Fixed time convergence dynamic surface counter electromotive force observation method and system of permanent magnet synchronous motor

Abstract

The invention discloses a fixed time convergence dynamic surface counter electromotive force observation method and system of a permanent magnet synchronous motor, and belongs to the field of permanent magnet synchronous motor sensorless control, and the method comprises the steps: constructing a virtual control law of an observer according to a semi-global fixed time consistent final bounded stability theory and a sliding mode theory; the actual control input of the observer is constructed by adopting a backstepping method, parameter adjustment is carried out on the observer to obtain an optimal observer, the back electromotive force of the permanent magnet synchronous motor is converged according to the optimal observer, and the dynamic response performance of the motor is improved; according to the method, the defect of unstable convergence of a traditional observer is overcome, and a solution with high robustness and wide adaptability is provided for permanent magnet synchronous motor control.

Description

Technical Field

[0001] The present invention relates to the field of sensorless control of permanent magnet synchronous motors, and specifically to a fixed-time convergence dynamic surface back electromotive force observation method and system for permanent magnet synchronous motors. Background Technique

[0002] Sensorless control technology is used to solve the problem that accurate motor position and speed information are required in the vector control process, while the traditional method is to use mechanical sensors such as resolvers and encoders, which will increase costs and reduce system reliability. The most effective way to solve this problem is to apply sensorless control technology. In sensorless control technology, model-based methods are a major category commonly used for medium and high speeds, and their main method is to output estimated values by correcting the mathematical model to approach the real model. Among many models, the extended back electromotive force has been widely used due to its advantages of simple and reliable model.

[0003] In model-based methods, sliding mode observers have been widely used due to their high robustness to motor parameters, but a major disadvantage of traditional sliding mode observers is that they cannot guarantee finite-time convergence because the derivative of the current error is non-zero, which will lead to position estimation errors.

[0004] Fixed-time stability is a further extension of finite-time stability, which can guarantee fixed-time convergence. Different from finite-time stability, the upper bound of the convergence time of fixed-time stability no longer depends on the initial conditions, but only on the design parameters. Therefore, stability can be achieved within a fixed upper bound in a finite time under any initial conditions through parameter design. This advantage has greatly promoted the application of fixed-time stability, but existing fixed-time stable observation methods are usually limited to low-order systems or only for disturbance observation, and cannot be applied to the fixed-time stable state observation of high-order systems. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a fixed-time convergence dynamic surface back electromotive force observation method and system for permanent magnet synchronous motors, realizing the fixed-time stable state observation of high-order systems.

[0006] The present invention is realized through the following technical solutions:

[0007] A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor includes the following processes:

[0008] Step 1: Construct an observer for the extended back electromotive force according to the current and voltage of the motor;

[0009] Step 2: Construct a virtual control law for the observer according to the semi-global fixed-time uniform ultimate bounded stability theory and sliding mode theory;

[0010] Step 3: Construct the actual control input of the observer using the backstepping method. The construction method of the actual control input is as follows:

[0011] Based on the basic form of the semi-global fixed-time uniform ultimate bounded stability theory and combined with the auxiliary error of the observer, construct a new state variable, which makes the auxiliary error converge when it is fixed;

[0012] Construct an error dynamic surface according to the new state variable and the extended back electromotive force, and make the estimated back electromotive force converge to the new state variable within the upper bound of the fixed convergence time according to the error dynamic surface;

[0013] Construct the actual control input of the observer according to the error dynamic surface, and make the error dynamic surface converge when it is fixed according to the actual control input;

[0014] Step 4: Adjust the parameters of the observer obtained in Step 3 to obtain an optimal observer, and make the back electromotive force of the permanent magnet synchronous motor converge according to the optimal observer to improve the dynamic response performance of the motor.

[0015] Preferably, the observer for constructing the extended back electromotive force according to the current and voltage of the motor in Step 1 includes:

[0016] Obtain the current and voltage of the actual stator of the motor;

[0017] Construct the dynamic equation of the extended back electromotive force model in the αβ coordinate system of the permanent magnet synchronous motor according to the current and voltage of the actual stator;

[0018] Construct an observer according to the dynamic equation of the extended back electromotive force model.

[0019] Preferably, the expression of the observer is as follows:

[0020]

[0021] where the superscript ^ represents the estimation of the actual state, κ is the virtual control law, ν is the control input, L d , L q represent the dq-axis inductances, R represents the stator resistance, J is the useful torque, ω e is the electrical angular velocity, and E is the extended back electromotive force.

