Sensorless Control Method and System for Highly Disturbance-Resistant Permanent Magnet Synchronous Linear Motor

Abstract

This invention discloses a sensorless control method and system for a permanent magnet synchronous linear motor (PMSM), belonging to the field of sensorless control technology for PMSMs. The method constructs an adaptive full-order state observer based on the current-state equation of the PMSM; utilizes the current-state error to construct an error feedback gain matrix; derives a parameter adaptive law based on Popov's hyperstability theorem to adjust the error between the observed current and the sampled current in real time; and designs an active disturbance rejection controller based on the motor's motion equation to further improve position observation accuracy by suppressing the influence of comprehensive system disturbances on the adaptive observer. This invention enables efficient sensorless control of PMSMs, eliminating the need for position sensor installation and improving position observation accuracy and system anti-interference capability.

Description

Technical Field

[0001] This invention belongs to the field of sensorless control technology for permanent magnet synchronous linear motors, and more specifically, relates to a sensorless control method and system for a highly disturbance-resistant permanent magnet synchronous linear motor. Background Technology

[0002] Permanent magnet synchronous linear motors (PMSMs) are a type of permanent magnet motor that directly converts electrical energy into linear motion without the need for intermediate transmission links. They offer advantages such as simple structure, high thrust, low noise, and low mechanical friction, making them widely popular in industrial applications. However, their control systems are significantly affected by time-varying uncertainties such as system parameter perturbations, external disturbances, and edge effects. To achieve high-performance control of PMSMs, speed and position signals need to be measured. Traditionally, mechanical sensors are used to directly measure speed and position signals, but this method suffers from drawbacks such as high cost, inconvenient installation, and susceptibility to harsh environments. In recent years, to overcome the problems associated with using mechanical sensors, researchers have extensively studied sensorless control strategies.

[0003] Since permanent magnet synchronous linear motors (PMSMs) were developed based on rotating PMSMs, and their working principles are essentially the same, their mathematical models are not significantly different. Theoretically, the sensorless methods applicable to PMSMs are also applicable to PMSMs. However, end effects are unavoidable in linear motors, and PMSMs are no exception. Therefore, the equations of motion for PMSMs differ somewhat from those for traditional rotating PMSMs. Directly applying the sensorless methods traditionally used for rotating PMSMs to PMSMs will not yield satisfactory observation accuracy.

[0004] Model reference adaptive control (MRC) is a simple, easy-to-implement, and high-performance adaptive control method. Previous studies have applied it to permanent magnet synchronous linear motors (PMSMs) with some success; however, most studies have not considered the inherent end-effects of linear motors. Furthermore, MRC is significantly affected by the motor parameters in the reference model and lacks error correction, thus its observation accuracy needs improvement. Since simply improving the observer itself cannot effectively reduce the impact of system end-effects, it is necessary to adopt a control strategy with strong anti-interference capabilities. This enhances the system's anti-interference ability, suppresses the thrust fluctuations caused by end-effects, and thereby improves the observer's accuracy. In conclusion, a sensorless control method with high observation accuracy and strong anti-interference performance is needed to achieve efficient control of PMSMs. Summary of the Invention

[0005] In response to the shortcomings and improvement needs of existing technologies, this invention provides a sensorless control method and system for a permanent magnet synchronous linear motor with strong anti-interference capability. The purpose is to solve the problems of low observation accuracy and poor anti-interference capability of existing sensorless algorithms.

[0006] To achieve the above objectives, the present invention provides a sensorless control method for a highly disturbance-resistant permanent magnet synchronous linear motor, comprising the following steps:

[0007] S1. The voltage and flux linkage equations of the permanent magnet synchronous linear motor are transformed to obtain the current state equation, and an adaptive full-order state observer based on current error is constructed.

[0008] S2. Based on the current state error, construct an error feedback system, configure the poles of the adaptive full-order state observer, and obtain the error feedback gain matrix;

[0009] S3. Based on Popov's superstability theorem, the parameter adaptive law is derived to obtain the observed electric angular velocity signal. The observed position signal can be obtained by integrating the observed electric angular velocity. Based on the proportional relationship between the observed electric angular velocity and the linear velocity of the motor's rotor, the observed linear velocity of the motor's rotor is calculated.

