A method for position-free control of permanent magnet linear synchronous motor

Abstract

The present invention discloses a positionless control method for a permanent magnet linear synchronous motor, comprising the following steps: taking a dual-three-phase permanent magnet linear synchronous motor as a control object, building a closed-loop control mathematical model of the linear motor; adopting a control mode of i d = 0 for closed-loop control of the motor, and providing twelve control signals for the drive module through a space vector pulse width modulation algorithm; establishing a speed observer model based on a linear quadratic regulator and a Kalman filter; conducting simulation tests, with both the inner loop control and the outer loop control of the motor adopting PI control; analyzing the stability of the LQR-KF speed observer model; setting the stator resistance and inductance of the motor to vary within a set range, and using mismatched motor parameters, studying the influence of parameter changes on the stability of the speed observer model through eigenvalue locus analysis; it is an optimal state observer of the system in the sense of minimum variance, which greatly reduces the complexity of the algorithm while achieving optimal speed observation of the motor, and is conducive to hardware implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a position-free control method of a permanent magnet linear synchronous motor. Background Art

[0002] Compared with rotary motors, linear motors have the advantages of simple structure, low noise, high speed and acceleration, easy maintenance and high reliability. Among them, the dual three-phase permanent magnet linear synchronous motor (DTP-PMLSM) can achieve high-power drive with low-voltage switching devices, effectively suppress the electromagnetic torque pulsation of the motor, and has broad application prospects in aerospace, rail transportation and electric vehicles. Due to the advantages of simple system design and accurate position detection, the use of mechanical sensors is given priority in engineering design. However, mechanical sensors not only increase the cost of system design, but also complex application conditions will reduce the accuracy of the sensor, thereby reducing the reliability of the system. Position-free control refers to estimating the position and speed of the motor through an algorithm without using a mechanical sensor. In the case of position-free control, the motor drive control unit controls the movement of the motor by calculating the feedback signal instead of controlling the movement of the motor through the feedback signal of the mechanical sensor. Position-free control improves the performance and reliability of the motor, while reducing the use of mechanical sensors and reducing the cost and complexity of the system.

[0003] Therefore, designing a vector speed control system to realize DTP-PMLSM without position sensor has important engineering value.

[0004] At present, the more mature motor sensorless control algorithms mainly include two categories: one is the high-frequency signal injection method based on the detection of the motor magnetic field salient pole position, which can realize the high-performance sensorless operation of the motor in the zero-speed domain. The other type of motor positionless control method is a control method based on back-EMF observation suitable for the medium and high-speed domain of the motor. In order to improve the observation accuracy, some closed-loop observation control strategies are applied to the motor positionless algorithm. Common methods include model reference adaptive system, sliding mode observer and extended Kalman filter. As an extended application of the Kalman filter (KF) algorithm in nonlinear systems, the extended Kalman filter (EKF) is a recursive calculation method for the optimal state observation of the system in the sense of minimum variance. It can effectively weaken the influence of random signals on the system and is widely used in autonomous driving, signal processing, system state observation and other fields. However, many EKF algorithms currently studied face the challenge of complex calculations. Even if modern digital signal processors are used to solve the problem of algorithm complexity, it will cost a lot to do so. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art. In view of the problems that mechanical sensors bring additional costs to the system and the accuracy decreases under complex working conditions, and the traditional position-free control algorithm is complicated to implement, a position sensor-free tracking control method based on a linear quadratic regulator and a Kalman filter (LQR-KF) is proposed to more accurately and simply track and control the motor speed in real time.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a position-free control method of a permanent magnet linear synchronous motor, comprising the following steps:

[0007] Step 1: Take the dual three-phase permanent magnet linear synchronous motor as the control object and build a linear motor closed-loop control mathematical model;

[0008] Step 2: Use i d =0 control mode to perform motor closed-loop control, calculate the motor control quantity based on the linear motor closed-loop control mathematical model built in step 1, and provide twelve control signals for the drive module through the space vector pulse width modulation algorithm;

[0009] Step 3: Establish an LQR-KF speed observer model based on a linear quadratic regulator LQR and a Kalman filter KF for a dual three-phase permanent magnet linear synchronous motor;

[0010] Step 4: Conduct simulation test. Both the inner and outer loops of the motor are controlled by PI control. The actual speed and displacement signals of the outer loop come from the LQR-KF speed observer model.

[0011] Step 5: Analyze the stability of the LQR-KF speed observer model; set the motor stator resistance and inductance to change within the set range, use the mismatched motor parameters, and use the characteristic root locus analysis method to study the impact of parameter changes on the stability of the speed observer model.