[0022] Preferably, the virtual control law is as follows:

[0023]

[0024] In the formula: the superscript "-" represents the error term,, k1, k2 respectively represent the gains to be designed, and ρ1, ζ1 are positive odd constants.

[0025] Preferably, the determination of the auxiliary error in Step 3 includes:

[0026] Determine the auxiliary error based on the extended back electromotive force and the virtual control law.

[0027] Preferably, the actual control input ν in step 3 is as follows:

[0028]

[0029] Where k3 and k4 respectively represent the gains to be designed, ε is the error dynamic surface, and φ is the state variable.

[0030] Preferably, the parameters of the observer in step 4 are adjusted. The parameters for adjustment are the gain and time constant of the observer. On the premise of system stability, select a sufficiently large k i And a sufficiently small γ1 to make the system satisfy the semi - global fixed - time uniform ultimate bounded stability condition.

[0031] A fixed - time convergence dynamic - surface back - electromotive - force observation system for a permanent - magnet synchronous motor, comprising:

[0032] An observer module, configured to construct an observer for the extended back electromotive force based on the current and voltage of the motor;

[0033] A virtual control law module, configured to construct the virtual control law of the observer according to the semi - global fixed - time uniform ultimate bounded stability theory and the sliding - mode theory;

[0034] A backstepping module, configured to construct the actual control input of the observer by using the backstepping method. The construction method of the actual control input is as follows:

[0035] Based on the basic form of the semi - global fixed - time uniform ultimate bounded stability theory and combined with the auxiliary error of the observer, construct a new state variable, and the new state variable makes the auxiliary error converge when fixed;

[0036] Construct an error dynamic surface according to the new state variable and the extended back electromotive force, and make the estimated back electromotive force converge to the new state variable within the upper bound of the fixed convergence time according to the error dynamic surface;

[0037] Construct the actual control input of the observer according to the error dynamic surface, and make the error dynamic surface converge when fixed;

[0038] An optimization module, configured to adjust the parameters of the observer to obtain an optimal observer, and make the back electromotive force of the permanent - magnet synchronous motor converge according to the optimal observer, so as to improve the dynamic response performance of the motor.

[0039] An electronic device, comprising:

[0040] A memory, configured to store a computer program;

[0041] A processor, which is used to implement the steps of the fixed-time convergence dynamic surface back electromotive force observation method for the permanent magnet synchronous motor when executing the computer program.

[0042] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the steps of the fixed-time convergence dynamic surface back electromotive force observation method for the permanent magnet synchronous motor.

[0043] Compared with the prior art, the present invention has the following beneficial technical effects:

[0044] A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor provided in this application combines the dynamic surface control technology with a high-order sliding mode observer, and introduces the semi-global fixed-time uniform ultimate bounded stability theory to construct a second-order back electromotive force observer applicable to high-order systems. The core of this method lies in: firstly, constructing an extended back electromotive force observer dynamic equation based on the motor current and voltage; secondly, designing a virtual control law through the sliding mode theory and the semi-global fixed-time stability theory, and combining the backstepping method to construct the actual control input, so that the auxiliary error converges within the upper bound of the fixed time; further, the fast and stable convergence of the estimated back electromotive force is realized through the design of the error dynamic surface, and the upper limit of its convergence time is only determined by design parameters such as the observer gain and time constant, and has nothing to do with the initial state of the system. Compared with the traditional sliding mode observer, this method not only solves the problem that the finite-time convergence depends on the initial conditions, but also effectively suppresses the chattering phenomenon through the high-order sliding mode design. Experimental verification shows that it can maintain high-precision back electromotive force estimation under no-load, loaded, and sudden load conditions in the full speed range (500 - 2000 rpm), and the dynamic response speed is significantly improved, especially the performance advantage is more prominent under low-speed conditions.

[0045] This application also proposes a fixed-time convergence dynamic surface back electromotive force observation system for a permanent magnet synchronous motor, an electronic device, and a computer storage medium, which have all the advantages of the above-mentioned fixed-time convergence dynamic surface back electromotive force observation method for the permanent magnet synchronous motor. Description of the Drawings

[0046] In order to more clearly illustrate the technical solutions of the embodiments of this application, the following will briefly introduce the drawings required to be used in the embodiments. It should be understood that the following drawings only show some embodiments of this application, and therefore should not be regarded as a limitation of the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0047] Figure 1 It is the structural block diagram of the fixed-time convergence dynamic surface back electromotive force observer of the present invention;

[0048] Figure 2The experimental waveform of the back electromotive force measured by the observer of the present invention under no-load conditions at 500 rpm of the motor.