[0010] S4. The active disturbance rejection controller is used to control the linear speed of the motor drive obtained by the observer. The second-order linear extended observer is used to observe the comprehensive disturbance of the system, and the nonlinear error feedback controller is used to control the speed signal and compensate for the observed disturbance.

[0011] S5. Perform i... on the reference current output by the active disturbance rejection controller. d =0 vector control, obtain d and q output voltages, and perform sensorless control of the motor through SVPWM modulation.

[0012] Further, the method described in step S1 includes:

[0013] The voltage and flux linkage equations of a permanent magnet synchronous linear motor in the dq coordinate system are as follows:

[0014]

[0015]

[0016] Among them, u d and u q R represents the voltage component along the dq axis. s ω is the resistance of each phase winding. e Let i be the mechanical angular velocity. d and i q Let ψ be the current component along the dq axis. d and ψ qLet ψ be the flux linkage component along the dq axis. f For the moving permanent magnet flux linkage, pψ d and pψ q For ψ d and ψ q The first derivative, L d and L q The equivalent inductance of the dq axis.

[0017] The current state equation is:

[0018]

[0019] Where, pi d and pi q For i d and i q The first derivative;

[0020] The adaptive full-order state observer based on current error is:

[0021]

[0022] in, Let G be the current observation value, and G be the feedback gain matrix. A s (t), G satisfies:

[0023]

[0024] Further, the method described in step S2 includes:

[0025] Current state error is The constructed error feedback system is as follows:

[0026]

[0027] in, The original poles of the system are found using the pole placement method:

[0028]

[0029] Where I is a positive definite matrix. The pole configuration of the observer proposed in this paper is as follows:

[0030]

[0031] The constructed error feedback gain matrix G is:

[0032]

[0033] Furthermore, the method described in step S3 includes:

[0034] The derived adaptive law for parameters is:

[0035]

[0036] Where, k p and k i For adaptive gain.

[0037] The observed position and linear velocity of the mover are obtained from the observed electric angular velocity as follows:

[0038]

[0039] Where τ is the motor pole pitch. For the position of the observed mover, The observed linear velocity of the moving part.

[0040] Further, the method described in step S4 includes:

[0041] The electromagnetic thrust of a permanent magnet synchronous linear motor is:

[0042]

[0043] The equation of motion is:

[0044]

[0045] Where M is the mass of the mover, B is the coefficient of friction, and F l For load force, F d This refers to thrust fluctuations caused by end effects.

[0046] Based on the above equation, the equation of motion can be rewritten as:

[0047]

[0048] We can obtain:

[0049]

[0050] To address various difficult-to-measure system disturbances such as thrust fluctuations, load, friction, and parameter variations, a second-order linearly extended observer is designed to observe these disturbances. Definition:

[0051]

[0052] By controlling a given speed The obtained current reference value Replace i q ,but:

[0053]

[0054] Where f represents the overall system disturbance.

[0055] The designed second-order linear extended state observer is as follows:

[0056]

[0057] Where β1 and β2 are the observer gains, z1 and For v s The tracking value of f.

[0058] Furthermore, the designed nonlinear error feedback controller is as follows:

[0059]

[0060] in, Given a speed, u0 is the control variable before compensation, l is the gain coefficient, and fal(e2,α,δ) is a nonlinear function satisfying:

[0061]

[0062] Where α is the nonlinearity factor and δ is the filtering factor.

[0063] Comprehensive perturbation to observation Compensation will be provided.

[0064]

[0065] Where u is the control law.

[0066] Another aspect of the present invention provides a sensorless control system for a highly disturbance-resistant permanent magnet synchronous linear motor, comprising: a computer-readable storage medium and a processor;

[0067] The computer-readable storage medium is used to store executable instructions;

[0068] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the sensorless control method for a highly disturbance-resistant permanent magnet synchronous linear motor as described in the first aspect of the present invention.

[0069] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0070] (1) The sensorless control method for a strong anti-disturbance permanent magnet synchronous linear motor provided by the present invention uses an adaptive full-order state observer to observe the position of the motor mover. Compared with the traditional model reference adaptive method, this observer introduces a current error feedback gain matrix to enable the current state error to converge quickly, which significantly improves the position observation accuracy.

