Permanent magnet linear motor sensorless control method combining super-spiral sliding-mode observer and double-second-order generalized integrator

Abstract

The invention discloses a permanent magnet linear motor sensorless control method combining a super-spiral sliding mode observer and a double-second-order generalized integrator, and belongs to the field of linear permanent magnet vernier motor control. Comprising the following steps that the current and the voltage of the linear motor are calculated by introducing a super-spiral sliding mode observer and a double-second-order generalized integrator, then the obtained estimated counter electromotive force serves as the input of a phase-locked loop, finally the estimated rotor position and the estimated speed of the motor can be obtained, and the control method has the advantages of being high in precision, high in thrust density and the like. According to the method, the chattering problem of the estimated counter electromotive force is reduced by introducing the super-spiral sliding-mode observer, then the estimated counter electromotive force is filtered by adopting the bisecond-order generalized integrator for harmonic disturbance caused by the positioning force of the permanent magnet vernier linear motor, the estimation precision is effectively improved, and the control performance is improved. Experimental results show that the control method can realize high-precision operation of the permanent magnet vernier linear motor under steady-state and variable-speed conditions.

Description

Technical Field

[0001] This invention relates to the field of control technology for linear permanent magnet vernier motors, and specifically to a sensorless control method for a permanent magnet linear motor that combines a super-helical sliding mode observer and a dual second-order generalized integrator. Background Technology

[0002] Compared to traditional permanent magnet linear motors (PMLMs), the linear permanent magnet vernier motor innovatively uses low-cost magnetic materials, effectively reducing manufacturing costs while improving thrust performance. This characteristic gives it a unique advantage in the rail transit field. However, deploying position sensors and signal processing systems across the entire stroke range to acquire position signals not only significantly increases system costs but also reduces reliability due to environmental interference. Against this backdrop, sensorless control technology offers an effective solution. Traditional sensorless control technology does not consider the impact of harmonics generated by the linear motor's positioning force and the inherent chattering of traditional SMOs on back EMF estimation, which reduces sensor estimation accuracy and leads to lower system operating accuracy. This invention uses an ST-SMO with an additional linear phase to solve the inherent chattering problem of traditional SMOs, while employing D-SOGI to filter out high-order harmonics generated by the linear motor's positioning force, improving the observer's estimation accuracy. At medium and high speeds, it has the advantages of being insensitive to parameter changes, high estimation accuracy, good dynamic performance, and strong system robustness.

[0003] In recent years, universities and research institutions both domestically and internationally have conducted in-depth research on sensorless control strategies for linear permanent magnet vernier motors (PMLMs) and achieved certain results. Chinese invention patent "A Sensorless Vector Control Method for PMSLMs Based on Sliding Mode Observer" (patent number CN201910264758.9) discloses a sensorless vector control method for PMSLMs based on a sliding mode observer. To address some drawbacks of closed-loop control systems, a digital PID control method is used for real-time control in the three-loop structure of position, speed, and current to achieve high-precision position tracking of the linear motor. However, this method does not consider the positioning force harmonic disturbance caused by the linear motor's own structure. Chinese invention patent "A Sensorless Permanent Magnet Synchronous Linear Motor Based on an Improved Phase-Locked Loop" (patent number CN202210499459.5) discloses a sensorless control method for a permanent magnet synchronous linear motor based on an improved phase-locked loop. It uses the extended back EMF of the sliding mode observer as the input of the improved phase-locked loop to estimate the rotor position and speed of the motor, while suppressing and eliminating AC components to improve observation accuracy and system stability. Chinese invention patent CN202311067677.2, entitled "A Sensorless Control Method for Low-Speed ​​Permanent Magnet Linear Motors," proposes a sensorless control method based on high-frequency sinusoidal voltage signal injection for low-speed linear motors. This method replaces the bandpass filter with a two-stage series pure delay filter to extract the high-frequency current response. Simultaneously, a high-pass filter in the synchronous shaft system is used to extract the clockwise rotational high-frequency current component, which is then used to estimate the speed and position of the mover. This method can improve the position estimation accuracy of sensorless control of linear motors at low speeds, but it is not applicable at medium and high speeds. Summary of the Invention

[0004] To address the inherent chattering problem of traditional sliding mode observers and the positioning force disturbance inherent in linear permanent magnet vernier motors (SMOs), this invention proposes a sensorless control method for SMOs that combines a super-helical sliding mode observer and a dual second-order generalized integrator. The method employs an ST-SMO (Slip Mode Observer-Mount Observer) with an additional linear phase to solve the inherent chattering problem of traditional SMOs, while using D-SOGI (Dual-Synchronous Positioning Gauge) to filter out high-order harmonics generated by the positioning force of the linear motor. This method can be used at medium to high speeds and has advantages such as insensitivity to parameter changes, high estimation accuracy, good dynamic performance, and strong system robustness.