[0049] Figure 3 The experimental waveform of the back electromotive force measured by the observer of the present invention under 50% rated load conditions at 2000 rpm of the motor.

[0050] Figure 4 The dynamic response experimental waveform of the back electromotive force measured by the observer of the present invention when suddenly applying 50% rated load at 2000 rpm.

[0051] Figure 5 The experimental waveforms of the rotational speed, angle error, and load torque measured by the observer of the present invention.

[0052] Figure 6 The experimental waveforms of the rotational speed, angle error, and load torque measured by the traditional second-order sliding mode observer. Detailed implementation manners

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. Components of the embodiments of the present application usually described and illustrated in the drawings here can be arranged and designed in various different configurations.

[0054] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the present application claimed, but merely represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts fall within the scope of protection of the present application.

[0055] A fixed-time convergence dynamic surface observation method for back electromotive force observation of a permanent magnet synchronous motor, comprising the following steps:

[0056] Step 1: Collect the current actual stator current i and voltage u of the motor.

[0057] Step 2: Construct the dynamic equation of the extended back electromotive force model in the αβ coordinate system of the permanent magnet synchronous motor according to the collected data, as follows:

[0058]

[0059] In the formula: L d , L q represent the dq-axis inductances; R represents the stator resistance, J is a utility matrix satisfying ω e is the electrical angular velocity; E is the extended back electromotive force, and its dynamic equation is:

[0060]

[0061] Then, an observer is constructed according to the dynamic equation of the extended back electromotive force model as follows:

[0062]

[0063] Where: the superscript ^ represents the estimation of the actual state; κ is the virtual control law; ν is the control input.

[0064] Step 3: According to the semi-global fixed-time uniform ultimate bounded stability theory and the sliding mode theory, construct the virtual control law κ in the observer.

[0065] To achieve the fixed-time convergence of the state observed by the above observer, combining the semi-global fixed-time uniform ultimate bounded stability theory and the sliding mode theory, the virtual control law κ in the observer is designed as follows:

[0066]

[0067] Where: the superscript "-" represents the error term. For example, represents the current error, satisfying k1 and k2 respectively represent the gains to be designed, which are sufficiently large positive constants; ρ1 and ζ1 are positive odd constants, satisfying ρ1 > ζ1 and (ρ1 + ζ1) / 2 is a positive odd constant; sign() is the standard sign function.

[0068] Step 4: Design the actual control input ν of the observer through the backstepping method.

[0069] S4.1. Determine the auxiliary error χ according to the extended back electromotive force and the virtual control law as follows:

[0070]

[0071] S4.2. Based on the basic form of the semi-global fixed-time uniform ultimate bounded stability theory and combined with the auxiliary error, construct a new state variable φ, which makes the auxiliary error χ converge when fixed.

[0072]

[0073] Where: γ1 is the time constant, satisfying 1 > γ1 > 0. Sufficiently large k1, k2 and sufficiently small γ1 can make the system stable.

[0074] S4.3. Construct the error dynamic surface ε according to the new state variable φ and the extended back electromotive force. The error dynamic surface ε makes the estimated back electromotive force converge to the new state variable φ within the upper bound of the fixed convergence time.

[0075]

[0076] S4.4. Construct the actual control input ν in the observer according to the error dynamic surface ε. The actual control input ν can make the error dynamic surface ε converge when it is fixed. The actual control input ν is as follows:

[0077]

[0078] where: k3 and k4 respectively represent the gains to be designed, which are sufficiently large positive constants.

[0079] Step 5: Adjust the parameters of the observer to obtain the optimal observer, and make the back electromotive force of the permanent magnet synchronous motor converge according to the optimal observer, so as to improve the dynamic response performance of the motor.

[0080] For the convenience of applying the designed observer in the actual control system, the parameter adjustment guidance of the observer is as follows:

[0081] Increase the gain k i , i = 1, 2, 3, 4 helps to reduce the upper bound of the convergence time; reducing the time constant γ1 helps to reduce the upper bound of the convergence time, thereby accelerating the convergence of the estimated state. However, too small a time constant γ1 will cause the measurement noise to be amplified, so that the accurate differential value cannot be obtained. Therefore, choosing a sufficiently large k i and a sufficiently small γ1 under the premise of not affecting the system stability can make the system satisfy the semi-global fixed-time uniform ultimate bounded stability condition. This will force all estimated states to converge to their actual values within the fixed upper bound time. The upper bound of the system convergence time is inversely proportional to the difference between the positive odd constants ρ1 and ζ1. Since the designed observer is designed to observe the extended back electromotive force E, and the electrical response time depends on the switching frequency, and the switching frequency is usually high, the difference between the positive odd constants ρ1 and ζ1 can be relatively large to ensure faster convergence.