[0071] (2) An active disturbance rejection controller is used to control the speed signal observed by the observer. The second-order linear extended observer is used to observe the comprehensive disturbance of the system, and the nonlinear error feedback controller is used to control the speed signal and compensate for the observed comprehensive disturbance, which greatly improves the anti-interference performance of the control system.

[0072] (3) The present invention combines an active disturbance rejection controller with an adaptive full-order state observer, and proposes a sensorless control method for a strong disturbance rejection permanent magnet synchronous linear motor with high disturbance rejection and high observation accuracy, which significantly improves the safety and reliability of the control system. Attached Figure Description

[0073] Figure 1 This is a block diagram of a sensorless control system for a highly disturbance-resistant permanent magnet synchronous linear motor based on an active disturbance rejection controller and an adaptive full-order state observer, provided in an embodiment of the present invention.

[0074] Figure 2 This is a system block diagram of the adaptive full-order state observer provided in an embodiment of the present invention;

[0075] Figure 3 This is a system block diagram of the active disturbance rejection controller provided in an embodiment of the present invention;

[0076] Figure 4 These are simulation results of two different sensorless methods for the motor from startup to stable operation provided in this embodiment of the invention: a proportional-integral controller and an adaptive full-order state observer, and an active disturbance rejection controller and an adaptive full-order state observer. (a) shows the control result of PI-AFO, and (b) shows the control result of ADRC-AFO.

[0077] Figure 5 The figures show simulation results of two different sensorless methods under the condition of sudden load addition during stable operation of the motor provided in the embodiments of the present invention: one using a proportional-integral controller and an adaptive full-order state observer, and the other using an active disturbance rejection controller and an adaptive full-order state observer; (a) is the control result of PI-AFO, and (b) is the control result of ADRC-AFO. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0079] On the one hand, the present invention provides a sensorless control method for a highly disturbance-resistant permanent magnet synchronous linear motor, the structural block diagram of which is shown below. Figure 1 As shown, it includes the following steps:

[0080] S1. The voltage and flux linkage equations of the permanent magnet synchronous linear motor are transformed to obtain the current state equation, and an adaptive full-order state observer based on current error is constructed.

[0081] Specifically, a Hall current sensor is used to collect the current signal in the dq coordinate of a permanent magnet synchronous linear motor.

[0082] The voltage and flux linkage equations of a permanent magnet synchronous linear motor in the dq coordinate system are as follows:

[0083]

[0084]

[0085] Among them, u d and u q R represents the voltage component along the dq axis. s ω is the resistance of each phase winding. e Let i be the mechanical angular velocity. d and i q Let ψ be the current component along the dq axis. d and ψ q Let ψ be the flux linkage component along the dq axis. f For the moving permanent magnet flux linkage, pψ d and pψ q For ψ d and ψ q The first derivative, L d and L q The equivalent inductance of the dq axis.

[0086] Based on the voltage and flux linkage equations, the current state equation is obtained as follows:

[0087]

[0088] The adaptive full-order state observer is designed based on the current-state equation as follows:

[0089]

[0090] in, Let G be the current observation value, and G be the feedback gain matrix. A s (t), G satisfies:

[0091]

[0092] S2. Based on the current state error, construct an error feedback system, configure the poles of the adaptive full-order state observer, and obtain the error feedback gain matrix.

[0093] Specifically, the current state error is The constructed error feedback system is as follows:

[0094]

[0095] in,

[0096] The original poles of the system are found using the pole placement method:

[0097]

[0098] Where I is a positive definite matrix. The pole configuration of the observer proposed in this paper is as follows:

[0099]

[0100] The constructed error feedback gain matrix G is:

[0101]

[0102] S3. Based on Popov's superstability theorem, the parameter adaptive law is derived to obtain the observed electric angular velocity signal. The observed position signal can be obtained by integrating the observed electric angular velocity. Based on the proportional relationship between the observed electric angular velocity and the linear velocity of the motor rotor, the observed linear velocity of the motor rotor is calculated.