[0005] To achieve the technical objectives, the present invention adopts the following technical solution:

[0006] A sensorless control method for a permanent magnet linear motor combining a super-helical sliding mode observer and a dual second-order generalized integrator includes the following steps:

[0007] Step 1: The equations for the flux linkage and voltage of the LVPM on the dq axis are as follows:

[0008] ;

[0009] ;

[0010] Among them, Ψ d For the d-axis flux linkage, Ψ q For q-axis flux linkage, Ψ f For permanent magnet flux linkage, u d u q It is the voltage on the dq axis, R s Indicates the stator resistance, i d i q It is the current along the dq axis, L d L q is the inductance along the dq axis, and p is the differential operator; It is the electric angular frequency of the mover flux linkage, τ s Stator pole pitch;

[0011] The voltage state equations under the α-β axes obtained after the inverse Park transform are:

[0012] ;

[0013] Among them, L s Indicates stator inductance, u α u β These represent the α-β axis stator voltages, i α i β These represent the stator currents along the α-β axes, e α e β These represent the back electromotive forces of the motor along the α-β axes, respectively.

[0014] Further derivation yields the current state equation as follows:

[0015] .

[0016] Step 2: Using the current and voltage in the α-β coordinate system as inputs, the ST-SMO equations are constructed as follows:

[0017] ;

[0018] Among them, I α I β L represents the estimated current. s The stator resistance is represented by k1 and k2, and the sliding mode gain is represented by k1 and k2. The estimated back electromotive force of the ST-SMO can be expressed as:

[0019] ;

[0020] Then eα e β It is used as input to the double second-order generalized integrator module for computation.

[0021] Step 3: By selecting a specific resonant frequency, SOGI can filter out the 2k±1st harmonics contained in the estimated back EMF without amplitude attenuation and phase delay, and solve the inherent resonance problem of ST-SMO, thereby improving the accuracy of estimated angle and velocity. The transfer function of SOGI is:

[0022] ,

[0023] ;

[0024] Where s is the Laplace operator, ω s k is the undamped natural frequency of SOGI. g Damping ratio; Damping ratio The selection of SOGI should comprehensively consider its dynamic performance and harmonic attenuation effect; k g The smaller the value, the longer the system settling time and the worse the dynamic performance; according to the relevant knowledge of automatic control principles, the damping coefficient of a second-order system... After comprehensive consideration, the optimal damping ratio is selected. , .

[0025] Step 4: The transfer function of the phase-locked loop is:

[0026] ;

[0027] Where, k p and k i These are the proportional and integral coefficients of the PI controller;

[0028] The estimated back EMF obtained after D-SOGI filtering is used as the input of the phase-locked loop, and the estimated angle and estimated speed of the motor can be obtained after calculation.

[0029] Step 5: Use the estimated angular velocity obtained from the phase-locked loop as the fundamental frequency of the DSOGI. The estimated linear velocity and estimated rotor position derived from the estimated angular velocity are input into the dual closed-loop control system of the linear motor. This enables the sensorless control strategy of the permanent magnet vernier linear motor that combines a super-helical sliding mode observer and a dual second-order generalized integrator.

[0030] This invention offers the following advantages: By employing ST-SMO instead of traditional SMO, it improves system robustness and estimation accuracy. Simultaneously, for the unique positioning force harmonic disturbances of permanent magnet vernier linear motors, DSOGI is used instead of LPF to filter out the 2k±1 harmonics in the estimated back EMF, and then combined with a phase-locked loop to estimate the rotor position and speed. This method exhibits excellent transient performance and robustness, significantly improving the operating performance of sensorless control of permanent magnet vernier linear motors. Experiments under different steady-state conditions and speed-changing tests demonstrate that this sensorless control strategy can achieve high-quality operation of permanent magnet vernier linear motors. Attached Figure Description

[0031] Figure 1 : A sensorless control block diagram of a permanent magnet linear motor combining a super-helical sliding mode observer and a dual second-order generalized integrator;

[0032] Figure 2 : Schematic diagram of the principle structure of a dual second-order generalized integrator;

[0033] Figure 3 : Schematic diagram of phase-locked loop (PLL) principle;

[0034] Figure 4 Comparative results of velocity estimation experiments using different sliding mode observers at 0.2 m / s and 0.3 m / s; (a) Estimated velocity at 0.2 m / s; (b) Estimated velocity at 0.3 m / s;

[0035] Figure 5 Comparative results of angle estimation experiments using different sliding mode observers at 0.2 m / s and 0.3 m / s; (a) Angle estimation at 0.2 m / s; (b) Angle estimation at 0.3 m / s;

[0036] Figure 6 Comparison of experimental results of LPF and DSOGI filtering and FFT analysis; (a) LPF filtering results and FFT analysis; (b) DSOGI filtering results and FFT analysis;

[0037] Figure 7 Results of the speed change experiment; (a) estimated speed waveform; (b) estimated angle waveform; (c) estimated back electromotive force waveform. Detailed Implementation

[0038] The following is an illustration of an embodiment of the present invention. Figures 1-7 The technical solutions in the embodiments of the present invention will be described in detail and completely.

