Permanent magnet synchronous motor control method based on improved super-spiral sliding mode observer

Abstract

This invention discloses a control method for a permanent magnet synchronous motor (PMSM) based on an improved superspiral sliding mode observer. The method includes: selecting the stator current in the PMSM and establishing an improved superspiral sliding mode observer; adding two linear terms of observation error to the traditional observer; adjusting the observer parameters using an adaptive parameter adjustment strategy, wherein the observer parameters are used to adjust the convergence speed of the sliding mode observer and its effect on suppressing chattering in steady state, thereby achieving adaptive speed adjustment; when the PMSM stabilizes on the sliding surface, estimating the back electromotive force, and further obtaining the speed and position of the PMSM, thus achieving control of the synchronous motor. This invention, by employing this improved superspiral sliding mode observer and introducing linear terms of observation error, not only effectively suppresses observer chattering but also enhances the dynamic performance of the system when the modes approach the sliding surface, thereby enhancing the system's robustness.

Description

Technical Field

[0001] This invention relates to the field of automatic control, and in particular to a control method for a permanent magnet synchronous motor based on an improved super-helical sliding mode observer. Background Technology

[0002] In recent years, permanent magnet synchronous motor (PMSM) control systems have been widely used in industries and fields such as metallurgy, petrochemicals, coal, building materials, public utilities, and home appliances. High-performance PMSM vector control systems require real-time, high-precision rotor position and speed information, necessitating the installation of rotor position sensors such as rotary transformers and encoders on the motor. However, installing mechanical position sensors increases the difficulty and cost of motor manufacturing; furthermore, position sensors are susceptible to environmental conditions such as temperature and electromagnetic interference during use, which can easily reduce system reliability. Motor control technology employing high-precision sensorless control algorithms can overcome these shortcomings and has promising application prospects and research value.

[0003] In sensorless observation technology for permanent magnet synchronous motors, the sliding mode observer method is widely used due to its superior anti-interference capability and robustness. However, traditional sliding mode observers inevitably suffer from chattering, resulting in a high content of high-order harmonics in the observed back EMF waveform, ultimately affecting the accuracy of rotor position estimation. This system improves the super-helical sliding mode observer and proposes an adaptive adjustment method for observer parameters, effectively enhancing observation performance and system robustness. Summary of the Invention

[0004] In order to overcome the above-mentioned shortcomings and deficiencies of the prior art, the purpose of this invention is to provide a permanent magnet synchronous motor control method based on an improved super-helical sliding mode observer.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A control method for a permanent magnet synchronous motor based on an improved superhelical sliding mode observer includes:

[0007] An improved super-helical sliding mode observer is established by selecting the stator current in a permanent magnet synchronous motor.

[0008] The improved super-helical sliding mode observer adds two linear terms of observation error to the traditional observer.

[0009] An adaptive parameter adjustment strategy is adopted to adjust the observer parameters, which are used to adjust the convergence speed of the sliding mode observer and the effect of suppressing chattering in steady state, thereby achieving adaptive adjustment of the rotational speed.

[0010] When the permanent magnet synchronous motor is stable on the sliding surface, the back electromotive force is estimated, and the speed and position of the permanent magnet synchronous motor are further obtained, so as to realize the control of the synchronous motor.

[0011] Furthermore, the improved superhelical sliding mode observer is as follows:

[0012]

[0013] Where R s and L s These are the phase resistance and phase inductance of the motor, i s and u s Let $x$ be the stator current and $x$ be the voltage, $k1$, $k2$, $k3$, and $k4$ be the observer parameters, and $F(x)$ be the sign function.

[0014] When the system stabilizes on the sliding surface, estimate the back electromotive force E. s It can be obtained from the following formula:

[0015]

[0016] Furthermore, the adaptive parameter adjustment strategy adjusts the observer parameters, which are k1 and k2, specifically as follows:

[0017]

[0018] Where λ1 and λ2 are adjustable parameters. f(ω) is a function of the motor rotor speed ω, and its expression is:

[0019] f(ω)=(1-c)ω+c,0≤c≤1.