[0103] Specifically, based on Popov's hyperstability theorem, the derived parameter adaptive law is as follows:

[0104]

[0105] Where, k p and k i For adaptive gain.

[0106] The observed position and linear velocity of the mover are obtained from the observed electric angular velocity as follows:

[0107]

[0108] Where τ is the motor pole pitch. For the position of the observed mover, The observed linear velocity of the moving part.

[0109] The position observer based on the adaptive full-order state observer constructed from S1-S3 is as follows: Figure 2 As shown.

[0110] S4. The active disturbance rejection controller (ADRC) is used to control the linear velocity of the motor drive, calculated by the observer. A second-order linear extended observer is used to observe the overall system disturbance, and a nonlinear error feedback controller is used to control the speed signal and compensate for the observed disturbance. Figure 3 As shown.

[0111] Specifically, the electromagnetic thrust of the permanent magnet synchronous linear motor is:

[0112]

[0113] The equation of motion is:

[0114]

[0115] Where M is the mass of the mover, B is the coefficient of friction, and F l For load force, F d This refers to thrust fluctuations caused by end effects.

[0116] The equations of motion are rewritten as follows:

[0117]

[0118] We can obtain:

[0119]

[0120] definition:

[0121]

[0122] By controlling a given speed The obtained current reference value Replace i q ,but:

[0123]

[0124] Where f represents the overall system disturbance.

[0125] Specifically, the designed second-order linear extended state observer is as follows:

[0126]

[0127] Where β1 and β2 are the observer gains, z1 and For v s The tracking value of f.

[0128] The designed nonlinear error feedback controller is as follows:

[0129]

[0130] in, Given a speed, u0 is the control variable before compensation, l is the gain coefficient, and fal(e2,α,δ) is a nonlinear function satisfying:

[0131]

[0132] Where α is the nonlinearity factor and δ is the filtering factor.

[0133] Comprehensive perturbation to observation Compensation will be provided.

[0134]

[0135] Where u is the control law.

[0136] The proposed sensorless control method with strong disturbance rejection is based on the traditional model reference adaptive method. It constructs an adaptive full-order state observer based on current error by introducing a current error feedback gain matrix to improve the observer's observation accuracy. Since the proposed observer does not consider the thrust fluctuation caused by end effects, a highly disturbance-resistant active disturbance rejection controller replaces the traditional PI controller. Specifically, a second-order linearly extended observer is used to observe the overall system disturbance, and a nonlinear error feedback controller is used to control the velocity signal and compensate for the observed disturbance. The current reference value output by the active disturbance rejection controller is used for i... d =0 vector control. According to the data information transmission, the input of the adaptive full-order state observer is the dq-axis sampled current, stator resistance, stator inductance, and dq-axis voltage obtained through vector control, and the output is the mover mechanical angular velocity and linear velocity; the input of the active disturbance rejection controller is the linear velocity signal output by the adaptive full-order state observer, and the output is the q-axis current reference value obtained by the nonlinear error feedback controller.

[0137] On the other hand, the present invention also provides a sensorless control system for a highly disturbance-resistant permanent magnet synchronous linear motor, comprising: a computer-readable storage medium and a processor;

[0138] The computer-readable storage medium is used to store executable instructions;

[0139] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described sensorless control method for a highly disturbance-resistant permanent magnet synchronous linear motor.

[0140] Example:

[0141] This embodiment takes a cylindrical permanent magnet synchronous linear motor as an example to simulate and verify the above method. The motor pole pitch τ is 51.8mm, the stator resistance is 1.5Ω, the d-axis inductance is 0.033H, the q-axis inductance is 0.033H, the permanent magnet flux linkage is 0.65Wb, and the mover mass is 22kg.

