k+1)=(1-Δ t ω c )C(k)+λ(k), and then we get: Select parameter Δ t and ω c So that: From formula (21), we know that Substituting formulas (19), (20), and (21) into formula (16), we obtain: in: Select the design parameter Δ t ,ω c , A, N, γ2, γ3, δ2, δ3, such that: From formula (22), we know that when the error formula and holds, and we further obtain ΔV(k)≤0, and then we know that for Established; Therefore, the system error e1(k) converges to a sufficiently small neighborhood of the origin, and the closed-loop system is semi-globally consistent and ultimately bounded.

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