[0020] Furthermore, c is between 0.3 and 0.8.

[0021] further,

[0022] The observer's dynamic error equation is shown below:

[0023]

[0024] in The disturbance term of the system is expressed as follows: in It is the linear part of the system disturbance term, and ρ can be regarded as other small disturbances in the system;

[0025] and The introduction of these two items enhances LSTA-SMO's ability to suppress dynamic errors and improves the system's convergence speed.

[0026] Furthermore, by adjusting λ1, λ2, and c, the gain parameters k1 and k2 are made to vary with the actual speed of the motor.

[0027] Furthermore, the controlled object is a permanent magnet synchronous motor with a relative order of first order.

[0028] further,

[0029] k3=λ3f(ω).

[0030] Furthermore, this includes permanent magnet synchronous motors, improved super-helical sliding mode observers, and phase-locked loops.

[0031] Input u of permanent magnet synchronous motor α ,u β Output actual current i α i β ;

[0032] The input to the improved sliding mode observer is u α ,u β Output estimated current

[0033] Interpolate the estimated current to the actual current to estimate the back electromotive force E. α E β ;

[0034] The back electromotive force is input into the phase-locked loop to obtain the electrical angle and speed of the permanent magnet motor;

[0035] The speed adopts an adaptive parameter adjustment strategy to adjust the observer parameters to ensure that the observer parameters are suitable for the current motor operating conditions.

[0036] Furthermore, during the motor startup phase, a high-frequency square wave injection method is used to obtain the initial rotor position and the real-time rotor position and speed in the low-speed domain. When the speed reaches 200 rpm, the sliding mode observer algorithm is activated, and a weighted smooth switching strategy is adopted for the switching method.

[0037] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0038] (1) The present invention uses the advanced super-spiral sliding mode observer and introduces a linear term for the observation error, which can not only effectively suppress observer chattering, but also enhance the dynamic performance of the system when the mode approaches the sliding surface and enhance the robustness of the system.

[0039] (2) The observer of the present invention adopts an adaptive parameter adjustment strategy, which enables the observer parameters to be adjusted in real time according to the motor speed, so that the system can operate stably without jitter in a wide speed range. Attached Figure Description

[0040] Figure 1 This is a diagram of the sliding mode trajectory of the superspiral sliding mode observer.

[0041] Figure 2 This is a sliding mode trajectory diagram for an improved sliding mode observer.

[0042] Figure 3 A block diagram illustrating the principle of the adaptive observer parameter adjustment strategy.

[0043] Figure 4 This is a block diagram of a phase-locked loop (PLL).

[0044] Figure 5 This is a block diagram of a permanent magnet synchronous motor control system based on an improved adaptive sliding mode observer.

[0045] Figures 6(a)-6(b) The sliding mode observer is used to observe the rotational speed waveform. Figure 6(a) shows the traditional sliding mode observer method, and Figure 6(b) shows the improved sliding mode observer method.

[0046] Figures 7(a)-7(b) Figure 7(a) shows the traditional sliding mode observer method, and Figure 7(b) shows the improved sliding mode observer method.

[0047] Figures 8(a)-8(b) The adaptive sliding mode observer is used to observe the rotational speed waveform, where Figure 8(a) shows the improved sliding mode observer method and Figure 8(b) shows the adaptive improved sliding mode observer method.

[0048] Figure 9 This is a graph showing the variation of the gain parameters of the improved adaptive sliding mode observer. Detailed Implementation

[0049] The present invention will be further described in detail below with reference to the embodiments, but the implementation of the present invention is not limited thereto.

[0050] A control method for permanent magnet synchronous motors based on an improved adaptive superspiral sliding mode observer is proposed. The method is applied to permanent magnet synchronous motors and includes analyzing the mathematical model of the permanent magnet synchronous motor, designing an improved superspiral sliding mode observer, designing an adaptive adjustment strategy for the observer, and designing and analyzing the performance of the improved adaptive sliding mode observer.

