Permanent magnet synchronous motor sensorless control method based on full-order sliding mode observer
By introducing the adaptive function γ(s) and the hyperbolic tangent function tanh(γs) to adjust the boundary layer thickness of the full-order sliding mode observer, and using an orthogonal phase-locked loop to eliminate interference signals, the jitter problem of the full-order sliding mode observer in the medium and high-speed domain in the prior art is solved, and the high response speed and stability of the system are achieved.
Patent Information
- Application Number
- CN202411706745.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-26
- Publication Date
- 2025-03-18
AI Technical Summary
The existing full-order sliding mode observers have high frequency jitter and noise in high-precision occasions, which limits their use in the medium and high-speed domain and is difficult to meet the requirements of system stability and dynamic response capabilities at the same time.
The adaptive function γ(s) is introduced to adjust the thickness of the sliding mode boundary layer, combined with the hyperbolic tangent function tanh(γs) as the switching function, and eliminate the interference signal through an orthogonal phase-locked loop, optimize the boundary layer thickness of the observer to balance dynamic performance and stability.
The system's response speed is improved, the vibration of speed estimation is suppressed, and the superior balance between dynamic performance and estimated state is achieved, which enhances the stability and response speed of the system.
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Figure CN119652193A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and in particular to a permanent magnet synchronous motor sensorless control method based on a full-order sliding mode observer. Background Art
[0002] The application of permanent magnet synchronous motors and related technologies has involved all aspects of human industrial production, and can be seen in related industries such as aerospace, industrial manufacturing, new energy and electricity, medical equipment, and household appliances. The key to the control strategy of permanent magnet synchronous motors lies in the acquisition of rotor angle. In the sensorless control technology of permanent magnet synchronous motors, the speed higher than 20% of the rated speed is classified as the medium and high speed domain. In the medium and high speed domain, the observer method is generally used to obtain the rotor angle. The full-order sliding mode observer came into being. It uses stator current and extended back electromotive force as state variables. Therefore, the full-order sliding mode observer can observe the motor speed and rotor position information more accurately.
[0003] The traditional full-order sliding mode observer constructs a hyperplane (sliding surface) with the current error. Under the action of the control function (sign function), the observed state quantity crosses the sliding surface back and forth and arrives at the end point in a sliding mode. At this time, the observed state variable value is close to the actual value. The traditional full-order sliding mode observer is affected by the discontinuous characteristics of the sliding surface structure control of the observed state variable, resulting in high-frequency jitter and noise in the estimated value, which limits the use of the full-order sliding mode observer in high-precision occasions. The chattering phenomenon of the traditional full-order sliding mode observer is caused by the high-frequency noise introduced in the estimation process. The boundary layer thickness of the observer is one of the important factors affecting high-frequency noise. The larger the boundary layer thickness of the sliding mode observer switching function, the stronger the suppression effect on high-frequency noise, i.e., chattering, but the response speed of the system will be weakened. The smaller the boundary layer thickness, the more dynamic performance of the system will be enhanced, but the suppression effect on chattering will be correspondingly weakened. In other words, it is difficult for a fixed boundary layer thickness to make the system meet the requirements of stability and dynamic response capability at the same time. Therefore, how to balance the fixed boundary layer thickness so that the system can meet the requirements of stability and dynamic response capability at the same time has become a key consideration. Summary of the invention
[0004] The technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and provide a sensorless control method for a permanent magnet synchronous motor based on a full-order sliding mode observer, which improves the response speed of the system and suppresses the speed estimation jitter.