[0039] Step 1: The equations for the flux linkage and voltage of the LVPM on the dq axis are as follows:

[0040] ;

[0041] ;

[0042] Among them, Ψ d For the d-axis flux linkage, Ψ q For q-axis flux linkage, Ψ f For permanent magnet flux linkage, u d u q It is the voltage on the dq axis, R s Indicates the stator resistance, i d i q It is the current along the dq axis, L d L q is the inductance along the dq axis, and p is the differential operator; It is the electric angular frequency of the mover flux linkage, τ s Stator pole pitch;

[0043] The voltage state equations under the α-β axes obtained after the inverse Park transform are:

[0044] ;

[0045] Among them, L s Indicates stator inductance, u α u β These represent the α-β axis stator voltages, i α i β These represent the stator currents along the α-β axes, e α e β These represent the back electromotive forces of the motor along the α-β axes, respectively.

[0046] Further derivation yields the current state equation as follows:

[0047] .

[0048] Step 2: Using the current and voltage in the α-β coordinate system as inputs, the ST-SMO equations are constructed as follows:

[0049] ;

[0050] Among them, I α I β L represents the estimated current. s The stator resistance is represented by k1 and k2, and the sliding mode gain is represented by k1 and k2. The estimated back electromotive force of the ST-SMO can be expressed as:

[0051] ;

[0052] Then e α e β It is used as input to the double second-order generalized integrator module for computation.

[0053] Step 3: By selecting a specific resonant frequency, SOGI can filter out the 2k±1st harmonics contained in the estimated back EMF without amplitude attenuation and phase delay, and solve the inherent resonance problem of ST-SMO, thereby improving the accuracy of estimated angle and velocity. The transfer function of SOGI is:

[0054] ,

[0055] ;

[0056] Where s is the Laplace operator, ω s k is the undamped natural frequency of SOGI. g Damping ratio; Damping ratio The selection of SOGI should comprehensively consider its dynamic performance and harmonic attenuation effect; k g The smaller the value, the longer the system settling time and the worse the dynamic performance; according to the relevant knowledge of automatic control principles, the damping coefficient of a second-order system... After comprehensive consideration, the optimal damping ratio is selected. , .

[0057] Step 4: The transfer function of the phase-locked loop is:

[0058] ;

[0059] Where, k p and k i These are the proportional and integral coefficients of the PI controller;

[0060] The estimated back EMF obtained after D-SOGI filtering is used as the input of the phase-locked loop, and the estimated angle and estimated speed of the motor can be obtained after calculation.

[0061] Step 5: Use the estimated angular velocity obtained from the phase-locked loop as the fundamental frequency of the DSOGI. The estimated linear velocity and estimated rotor position derived from the estimated angular velocity are input into the dual closed-loop control system of the linear motor. This enables the sensorless control strategy of the permanent magnet vernier linear motor using a combination of a super-helical sliding mode observer and dual second-order generalized integrators.

[0062] Step 6: Select appropriate control parameters. First, run the system under two conditions: 0.2 m / s and 0.3 m / s. Record and compare the estimated speed and angle waveforms obtained by different methods. Next, record the estimated back EMF waveform after LPF and DSOGI filtering under the 0.2 m / s condition and perform FFT analysis. Finally, allow the motor to run stably at a speed of 0.2 m / s from 0 to 2.5 seconds. At 2.5 seconds, the given speed abruptly changes to 0.3 m / s, and record the estimated speed, estimated back EMF, and estimated angle waveforms of the motor. Steady-state experiments and variable-speed experiments verify that the sensorless control strategy of the permanent magnet vernier linear motor combining the super-helical sliding mode observer and the dual second-order generalized integrator has excellent transient performance and robustness.