[0051] The specific process is as follows:

[0052] Analysis of the mathematical model of permanent magnet synchronous motor

[0053] The voltage equations for a surface-mounted permanent magnet synchronous motor (PMSM) in the stationary coordinate system along the α-β axes can be expressed as:

[0054] u s =(R s +pL s )i s +E s ,

[0055] In the formula: R s L is the phase resistance. s For phase inductance, For differential operators, Represents the stator voltage in the stationary coordinate system. Represents stator current. To extend the back electromotive force, and satisfy:

[0056]

[0057] In the formula ω e ψ represents the electric angular velocity of the motor. f θ represents the flux linkage of a permanent magnet. e This represents the electrical angle. As can be seen from the formula above, the extended back EMF contains electrical angle information. By designing a back EMF observer to accurately obtain the motor's back EMF, all information regarding the motor's rotor speed and position can be obtained.

[0058] Design an improved superspiral sliding mode observer

[0059] The Super Twisting Algorithm Sliding-Mode Observer (STA-SMO) is a second-order sliding mode algorithm where the trajectory of the second-order sliding control surface spirals around the origin. Because an integral term of the sliding mode switching function is included in the observer, the sliding trajectory is smooth and continuous, effectively reducing system chattering. Figure 1 As shown, this invention designs an improved adaptive superspiral sliding mode observer, which overcomes the shortcomings of traditional superspiral sliding mode observers, such as insufficient disturbance resistance and poor robustness of observer parameters. This observer adds a linear term for the observation error to the traditional superspiral sliding mode observer, enhancing the dynamic performance and disturbance resistance of the system's modal approach process.

[0060] The structure of a traditional superspiral sliding mode observer is as follows:

[0061]

[0062] In the formula For the estimated values ​​of the state variables, For observation error, k i ρ is the observer gain parameter. i Let i be the disturbance term, i = 1, 2. F(x) is the sign function:

[0063]

[0064] In the control system of a permanent magnet synchronous motor, the stator current i is selected as the state variable. s The voltage equation can be rewritten as:

[0065]

[0066] The superhelical sliding mode observer model is established as follows:

[0067]

[0068] When the system stabilizes on the sliding surface, the back electromotive force can be directly estimated:

[0069]

[0070] This method can overcome the sliding mode chattering phenomenon, but the algorithm has a long convergence time, which is only related to the observer gain coefficient and the upper bound of the system disturbance. Therefore, although the traditional super-spiral sliding mode has strong disturbance rejection capability near the sliding surface, the observer cannot quickly return to the sliding surface when the system moves away from the sliding surface due to disturbance.

[0071] To address the aforementioned shortcomings, this invention designs a sensorless vector control system based on an improved super-twisting algorithm sliding-mode observer (LSTA-SMO). The basic structure of the observer is as follows:

[0072]

[0073] The improved method adds two linear terms of observation error to the basic architecture of the traditional observer: like Figure 2 As shown, these linear terms enable the observer to converge exponentially rather than in finite time, enhancing the dynamic performance of the system's modal approach process. While retaining the strong disturbance rejection capability of the superhelical sliding mode observer at the system origin, it can also suppress strong disturbances far from the origin, greatly enhancing the system's anti-interference capability.

[0074] In the presence of a disturbance, as long as the disturbance satisfies its upper bound:

[0075]

[0076] This ensures the stability of the system, where parameters δ1, δ2, δ3, δ4 ≥ 0. The following formula shows the range of the observer parameters; it can be seen that as long as the observer parameters are chosen to be sufficiently large, the system can be guaranteed to converge to the sliding surface.

[0077]

[0078] in:

[0079]

[0080] In permanent magnet synchronous motors, an improved super-helical sliding mode observer is established:

[0081]

[0082] When the system is stable on the sliding surface, the back electromotive force can be estimated by the following formula:

[0083]

[0084] The observer's dynamic error equation is shown below:

[0085]

[0086] in The disturbance term of the system is expressed as follows: in It is the linear part of the system disturbance term, and ρ can be regarded as other small disturbances in the system.