[0005] The technical solution adopted by the present invention to solve the technical problem is: a sensorless control method of a permanent magnet synchronous motor based on a full-order sliding mode observer, comprising the following steps:
[0006] S1. Obtain the stator voltage u of the permanent magnet synchronous motor in the two-phase stationary coordinate system = [uα u β ] T , after the improved full-order sliding mode observer, the stator current observation value is output The stator current observation value With the stator current value i=[i α i β ] T The difference between
[0007] S2. The stator current observation error After passing through the adaptive module and the control module in sequence, the adaptive sliding mode control function H(s) of the permanent magnet synchronous motor in the two-phase stationary coordinate system is output;
[0008] S3. The adaptive sliding mode control function H(s) enters the full-order sliding mode observer after passing through the sliding mode gain matrix K, and outputs the back electromotive force observation value
[0009] S4. The back electromotive force observation value As a state variable, it is fed back to the full-order sliding mode observer to participate in the update calculation. The rotor position observation value is output after being processed by the orthogonal phase-locked loop and speed observations The speed observation value Feedback to the full-order sliding mode observer as its input;
[0010] The stator current observation value in the full-order sliding mode observer and the observed value of back EMF It is obtained by the observer equation, which is as follows:
[0011]
[0012] H(s)=tanh(γs)
[0013]
[0014] Where p is the differential operator, is the current error in the input stationary coordinate system, a, b and h are the modulation parameters of the adaptive function γ(s), A 12 =-1 / L d I, B1=1 / L d I, k and l are the observer gain coefficients, R is the stator resistance of the permanent magnet synchronous motor, and L dis the stator inductance of the permanent magnet synchronous motor.
[0015] Furthermore, the working steps of the orthogonal phase-locked loop in step S4 are as follows:
[0016] S41. Rotor position observation value After cosine operation, the observed value of α-axis back electromotive force Multiply them together and you get The rotor position observation After sine operation, the observed value of the β-axis back electromotive force Multiply them together and you get
[0017] S42.Yes and Perform heterodyne processing to obtain the rotor position error signal
[0018]
[0019] S43. Normalize the rotor position error signal ε to obtain a normalized rotor position error signal
[0020] S44. The rotor position error signal ε n After proportional amplification and integration, the speed observation value is obtained. Speed observation value Perform the integral process to obtain the rotor position observation value The rotor position observation As the feedback signal of the orthogonal phase-locked loop, it repeats in sequence.
[0021] Furthermore, the observer equation uses Lyapunov function to perform stability analysis.
[0022] The beneficial effects of the present invention are:
[0023] (1) The present invention introduces an adaptive function γ(s) to adaptively adjust the thickness of the sliding mode boundary layer according to the size of the current error. When the current error is large, the thickness of the sliding mode boundary layer is reduced to improve the response speed of the system and reduce the static error. When the current error is small, the thickness of the sliding mode boundary layer is increased to suppress the jitter of the speed estimation, thereby achieving a balance between superior dynamic performance and estimation state.
[0024] (2) The present invention selects the hyperbolic tangent function tanh(γs) as the switching function of the full-order sliding mode observer. Since the hyperbolic tangent function has continuous saturation, continuous control is adopted within the boundary layer, and traditional sliding mode control is adopted outside the boundary layer, which can weaken the vibration to a certain extent.
[0025] (3) The present invention eliminates interference signals through the setting of an orthogonal phase-locked loop, so that the system can better cope with frequency changes and maintain stable bandwidth characteristics, so that the system can respond to changes in input signals more quickly and accurately, thereby further improving the response speed and stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] The present invention is further described below in conjunction with the accompanying drawings and embodiments.
[0027] Figure 1 It is a block diagram of the rotor position estimation principle of the full-order sliding mode observer in the present invention;
[0028] Figure 2 It is a principle block diagram of an orthogonal phase-locked loop in the present invention;
[0029] Figure 3 It is the principle diagram of the hyperbolic tangent function in the present invention;
[0030] Figure 4 It is a schematic diagram of the adaptive function transformation rate in the present invention.
[0031] In the figure: 1. Full-order sliding mode observer; 2. Adaptive module; 3. Control module; 4. Orthogonal phase-locked loop. DETAILED DESCRIPTION
[0032] The present invention will now be further described in conjunction with the accompanying drawings and preferred embodiments. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.