[0082] The stability proof and the calculation of the upper bound of the convergence time of the above observation method are given below. For the convenience of subsequent derivation, the following lemma is introduced:

[0083] Lemma 1: Consider the differential system: x(0) = x0, assume that there exists an equation V(x): U → R satisfying:

[0084] (1) V(x) is positive definite;

[0085] (2) There exist positive constants α, β, arbitrarily small positive real numbers ε, positive odd integers m, n, p, q satisfying m > n, p < q, and a compact set W0 such that x0 ∈ W0 holds.

[0086] Then the system x(0) = x0 satisfies semi - globally fixed - time uniformly ultimately bounded stability, and the system satisfies V(t) ≤ 2γ1 within a finite time, and and the upper - bound of the convergence time is

[0087] Lemma 2: For any positive real numbers a, b, c and p, q satisfying 1 / p + 1 / q = 1, we have:

[0088] Considering the constructed observer (11), for the convenience of subsequent stability analysis, rewrite the derivative of the estimated output current as follows:

[0089]

[0090] For the following analysis, construct the Lyapunov function as follows:

[0091]

[0092] where: V = [V α V β T . It should be noted that the DSP processing frequency is much higher than the current change frequency. Therefore, within one processing cycle, it can be considered that Therefore, the derivative of V can be written as:

[0093]

[0094] Then, according to Lemma 2, there is the following inequality:

[0095]

[0096] where: λ1, η1 are positive real numbers, Substitute Equation (20) into (19), then we have:

[0097]

[0098] Next, reasonably select the parameters such that: holds.

[0099] Then select the following coefficients:

[0100]

[0101] where: Substitute Equation (22) into (21), then we have:

[0102]

[0103] ​According to (23), the system is stable when parameters are reasonably selected to make the following inequality hold:

[0104]

[0105] Then, the upper bound of the convergence time of the closed-loop system can be obtained by solving the following equation:

[0106]

[0107] The approximate solution of equation (25) can be obtained by solving the following inequality:

[0108]

[0109] Then, from equation (26) and according to Lemma 1, the upper bound of the convergence time of the closed-loop system of the observer is:

[0110]

[0111] Thus, the stability proof and the calculation of the upper bound of the convergence time are completed. The results prove that the observer designed by this method can indeed achieve convergence within the fixed upper bound of the convergence time, and this upper bound of the convergence time only depends on the designed parameters and is independent of the initial state and parameters of the system, thereby improving the dynamic response of the observer.

[0112] Refer to Figures 2 - 6, Figure 2 is the experimental waveform of the back electromotive force measured by the observer when the motor is no-load at 500 rpm. It can be seen from the estimated back electromotive force waveform shown in the figure that an accurate estimated back electromotive force can be obtained under no-load conditions at medium and low speeds; Figure 3 is the experimental waveform of the back electromotive force measured by the observer when the motor is at 2000 rpm with 50% rated load, showing that an accurate estimated back electromotive force can be obtained at medium and high speeds with load; Figure 4 is the dynamic response experimental waveform of the back electromotive force measured by the observer when a 50% rated load is suddenly applied at 2000 rpm, showing the convergence speed and dynamic performance of the observer of the present invention; Figure 5 is the experimental waveform of the rotational speed, angle error, and load torque measured by the observer. The given value of the motor rotational speed slowly decreases from 3000 rpm to 300 rpm. After a certain period of time, the speed given value rises to 3000 rpm with the same slope.

[0113] Figure 6 is the experimental waveform of the rotational speed, angle error, and load torque measured by the traditional second-order sliding mode observer. The given value of the motor rotational speed is Figure 5 kept consistent. By comparing Figure 5 and Figure 6, it can be seen that although the traditional method shows satisfactory performance at high speeds, its performance will rapidly decline as the rotational speed decreases. The observer of the present invention shows better convergence performance in a wider range of rotational speeds, providing a smaller estimation error.