[0087] and The introduction of these two features enhances the LSTA-SMO's ability to suppress dynamic errors and improves the system's convergence speed. For minor disturbances caused by cross-coupling effects or small perturbations in motor parameters during permanent magnet synchronous motor operation, the LSTA-SMO exhibits strong disturbance rejection near the sliding surface. For larger disturbances such as sudden load increases or speed changes during operation, the LSTA-SMO can return to the sliding surface more quickly. Therefore, the improved sliding mode observer enhances the dynamic performance of the system as its modes approach the sliding surface, thereby improving system robustness.

[0088] Design an adaptive adjustment strategy for observer parameters.

[0089] In the LSTA-SMO described above, observer parameters k1 and k2 are used to construct the super-helical sliding mode observer, mainly determining the convergence speed of the sliding mode observer and its effect on suppressing chattering in steady state. Parameters k3 and k4 are newly added linear terms, mainly used to improve the dynamic performance and disturbance rejection capability of the system convergence. In the low-speed domain of the sensorless permanent magnet synchronous motor control system, excessively large observer parameters can lead to system chattering; in the high-speed domain, parameters that are too small can lead to system instability, which makes the selection of observer parameters difficult. k1 and k2 mainly reflect the effect of suppressing chattering in steady state, while k3 and k4 affect the dynamic response stage of the motor. Therefore, adaptive adjustment of k1 and k2 based on speed can solve the problem of parameter mismatch in a wide speed domain.

[0090] This invention designs a robust adaptive parameter adjustment method suitable for a wide speed range. This algorithm is used to adaptively adjust the parameters k1 and k2 of an improved sliding mode observer, and its expression is as follows:

[0091]

[0092] In the formula, λ1 and λ2 are adjustable parameters. f(ω) is a function of the motor rotor speed ω, and its expression is:

[0093] f(ω)=(1-c)ω+c,0≤c≤1

[0094] Clearly, f(ω) has upper and lower bounds, satisfying c ≤ f(ω) ≤ ω. Similarly, f 2 (ω) also has upper and lower bounds, satisfying c 2 ≤f 2 (ω)≤ω 2 .

[0095] Consider the selection of parameter c. If c = 1, then f(ω) = 1, and parameters k1 and k2 are fixed constants. If c = 0, then f(ω) = ω, and parameters k1 and k2 are proportional to ω. This will result in very small observer gain when the motor speed ω is small, which may cause the observer to fail to converge. Therefore, c represents the correlation between k1, k2 and speed ω, and it is recommended to select a value between 0.3 and 0.8.

[0096] Next, we analyze the selection of parameters λ1 and λ2. For LSTA-SMO to be stable, the perturbation term must satisfy:

[0097]

[0098] in This is the current tracking error. When the system is stable, this error has upper and lower bounds, satisfying the following:

[0099]

[0100] The parameters δ1, δ2, δ3, and δ4 need to be chosen as sufficiently large constants to satisfy the stability conditions of LSTA-SMO, since f(ω), f 2 Since (ω) has both upper and lower bounds, it is certain that a suitable parameter η can be chosen. i For i = 1, ..., 4, the following equation holds:

[0101]

[0102] At the same time, the stability condition still holds:

[0103]

[0104] To satisfy the stability condition, the range of the k1 parameter must meet the following requirements:

[0105]

[0106] The parameters δ1 and δ3 are selected according to the method described above, resulting in:

[0107]

[0108] We can choose a suitable λ1 such that the following equation holds:

[0109]

[0110] Therefore, the value of k1 can satisfy the system stability.

[0111] Similarly, according to the system stability conditions of LSTA-SMO, the value of k3 must satisfy:

[0112]

[0113] Clearly, by choosing a suitable λ3, the following equation can be made true:

[0114] k3=λ3f(ω).

[0115] Given that parameters λ1, λ3, η1, η2, and η3 have been selected using the above method, k2 must satisfy the following stability condition:

[0116]

[0117] Where the expression is: and Since all parameters are definite quantities, c1 and c2 can be chosen as appropriate constants such that: k2 = max(c1f) 2 (ω),c2f 2 (ω) holds, and thus we can choose a suitable λ2 such that the following equation holds:

[0118] k2=λ2f 2 (ω).