[0012] Furthermore, the linear motor closed-loop control mathematical model in step 1 includes a mathematical model of the dual three-phase permanent magnet linear synchronous motor in a three-phase stationary coordinate system, and the mathematical model of the dual three-phase permanent magnet linear synchronous motor in a three-phase stationary coordinate system is as follows:

[0013]

[0014] In the above formula, is the stator phase voltage, the subscripts a, b, c, u, v, w are the stator winding numbers, is the resistance coefficient matrix, , R s is the resistance, is the stator phase current, is the stator flux per phase, is the inductance matrix, is the electrical angle;

[0015] The torque equation of this motor is:

[0016]

[0017] Among them, F e is the electromagnetic force output by the motor; τ is the motor pole pitch; i d 、i q are the motor d-axis and q-axis currents, L q is the quadrature-axis inductance, L d is the direct-axis inductance, φ f is the permanent magnet flux of the motor.

[0018] Furthermore, the linear motor closed-loop control mathematical model in step 1 also includes a mathematical model in a VSD coordinate system, and the mathematical model in the VSD coordinate system is:

[0019] The vector space decoupling transformation coordinate transformation method is used to map the various variables of DTP-PMLSM to three mutually orthogonal subspaces, namely, dq subspace, xy subspace and zero-sequence subspace; therefore, the mathematical model of DTP-PMLSM in the VSD coordinate system is:

[0020]

[0021] In the formula, u d 、u q are the motor d-axis and q-axis voltages, u x 、u y are the voltages on the α-axis and β-axis of the motor, is the mechanical angular velocity of the motor, φ f is the motor flux. For surface-mount motors, the d-axis inductance is equal to the q-axis inductance, and L s Indicates that the x-axis inductance is equal to the y-axis inductance, expressed as L z Indicates; R is resistance; i d and i q They are the motor d-axis and q-axis currents respectively, i x , i y are the currents on the α-axis and β-axis of the motor respectively.

[0022] Further, the step 2 adopts i d=0 control method for closed-loop control of the motor includes: the d-axis component id of the stator current is zero, that is, id is not controlled and kept at zero, and by adjusting the id component of the current, only the q-axis component iq of the stator current is controlled to keep a constant torque of the motor during operation.

[0023] Furthermore, the method of providing twelve control signals to the driving module through the space vector pulse width modulation algorithm in step 2 is:

[0024] Calculate multiple sine wave voltages and multiple cosine wave voltages of the dual three-phase permanent magnet linear synchronous motor and multiple corresponding sector numbers through the SVPWM algorithm;

[0025] According to the sector number and the control amount of the motor, the power tubes that need to be turned on and off are calculated to generate the SVPWM waveform;

[0026] The SVPWM waveform is input into the drive module to drive the dual three-phase permanent magnet linear synchronous motor to operate.

[0027] Furthermore, from the LQR theory, we know that for a linear steady-state system with feedback control input u=Kx, the closed-loop system can be expressed as:

[0028]

[0029] Among them, K represents the gain matrix of the state feedback controller, A is the state transfer matrix of the system, B is the control input matrix of the system, x represents the system state quantity, is the first-order derivative of x;

[0030] Assume that at time t, an optimal control law u(t) is sought to minimize the performance index function J. The performance index function J is calculated as:

[0031]

[0032] in, Q and R Represents the state variables x and input u The weights are diagonal matrices;

[0033] (2) According to the KF algorithm, assuming that there is noise in both the state equation and the output equation of the system, the linear steady-state system can be expressed as:

[0034]

[0035] Among them, y is the output of the system, A, B, C and D are the state transfer matrix, control input matrix, output matrix and dynamic feedback matrix of the system respectively; by adjusting D, the output of the system is adjusted to improve the performance of the system, and is an uncorrelated, zero-mean, Gaussian white noise random vector;

[0036] Therefore, under the premise of knowing the random characteristics of the noise, the system state observer is written in the following form:

[0037]

[0038] in, is an estimate of the system state x, is the estimated value of the system output y, K e is the Kalman gain matrix, which is obtained by matrix recursion and update operations in the KF algorithm;

[0039] For the KF algorithm, the goal of optimal state observation is achieved by minimizing the expectation of observation error. By derivation, the observation error The expectation can be expressed as follows:

[0040]

[0041] and Γ represent the covariance matrices of system noise and measurement noise, respectively. β 0 is the time parameter;

[0042] (3) Compare the equation of the performance index function J in LQR with the expected error of the KF algorithm Based on the duality principle, we get the following equivalent formula:

[0043]

[0044] Therefore, solving K through the LQR algorithm is equivalent to solving Ke in the KF algorithm; finally, combined with the system state observer, the optimal observation of the system can be achieved.