[0114] This application uses fixed-time stability combined with dynamic surface design for the observer, which solves one of the main drawbacks of the traditional sliding mode observer, namely the convergence problem. The observer designed by this method can achieve convergence within a fixed upper bound of the convergence time, and this upper bound of the convergence time depends only on the designed parameters and is independent of the initial state and parameters of the system, thereby improving the dynamic response of the observer. At the same time, due to the use of high-order sliding mode design, it also has a certain inhibitory effect on the inherent chattering phenomenon of the traditional sliding mode observer.

[0115] Based on the above fixed-time convergence dynamic surface back electromotive force observation method for permanent magnet synchronous motors, correspondingly, this application also provides a fixed-time convergence dynamic surface back electromotive force observation system for permanent magnet synchronous motors, which may include:

[0116] An observer module, used to construct an observer for the extended back electromotive force according to the current and voltage of the motor;

[0117] A virtual control law module, used to construct the virtual control law of the observer according to the semi-global fixed-time uniform ultimate bounded stability theory and the sliding mode theory;

[0118] A backstepping module, used to construct the actual control input of the observer by using backstepping. The construction method of the actual control input is as follows:

[0119] Based on the basic form of the semi-global fixed-time uniform ultimate bounded stability theory and combined with the auxiliary error of the observer, a new state variable is constructed, and this new state variable enables the auxiliary error to converge in fixed time;

[0120] According to the new state variable and the extended back electromotive force, an error dynamic surface is constructed, and according to the error dynamic surface, the estimated back electromotive force converges to the new state variable within the fixed upper bound of the convergence time;

[0121] According to the error dynamic surface, the actual control input of the observer is constructed, and according to the actual control input, the error dynamic surface converges in fixed time;

[0122] An optimization module, used to adjust the parameters of the observer to obtain an optimal observer, and according to the optimal observer, the back electromotive force of the permanent magnet synchronous motor converges, improving the dynamic response performance of the motor.

[0123] A fixed-time convergence dynamic surface back electromotive force observation system for a permanent magnet synchronous motor according to the present application. This system introduces the dynamic surface into the high-order sliding mode and introduces the semi-global fixed-time uniform ultimate bounded stability into the backstepping dynamic surface design, and then constructs a second-order back electromotive force observer. The upper limit of the convergence time of this observation method depends only on the design parameters, enabling the system to reach convergence within a finite time with a fixed upper time limit under any initial conditions. It should be noted that in several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of each module is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules can be combined or integrated into another device, or some features can be ignored or not executed. The modules described as separate components may or may not be physically separated. The components shown as modules can be one physical unit or multiple physical units, that is, they can be located in one place or distributed to multiple different places. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0124] In addition, in each embodiment of the present invention, the modules can be integrated in a processing unit, or each module can exist physically alone, or two or more modules can be integrated in a unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

[0125] An electronic device provided by an embodiment of the present application includes a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps of the fixed-time convergence dynamic surface back electromotive force observation method for the permanent magnet synchronous motor described in any one of the above embodiments are implemented.

[0126] Another electronic device provided by an embodiment of the present application may further include: an input port connected to the processor for transmitting multi-modal data collected by an external acquisition device to the processor; and a display unit connected to the processor for displaying the processing result of the processor to the outside; a communication module connected to the processor for realizing the communication between the electronic device and the outside. The display unit can be a display panel, a laser scanning display, etc.; the communication methods adopted by the communication module include but are not limited to Mobile High-Definition Link technology (HML), Universal Serial Bus (USB), High-Definition Multimedia Interface (HDMI), wireless connection (including Wireless Fidelity technology (WiFi), Bluetooth communication technology, Low-Energy Bluetooth communication technology, communication technology based on IEEE802.11s).

[0127] A computer-readable storage medium provided by an embodiment of the present application stores a computer program. When the computer program is executed by a processor, the steps of the fixed-time convergence dynamic surface back electromotive force observation method of the permanent magnet synchronous motor described in any of the foregoing embodiments are implemented.

[0128] For the description of the relevant parts in the fixed-time convergence dynamic surface back electromotive force observation system, electronic device, and computer-readable storage medium of the permanent magnet synchronous motor provided by the embodiments of the present application, please refer to the detailed description of the corresponding parts in the fixed-time convergence dynamic surface back electromotive force observation method of the permanent magnet synchronous motor provided by the embodiments of the present application, which will not be elaborated here. In addition, the parts of the above technical solutions provided by the embodiments of the present application that are consistent with the implementation principles of the corresponding technical solutions in the prior art are not described in detail to avoid excessive elaboration.

[0129] The above content is only to illustrate the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any modifications made on the basis of the technical solution according to the technical idea proposed by the present invention fall within the protection scope of the claims of the present invention.