[0142] Specifically, Figure 4 The simulation results show the control results of two different sensorless control methods for the motor from startup to stable operation: a proportional-integral (PI) controller with an adaptive full-order state observer (AFO) and an active disturbance rejection controller (ADRC) with an adaptive full-order state observer. (a) shows the control result of PI-AFO, and (b) shows the control result of ADRC-AFO. It can be seen that the speed observation error of PI-AFO is 0.00012 m / s, and the position observation error is 0.00082 rad, while the speed observation error of ADRC-AFO is 0.00004 m / s, and the position observation error is 0.00037 rad. The simulation results show that the proposed ADRC-AFO has higher observation accuracy than the traditional PI-AFO. To better highlight the superiority of the proposed method, after the motor has been running stably at 0.1 m / s, a sudden load of 180 N is applied. The simulation results of the two different sensorless control methods are as follows: Figure 5 As shown, (a) represents the control results of PI-AFO, and (b) represents the control results of ADRC-AFO. It can be seen that after a sudden load increase, the velocity observation error of the traditional PI-AFO is 0.00015 m / s, and the position observation error is 0.00185 rad, while the proposed ADRC-AFO has a velocity observation error of 0.00006 m / s and a position observation error of 0.00141 rad. Clearly, the proposed method has higher observation accuracy than the PI-AFO method, which does not consider system thrust fluctuations, and the impact of sudden load changes on the proposed method is smaller, indicating that the ADRC-AFO method has strong anti-interference performance.

[0143] In summary, the sensorless control method with strong anti-interference capability based on active disturbance rejection controller and adaptive full-order state observer provided by this invention has strong anti-interference performance and can obtain relatively accurate velocity and position observation results.

[0144] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sensorless control method for a highly disturbance-resistant permanent magnet synchronous linear motor, characterized in that, Includes the following steps: S1. The voltage and flux linkage equations of the permanent magnet synchronous linear motor are transformed to obtain the current state equation, and an adaptive full-order state observer based on current error is constructed; the adaptive full-order state observer is: in, These are current observations. For the feedback gain matrix, , , , satisfy: , , , ;in, The resistance of each phase winding, For mechanical angular velocity, and for Current components of the shaft, For the permanent magnet flux linkage. and for Shaft equivalent inductance; S2. Based on the current state error, construct an error feedback system, configure the poles of the adaptive full-order state observer, and obtain the error feedback gain matrix; the current state error is... The constructed error feedback system is as follows: in, , , ; The system's original poles are: in, The matrix is ​​positive definite; the pole configuration of the adaptive full-order state observer is as follows: Error feedback gain matrix for: ， ； S3. Based on Popov's superstability theorem, the parameter adaptive law is derived to obtain the observed electric angular velocity signal. The observed position signal can be obtained by integrating the observed electric angular velocity. Based on the proportional relationship between the observed electric angular velocity and the linear velocity of the motor's rotor, the observed linear velocity of the motor's rotor is calculated. S4. The active disturbance rejection controller is used to control the linear speed of the motor drive obtained by the observer. The second-order linear extended observer is used to observe the comprehensive disturbance of the system, and the nonlinear error feedback controller is used to control the speed signal and compensate for the observed disturbance. S5. Adjust the reference current output by the active disturbance rejection controller. Vector control, to obtain , The output voltage is modulated by SVPWM to control the motor without a position sensor.

2. The control method according to claim 1, characterized in that, In step S1, the permanent magnet synchronous linear motor The equations for voltage and flux linkage in the coordinate system are: in, and for Voltage components of the axis, and for The magnetic flux component of the shaft, and for and The first derivative; The current state equation is: in, and for and The first derivative.

3. The control method according to claim 2, characterized in that, The parameter adaptive law derived in step S3 is as follows: in, and For adaptive gain; The observed mover position and mover linear velocity are obtained from the observed electric angular velocity as follows: ， in, The pole pitch of the motor. For the position of the observed mover, The observed linear velocity of the moving part.

4. The control method according to claim 3, characterized in that, The second-order linear extended state observer in the active disturbance rejection controller in step S4 is: in, and For observer gain, Based on speed reference value The current reference value obtained by control and for and The tracking value, For system-wide disturbances; The nonlinear error feedback controller is: in, For a given speed, For the control variables before compensation, This is the gain coefficient. It is a nonlinear function that satisfies: in, It is a nonlinear factor. The filter factor; The compensation for the disturbance is as follows: in, This is a control law.

5. A sensorless control system for a highly disturbance-resistant permanent magnet synchronous linear motor, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the sensorless control method for a strong disturbance-resistant permanent magnet synchronous linear motor according to any one of claims 1 to 4.

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