[0045] Furthermore, the LQR_KF speed observer model is finally expressed as:

[0046]

[0047] in, B v is the damping coefficient, M is the load mass, i d 、i q They are the motor d-axis and q-axis currents respectively,i x , i y are the currents on the α-axis and β-axis of the motor respectively, L x , L y are the inductances on the α-axis and β-axis of the motor respectively; the input of the speed observer model is dq axis, xy The shaft current, voltage, and output are dq Observed shaft current value, xy Shaft current observation value, motor speed observation value, displacement observation value, τ is the motor pole pitch, φ f is the permanent magnet flux of the motor; is the control voltage, and u d , u q The following relationship exists, where is the electrical angle, is the mechanical angular velocity of the motor:

[0048]

[0049] The input of the speed observer model is the dq axis and xy axis current (i d 、i q 、i x 、i y ), voltage, and the outputs are dq axis current observation value, xy axis current observation value, motor speed observation value, displacement observation value, with superscript The parameters of represent the observed values ​​of the corresponding parameters.

[0050] Furthermore, the method of studying the influence of parameter changes on the stability of the speed observer model by characteristic root locus analysis is as follows: performing LQR-KF speed observation stability analysis, by comparing the difference between the actual system and the observed system state quantity Whether it diverges, analyze the stability of the LQR-KF reduced-order observer; According to automatic control theory: if all the real parts of the characteristic roots of the state matrix A are negative, then the system described is stable, that is, the error It will eventually approach zero, and the observer state gradually approaches the actual object state.

[0051] The beneficial effects and features of the present invention are:

[0052] (1) The main control object of the linear quadratic regulator LQR is a linear system described in state space. The objective function is a quadratic function of the state quantity of the controlled object and the external control input. The main purpose is to minimize the objective function. The Kalman filter KF algorithm is a recursive calculation method for the optimal state estimation of a nonlinear system in the sense of minimum variance. It can effectively weaken the influence of random signal interference and measurement noise. Compared with general speed estimation methods, it is easier to overcome the nonlinearity and uncertainty of the motor model.

[0053] (2) The LQR-KF speed observer model designed by the present invention adopts the LQR optimal control theory and the KF optimal observation concept, and minimizes the state quantity observation error of the KF algorithm by minimizing the LQR performance index function. Therefore, the LQR-KF speed observer model is an optimal state observer.

[0054] (3) Compared with the prior art, the LQR-KF speed observer model of the present invention solves the Kalman gain matrix with a simple calculation method, which reduces the complexity of algorithm implementation and facilitates hardware implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a model diagram of a dual three-phase permanent magnet linear synchronous motor of a preferred embodiment of the present invention;

[0056] Figure 2 It is a block diagram of the principle of position-free control of a dual three-phase permanent magnet linear synchronous motor according to a preferred embodiment of the present invention;

[0057] Figure 3 is the stability analysis curve of the LQR-KF observer of the preferred embodiment of the present invention (the state matrix root locus with resistance change);

[0058] Figure 4 is the stability analysis curve of the LQR-KF observer of the preferred embodiment of the present invention (the state matrix root locus with the change of inductance);

[0059] Figure 5 The motor speed observation curve and the observation error curve (observation speed and reference speed comparison curve) when no-load are shown in the preferred embodiment of the present invention;

[0060] Figure 6 The motor speed observation curve and the observation error curve (the error waveform between the observation speed and the reference speed) when no-load is shown in the preferred embodiment of the present invention;

[0061] Figure 7 is the motor speed observation curve when the motor parameters of the present invention do not match;

[0062] The reference numerals in the figure represent: 1-mover, 2-stator. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] The dual three-phase motor model in the specific embodiment of the present invention is as follows: Figure 1 As shown, a long primary bilateral permanent magnet linear synchronous motor with a double-layer Halbach structure and a C-type winding is used.

[0065] like Figure 2 As shown in the figure, a block diagram of the position-free control principle of a dual three-phase permanent magnet linear synchronous motor is provided. The linear motor control principle mainly includes the following aspects:

[0066] (1) The linear motor closed-loop control system adopts dual-loop control, which mainly includes the inner current loop and the outer speed and position loop. The input of the outer loop control is the motor reference speed. V ref , reference position X ref , reference acceleration A ref And the motor observed speed and position signals output by the LQR-KF observer. q Shaft current i dref As the reference input of the current inner loop. And the current inner loop input also includes d Shaft current reference value i dref and xy Shaft current reference value i xy,ref .