Claims

1. A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor, characterized in that It includes the following processes: Step 1: Construct an observer for the extended back electromotive force based on the current and voltage of the motor; Step 2: Construct the virtual control law of the observer according to the semi-global fixed-time uniform ultimately bounded stability theory and the sliding mode theory; Step 3: Use the backstepping method to construct the actual control input of the observer. The construction method of the actual control input is as follows: Based on the basic form of the semi-global fixed-time uniform ultimately bounded stability theory and combined with the auxiliary error of the observer, construct a new state variable, which makes the auxiliary error converge when it is fixed; Construct an error dynamic surface according to the new state variable and the extended back electromotive force, and make the estimated back electromotive force converge to the new state variable within the upper bound of the fixed convergence time according to the error dynamic surface; Construct the actual control input of the observer according to the error dynamic surface, and make the error dynamic surface converge when it is fixed according to the actual control input; Step 4: Adjust the parameters of the observer obtained in Step 3 to obtain an optimal observer, and make the back electromotive force of the permanent magnet synchronous motor converge according to the optimal observer to improve the dynamic response performance of the motor.

2. The fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor according to claim 1, characterized in that The construction of the observer for the extended back electromotive force based on the current and voltage of the motor in Step 1 includes: Obtain the current and voltage of the actual stator of the motor; Construct the dynamic equation of the extended back electromotive force model in the αβ coordinate system of the permanent magnet synchronous motor according to the current and voltage of the actual stator; Construct an observer according to the dynamic equation of the extended back electromotive force model.

3. A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor according to claim 1, characterized in that The expression of the observer is as follows: where the superscript ^ denotes the estimation of the actual state, κ is the virtual control law, ν is the control input, L d , L q represents the dq-axis inductance, R represents the stator resistance, J is the utility torque, ω e is the electrical angular velocity, and E is the extended back electromotive force.

4. A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor according to claim 1, characterized in that, The virtual control law is as follows: In the formula: the superscript "-" represents the error term,, k1, k2 respectively represent the gains to be designed, and ρ1, ζ1 are positive odd constants.

5. A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor according to claim 1, characterized in that The determination of the auxiliary error in Step 3 includes: Determine the auxiliary error according to the extended back electromotive force and the virtual control law.

6. A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor according to claim 1, characterized in that, The actual control input ν in Step 3 is as follows: Wherein, k3, k4 respectively represent the gains to be designed, ε is the error dynamic surface, and φ is the state variable.

7. A fixed-time convergence dynamic surface back electromotive force observation method for a permanent magnet synchronous motor according to claim 1, characterized in that, Adjust the parameters of the observer described in Step 4. The parameters to be adjusted are the gain and time constant of the observer. On the premise of system stability, select a sufficiently large k i and a sufficiently small γ1 to make the system satisfy the semi-global fixed-time uniform ultimate bounded stability condition.

8. A fixed-time convergence dynamic surface back electromotive force observation system for a permanent magnet synchronous motor, characterized in that, It includes: An observer module, used to construct an observer for the extended back electromotive force according to the current and voltage of the motor; A virtual control law module, used to construct the virtual control law of the observer according to the semi-global fixed-time uniform ultimately bounded stability theory and the sliding mode theory; A backstepping method module, used to construct the actual control input of the observer by using the backstepping method. The construction method of the actual control input is as follows: Based on the basic form of the semi-global fixed-time uniform ultimately bounded stability theory and combined with the auxiliary error of the observer, construct a new state variable, which makes the auxiliary error converge when it is fixed; Construct an error dynamic surface according to the new state variable and the extended back electromotive force, and make the estimated back electromotive force converge to the new state variable within the upper bound of the fixed convergence time according to the error dynamic surface; Construct the actual control input of the observer according to the error dynamic surface, and make the error dynamic surface converge when it is fixed according to the actual control input; An optimization module, used to adjust the parameters of the observer to obtain an optimal observer, and make the back electromotive force of the permanent magnet synchronous motor converge according to the optimal observer to improve the dynamic response performance of the motor.

9. An electronic device, characterized in that, It includes: A memory, used to store computer programs; A processor, used to implement the steps of the fixed-time convergence dynamic surface back electromotive force observation method for the permanent magnet synchronous motor as described in claims 1-7 when executing the computer program.

10. A computer-readable storage medium, characterized in that, A computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, the steps of the fixed-time convergence dynamic surface back electromotive force observation method for the permanent magnet synchronous motor described in claims 1-7 are implemented.

Images