[0033] like Figure 1 and Figure 3 As shown, a sensorless control method for a permanent magnet synchronous motor based on a full-order sliding mode observer comprises the following steps:
[0034] S1. Obtain the stator voltage u of the permanent magnet synchronous motor in the two-phase stationary coordinate system = [u α u β ] T , after the improved full-order sliding mode observer 1, the stator current observation value is output Stator current observation value With the stator current value i=[i α i β ] T The difference between
[0035] S2. Stator current observation error After passing through the adaptive module 2 and the control module 3 in sequence, the adaptive sliding mode control function H(s) of the permanent magnet synchronous motor in the two-phase stationary coordinate system is output;
[0036] S3. The adaptive sliding mode function H(s) enters the improved full-order sliding mode observer 1 after passing through the sliding mode gain matrix K, and outputs the back electromotive force observation value
[0037] S4. Back EMF Observation Value As a state variable, it is fed back to the improved full-order sliding mode observer 1 to participate in the update calculation, and the back EMF observation value After being processed by the orthogonal phase-locked loop 4, the rotor position observation value is output and speed observations Speed observation value Feedback to the improved full-order sliding mode observer 1 as its input;
[0038] Stator current observation value in full-order sliding mode observer 1 and the observed value of back EMF It is obtained through the observer equation, which is as follows:
[0039]
[0040] H(s)=tanh(γs)
[0041]
[0042] Where p is the differential operator, is the current error in the input stationary coordinate system, a, b and h are the modulation parameters of the adaptive function γ(s), a determines the height of the function, b determines the rate of change of the function, and h determines the zero position of the function. A 12 =-1 / L d I, B1=1 / L d I, k and l are the observer gain coefficients, R is the stator resistance of the permanent magnet synchronous motor, and L d is the stator inductance of the permanent magnet synchronous motor.
[0043] When s→∞, γ(s)→(a+h); when s→0, γ(s)→h. Figure 4 As shown in the figure, according to the control variable method, a=2, h=0.2 are fixed, the value of parameter b is constantly changed, and its influence on the change rate of the adaptive function γ(s) is observed. Figure 4 It can be seen that when the values of a and h are fixed, as the value of b increases, the convergence rate of γ(s) increases, and vice versa, the convergence rate of γ(s) decreases. It is worth noting that when the sliding mode appears, that is, when the sliding mode moves near the sliding surface, the shape coefficient should be continuously adjusted in a slight manner.
[0044] An adaptive function γ(s) is introduced into the observer equation to adaptively adjust the thickness of the sliding mode boundary layer according to the size of the current error. When the current error is large, the thickness of the sliding mode boundary layer is reduced to improve the response speed of the system and reduce the static error. When the current error is small, the thickness of the sliding mode boundary layer is increased to suppress the chattering of the speed estimation, achieving a balance between superior dynamic performance and estimated state. The hyperbolic tangent function tanh(γs) is selected as the switching function of the full-order sliding mode observer 1. Since the hyperbolic tangent function has continuous saturation, continuous control is used within the boundary layer, and traditional sliding mode control is used outside the boundary layer, which can weaken the chattering to a certain extent.
[0045] like Figure 2 As shown, the working steps of the orthogonal phase-locked loop 4 in step S4 are as follows:
[0046] S41. Rotor position observation value After cosine operation, the observed value of α-axis back electromotive force Multiply them together and you get The rotor position observation After sine operation, the observed value of the β-axis back electromotive force
[0047] Multiply them together and you get
[0048] S42.Yes and Perform heterodyne processing to obtain the rotor position error signal The specific process is as follows:
[0049]
[0050] Among them, ε is the error variable calculated by heterodyne method, E ex is the estimated magnitude of the extended back EMF, which is related to the estimated speed is directly proportional to the size.
[0051] When the full-order sliding mode observer 1 is estimated to be stable, the rotor position error signal ε can be simplified as:
[0052]
[0053] S43. Normalize the rotor position error signal ε to obtain a normalized rotor position error signal
[0054] S44. Rotor position error signal ε n After proportional amplification and integration, the speed observation value is obtained.
[0055] Speed observation value Perform the integral process to obtain the rotor position observation value The rotor position observation As the feedback signal of the orthogonal phase-locked loop 4, it reciprocates in sequence.
[0056] By setting up the orthogonal phase-locked loop 4 to eliminate interference signals, the system can better cope with frequency changes and maintain stable bandwidth characteristics, so that the system can respond to changes in input signals more quickly and accurately, thereby further improving the response speed and stability of the system.
[0057] The observer equation uses Lyapunov function for stability analysis, the specific analysis is as follows:
[0058] First, construct the Lyapunov function as follows:
[0059]
[0060] Full-order sliding mode observer that meets stability requirements 1 but The derivation process is as follows:
[0061]
[0062]
[0063] in,
[0064]
[0065] Obviously, V1<0, so we only need to prove V2>0.