[0119] Therefore, appropriate parameters λ1, λ2, c can be selected so that the gain parameters k1, k2 change with the actual speed of the motor, thereby ensuring the stability of the system and preventing the motor from exhibiting chattering problems in a wide speed range.

[0120] Figure 3 This is a structural diagram of the improved adaptive super-twisting algorithm sliding-mode observer (AGLSTA-SMO). Figure 3 As shown, the input to the improved sliding mode observer is u. α ,u β The output is the estimated current E.α E β The estimated current and the actual current i measured by the original system will be compared. α i β The difference is calculated, and then the estimated back electromotive force (EMF) is obtained. As can be seen from the mathematical model of a permanent magnet synchronous motor, the back EMF contains rotor position information. By inputting the estimated back electromotive force into the phase-locked loop, the observed electrical angle and speed can be obtained. The adaptive parameter adjustment strategy adjusts the observer parameters k1 and k2 according to the estimated speed to ensure that the observer parameters are suitable for the current motor operating conditions.

[0121] Figure 4 This is a diagram of a phase-locked loop (PLL). By inputting the filtered back electromotive force into the PLL, the observed electrical angle and rotational speed can be obtained.

[0122] Design and performance analysis methods for improved adaptive sliding mode observers

[0123] Simulation verification was performed using Matlab / Simulink. During the motor startup phase, a high-frequency square wave injection method was used to obtain the initial rotor position and the real-time rotor position and speed in the low-speed domain. When the speed reached 200 rpm, the sliding mode observer algorithm was activated, and a weighted smooth switching strategy was adopted for the switching method.

[0124] Figure 5 This is a block diagram of the sensorless permanent magnet synchronous motor control system based on AGLSTA-SMO proposed in this invention.

[0125] The parameters of the permanent magnet synchronous motor in the simulation platform are shown in the table below:

[0126]

[0127] The performance of STA-SMO and AGLSTA-SMO was compared through simulation experiments.

[0128] In Experiment 1, the motor was started under no-load, with a given speed of 1500 rpm (0.5 times the rated speed). At 0.25 s, a step speed command was given, resulting in a rated speed of 3000 rpm. At 0.5 s, a sudden load of 1.33 N·m was applied to the motor. Figures 6(a) and 6(b) show a comparison of the speeds measured by the traditional and improved super-spiral sliding mode observers, with Figure 6(a) showing the speed measured by STA-SMO and Figure 6(b) showing the speed measured by LSTA-SMO. The speed estimated by LSTA-SMO was more stable than that of STA-SMO under different operating conditions, and the chattering problem was effectively suppressed. Under a given step speed command, the overshoot and speed chattering range of LSTA-SMO were smaller than those of STA-SMO. Under a sudden load, the speed chattering range of LSTA-SMO was smaller than that of STA-SMO, and the speed curve was smoother. Therefore, the control system using LSTA-SMO had a faster response speed and stronger anti-interference capability than that using STA-SMO.

[0129] Figures 7(a) and 7(b) compare the observation angles of the traditional and improved super-spiral sliding mode observers, with Figure 7(a) showing the observation angle error of STA-SMO and Figure 7(b) showing the observation angle error of LSTA-SMO. Under operating conditions of 0.5 times rated speed, rated speed, and sudden load increase at rated speed, LSTA-SMO exhibits smaller lag in observation angle error. During the acceleration transition process (0.25s to 0.31s) after a sudden change in motor speed, the maximum observation angle error of STA-SMO is 7.53°, while that of LSTA-SMO is 5.42°. Simulation experiment one demonstrates that LSTA-SMO can effectively improve the dynamic performance of the system approaching the sliding surface, thereby suppressing system disturbances and improving system performance.

[0130] In Experiment 2, sensorless permanent magnet synchronous motor control systems based on LSTA-SMO and AGLSTA-SMO methods were used respectively. The motor was started under no-load using a high-frequency square wave injection method, with a given speed of 0.5 times the rated speed (1500 rpm). At 0.25 s, the speed command was changed to the rated speed of 3000 rpm.