[0063] Figure 1 A block diagram of sensorless control for a permanent magnet vernier linear motor combining a super-helical sliding mode observer and a double second-order generalized integrator is presented. Figure 2 A block diagram illustrating the principle and structure of a dual second-order generalized integrator is presented. Figure 3 The structural block diagram of the orthogonal phase-locked loop is given; Figure 4 (a) and Figure 4 (b) The results of the estimated velocity and estimated angle of different sliding mode observers at 0.2 m / s are presented; Figure 5 (a) and Figure 5 (b) The comparison results of the estimated velocity and estimated angle of different sliding mode observers at 0.2 m / s are given. It is not difficult to find that the sensorless control strategy of ST-DSOGI-SMO has the highest estimation accuracy under different working conditions. Figure 6 (a) and Figure 6 (b) The filtering results of LPF and DSOGI for estimating back EMF at 0.2 m / s are given, and FFT analysis is performed. It can be seen from the figure that DSOGI has a better filtering effect on the 2k±1 harmonic in the estimated back EMF. Figure 7 (a) Figure 7 (b) and Figure 7 (c) The estimated speed, estimated angle and estimated back EMF of ST-DSOGI-SMO under variable speed conditions are given respectively. It is easy to see that the method has excellent dynamic performance and robustness.

[0064] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A sensorless control method for a permanent magnet linear motor combining a superspiral sliding mode observer and a dual second-order generalized integrator, characterized in that, Includes the following steps: Step 1: Based on the motor equations in the three-phase natural coordinate system ABC, the motor equations in the rotating coordinate system dq are derived. After inverse Park transformation, the voltage state equations in the α-β axis are obtained, and the current state equations are derived. At the same time, considering the cogging force and end force generated by the slotted stator of the linear motor, a mathematical model of the linear motor considering the positioning force is built. Step 2: Use the voltage state equation obtained in Step 1 to derive the current state equation, take the current and voltage under the α-β axis as input, and construct the state equation of the super-spiral sliding mode observer ST-SMO. Step 3: Input the α-β axis estimated back EMF obtained from ST-SMO into a SOGI. At the same time, use the angular velocity corresponding to the linear velocity of the motor as the fundamental frequency and select an appropriate damping ratio to filter out the 2k±1 harmonics in the estimated back EMF and obtain the α-β axis estimated back EMF with higher estimation accuracy. Step 4: Using a phase-locked loop, calculate the estimated back EMF after filtering by the dual second-order generalized integrator DSOGI. After selecting an appropriate PI regulator coefficient, the estimated angular velocity and estimated rotor angle can be obtained. Step 5: Use the estimated angular velocity obtained from the phase-locked loop as the fundamental frequency of the DSOGI. The estimated linear velocity and estimated rotor position derived from the estimated angular velocity are input into the dual closed-loop control system of the linear motor. This enables the sensorless control strategy of the permanent magnet vernier linear motor that combines a super-helical sliding mode observer and a dual second-order generalized integrator.

2. The method according to claim 1, characterized in that, In step 1, the flux linkage and voltage equations of the motor on the dq axis are as follows: ； ； Among them, Ψ d For the d-axis flux linkage, Ψ q For q-axis flux linkage, Ψ f For permanent magnet flux linkage, u d u q It is the voltage on the dq axis, R s Indicates the stator resistance, i d i q It is the current along the dq axis, L d L q is the inductance along the dq axis, and p is the differential operator; It is the electric angular frequency of the mover flux linkage, τ s Stator pole pitch; The voltage state equations under the α-β axes obtained after the inverse Park transform are: ； Among them, L s Indicates stator inductance, u α u β These represent the α-β axis stator voltages, i α i β These represent the stator currents along the α-β axes, e α e β These represent the back electromotive forces of the motor along the α-β axes, respectively. Further derivation yields the current state equation as follows: 。 3. The method according to claim 2, characterized in that, In step 2, Using the current and voltage in the α-β coordinate system as inputs, the ST-SMO state equations are constructed as follows: ； Among them, I α I β L represents the estimated current. s The stator resistance is represented by k1 and k2, and the sliding mode gain is represented by k1 and k2. The estimated back electromotive force of the ST-SMO can be expressed as: ； Then e α e β It is used as input to the double second-order generalized integrator module for computation.

4. The method according to claim 1, characterized in that, In step 3, By selecting a specific resonant frequency, SOGI can filter out the 2k±1st harmonics contained in the estimated back EMF without amplitude attenuation and phase delay, and solve the inherent resonance problem of ST-SMO, thus improving the accuracy of estimated angle and velocity. The transfer function of SOGI is: ， ； Where s is the Laplace operator, ω s k is the undamped natural frequency of SOGI. g Damping ratio; Damping ratio The selection of SOGI should comprehensively consider its dynamic performance and harmonic attenuation effect; k g The smaller the value, the longer the system settling time and the worse the dynamic performance; according to the relevant knowledge of automatic control principles, the damping coefficient of a second-order system... After comprehensive consideration, the optimal damping ratio is selected. , .

5. The method according to claim 1, characterized in that, In step 4, The transfer function of the phase-locked loop is: ； Where kp and ki are the proportional coefficient and integral coefficient of the PI controller; The estimated back EMF obtained after D-SOGI filtering is used as the input of the phase-locked loop, and the estimated angle and estimated speed of the motor can be obtained after calculation.

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