[0066] If V2>0, the following two inequalities are obtained:
[0067]
[0068] From the above two inequalities, it can be deduced that the full-order sliding mode gain must satisfy:
[0069] If satisfied Then the convergence condition of the full-order sliding mode observer 1 is established. When entering the sliding mode, and will approach 0, and the current state variable output by the full-order sliding mode observer 1 will be equal to the actual value.
[0070] According to the current state error equation:
[0071]
[0072] According to the observer equation, the error equation of the extended back electromotive force can be obtained:
[0073]
[0074] Substituting the current state error equation into the back-EMF error equation, we get the converted extended back-EMF error state equation:
[0075]
[0076] From the extended back-EMF error equation and the converted extended back-EMF error state equation, it can be seen that the extended back-EMF mathematical model has a structure similar to the extended Kalman filter. The extended back-EMF state equation is expressed as the prediction stage of the Kalman filter. The extended back-EMF error state equation has This gain term can represent the measurement correction stage. The above two stages are the two basic stages of the extended Kalman filter. Therefore, the extended back-EMF state equation can utilize the characteristics of the extended Kalman filter to enable the full-order sliding mode observer to omit the low-pass filter in the traditional sliding mode observer, which can greatly reduce the phase delay of the traditional sliding mode observer.
[0077] The characteristic equation and characteristic root are solved according to the converted extended back-EMF error state equation, and the estimated speed is calculated in one sampling cycle. Assuming it to be a constant, then:
[0078]
[0079] Continue to solve to get the characteristic root
[0080] Among them, s is the Laplace operator and j represents an imaginary number.
[0081] Since l and k are both positive numbers greater than 0, according to classical control theory, the characteristic root s 1,2 are all on the left side of the x-axis, which leads to the asymptotic convergence of the improved full-order sliding mode observer 1.
[0082] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with this technology to understand the content of the present invention and implement it. They cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the protection scope of the present invention.
Claims
1. A sensorless control method for a permanent magnet synchronous motor based on a full-order sliding mode observer, characterized in that: The steps include: S1. Obtain the stator voltage u of the permanent magnet synchronous motor in the two-phase stationary coordinate system = [u α u β ] T , after the improved full-order sliding mode observer (1), the stator current observation value is output The stator current observation value With the stator current value i=[i α i β ] T The difference between S2. The stator current observation error After passing through the adaptive module (2) and the control module (3) in sequence, an adaptive sliding mode control function H(s) of the permanent magnet synchronous motor in a two-phase stationary coordinate system is output; S3. The adaptive sliding mode control function H(s) enters the full-order sliding mode observer (1) after passing through the sliding mode gain matrix K, and outputs the back electromotive force observation value S4. The back electromotive force observation value As a state variable, it is fed back to the full-order sliding mode observer (1) to participate in the update calculation. The back electromotive force observation value After being processed by the orthogonal phase-locked loop (4), the rotor position observation value is output and speed observations The speed observation value Feedback to the full-order sliding mode observer (1) as its input; The stator current observation value in the full-order sliding mode observer (1) and the observed value of back EMF It is obtained by the observer equation, which is as follows: H(s)=tanh(γs) Where p is the differential operator, is the current error in the input stationary coordinate system, a, b and h are the modulation parameters of the adaptive function γ(s), A 12 =-1 / L d I, B1=1 / L d I, k and l are the observer gain coefficients, R is the stator resistance of the permanent magnet synchronous motor, and L d is the stator inductance of the permanent magnet synchronous motor.
2. The sensorless control method of a permanent magnet synchronous motor based on a full-order sliding mode observer according to claim 1 is characterized in that: The working steps of the orthogonal phase-locked loop (4) in step S4 are as follows: S41. Rotor position observation value After cosine operation, the observed value of α-axis back electromotive force Multiply them together and you get The rotor position observation After sine operation, the observed value of the β-axis back electromotive force Multiply them together and you get S42.Yes and Perform heterodyne processing to obtain the rotor position error signal S43. Normalize the rotor position error signal ε to obtain a normalized rotor position error signal S44. The rotor position error signal ε n After proportional amplification and integration, the speed observation value is obtained. Speed observation value Perform the integral process to obtain the rotor position observation value The rotor position observation As the feedback signal of the orthogonal phase-locked loop (4), it repeats in sequence.
3. The sensorless control method of permanent magnet synchronous motor based on full-order sliding mode observer according to claim 1 is characterized in that: The observer equation uses Lyapunov function for stability analysis.