[0131] Figures 8(a) and 8(b) show the speed comparison of LSTA-SMO after using the adaptive observer parameter adjustment strategy, where Figure 8(a) shows the observed speed of LSTA-SMO and Figure 8(b) shows the observed speed of AGLSTA-SMO. After adopting the adaptive observer parameter adjustment method, the chattering phenomenon in the low-speed domain of the motor was improved, and the speed chattering range decreased from 2% to 0.8%. Figure 9This paper demonstrates that an adaptive observer parameter adjustment method can adjust the values ​​of observer parameters k1 and k2 in real time under different motor speed conditions. When the motor operates in the low-speed domain, observer parameters k1 and k2 ensure that chattering is prevented while the motor is stable. When the motor operates in the high-speed domain, parameters k1 and k2 automatically increase to maintain observer stability and high performance. This adaptive method enables the AGLSTA-SMO algorithm to effectively suppress chattering under both high- and low-speed conditions, improving the robustness of the system.

[0132] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A control method of permanent magnet synchronous motor based on improved hyper- spiral sliding mode observer, characterized in that, include: An improved super-helical sliding mode observer is established by selecting the stator current in a permanent magnet synchronous motor. The improved super-helical sliding mode observer adds two linear terms of observation error to the traditional observer. An adaptive parameter adjustment strategy is adopted to adjust the observer parameters, which are used to adjust the convergence speed of the sliding mode observer and the effect of suppressing chattering in steady state, thereby achieving adaptive adjustment of the rotational speed. When the permanent magnet synchronous motor is stable on the sliding surface, the back electromotive force is estimated, and the speed and position of the permanent magnet synchronous motor are further obtained to realize the control of the synchronous motor. The improved superspiral sliding mode observer is: in and These are the phase resistance and phase inductance of the motor, respectively. and These are the stator current and voltage, respectively. For observer parameters, It is a symbolic function; Estimating back EMF when the system is stabilized on the sliding surface is found from ； The adaptive parameter adjustment strategy adjusts the observer parameters, which are: Specifically: in It is an adjustable parameter. It is about the rotor speed of the motor The function is expressed as: 。 2. The permanent magnet synchronous motor control method according to claim 1, characterized in that, The exist between.

3. The permanent magnet synchronous motor control method according to claim 1, characterized in that, The observer's dynamic error equation is shown below: in The disturbance term of the system is expressed as follows: ,in It is the linear part of the system disturbance term. These can be considered as other minor perturbations in the system; and The introduction of these two items enhances the ability of the improved superspiral sliding mode observer to suppress dynamic errors and improves the convergence speed of the system.

4. The control method of a permanent magnet synchronous motor according to claim 1, characterized by, By adjusting the gain parameter as a function of the actual speed of the motor.

5. The control method of a permanent magnet synchronous motor according to any one of claims 1 to 4, characterized by, The controlled object is a permanent magnet synchronous motor with a relative order of first order.

6. The permanent magnet synchronous motor control method according to claim 1, characterized in that, 。 7. A system implementing the method of controlling a permanent magnet synchronous motor according to any one of claims 1 to 6, characterized in that, This includes permanent magnet synchronous motors, an improved super-helical sliding mode observer, and phase-locked loops. Input to a permanent magnet synchronous motor , output actual current ; The input of the improved sliding mode observer is Output estimated current ; Calculate the difference between the estimated current and the actual current to estimate the back electromotive force. ; The back electromotive force is input into the phase-locked loop to obtain the electrical angle and speed of the permanent magnet motor; The speed adopts an adaptive parameter adjustment strategy to adjust the observer parameters to ensure that the observer parameters are suitable for the current motor operating conditions.

8. The system of claim 7, wherein, During the motor startup phase, a high-frequency square wave injection method is used to obtain the initial rotor position and the real-time rotor position and speed in the low-speed range. When the speed reaches... The sliding mode observer algorithm is started at the specified time, and the switching method adopts a weighted smooth switching strategy.

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