[0067] In order to improve the control performance of the motor, the current inner loop adopts the improved vector control algorithm of VSD coordinate transformation, that is, the current inner loop contains dq PI regulator under subspace and xy Proportional resonant PR regulator in harmonic subspace. To ensure that the motor has the minimum stator copper loss when outputting the same electromagnetic torque, xy The harmonic subspace setpoint is set to zero.

[0068] When the VSD coordinate transformation method is used, xy The variable obtained in the subspace is the AC quantity. Due to the gain and bandwidth limitations of the conventional Pl regulator, it is impossible to achieve zero-static-error regulation of the AC quantity, so the control result obtained is not optimal. In order to solve the above problems, xyThe current regulator of the subspace adopts PR control to obtain better control performance.

[0069] (2) The voltage output by the motor control is used as the input of the inverter, and the six-phase voltage of the dual three-phase motor is obtained through the space vector modulation SVPWM algorithm. The advantages of the SVPWM algorithm are as follows: SVPWM has a relatively high degree of harmonic optimization, better harmonic elimination effect than SPWM, easy implementation, and improved voltage utilization; the SVPWM algorithm improves the DC voltage utilization of the voltage source inverter and the dynamic response speed of the motor, while reducing the torque pulsation of the motor; it is more suitable for digital control systems.

[0070] (3) Six-phase output current of DTP-PMLSM i abc,uvw After vector decoupling transformation, VSD is sent to the position-free control module and the current PI regulator module respectively. The mathematical model of DTP-PMLSM in the VSD coordinate system is:

[0071]

[0072] The torque equation is:

[0073]

[0074] Among them, F e is the electromagnetic force output by the motor; τ is the motor pole pitch; i d 、i q are the motor d-axis and q-axis currents, L q is the quadrature-axis inductance, L d is the direct axis inductance, φ f is the permanent magnet flux of the motor.

[0075] (4) The LQR-KF positionless control module takes the motor measured current and control voltage as input and outputs the observed speed V and observation location X Participate in the closed-loop control of the motor. The observed position signal is transformed into an angle through coefficient transformation, which is used for the coordinate transformation of the motor control.

[0076] Figure 3 is the LQR-KF stability analysis curve. Figure 3 is the state matrix root locus as the resistance changes, Figure 4 is the state matrix root trajectory with inductance change. The motor parameters (resistance, inductance) are set to change within the range of ±20%, and the characteristic root trajectory distribution diagram of the state matrix is ​​obtained. As can be seen from the figure, with the change of parameters, the characteristic roots of the system state matrix move in the left half plane of the complex plane and never appear in the right half plane. The LQR-KF reduced-order observer is always stable.

[0077] Figure 5 , Figure 6 is the motor speed observation curve. In the simulation system, set: t = 0s-0.2s, the motor runs at uniform acceleration; t = 0.2s-0.3s, the motor runs at a constant speed of 4m / s; t = 0.3s-0.5s, the motor runs at a uniform deceleration rate. Figure 5 is the comparison curve between the observed speed and the reference speed, Figure 6 is the error waveform between the observed speed and the reference speed. As can be seen from the figure, the observed value is basically consistent with the given value curve. The maximum error of the motor observed speed given speed value is 0.056m / s. This verifies the effectiveness and accuracy of the position-free control algorithm proposed in the present invention.

[0078] Figure 7 The motor speed observation curve when the motor parameters do not match. To continue to verify the robustness of the observer, a non-periodic transient operation state of the motor is simulated in the simulation, that is, the speed of the motor changes all the time during operation. The maximum speed is 10m / s, and the motor takes less than 0.5s to complete one action from start to stop. Considering that the motor resistance will increase with the increase of temperature, the motor stator resistance value is set to change by +20%. From Figure 5 It can be seen that the change of the resistance value in the motor model within a certain range will not affect the observation effect of the LQR-KF reduced-order observer on the motor speed, and the PMLSM system always runs stably.

[0079] Based on the Linear Quadratic Regulator (LQR) and Kalman Filter (KF) control algorithms, the present invention designs an LQR-KF motor speed observer model to calculate the speed and position of the motor in real time. Taking the dual three-phase permanent magnet linear synchronous motor as the research object, the motor system mathematical model is selected to establish the state space equation, and the Kalman gain matrix in the KF algorithm is equivalently solved through the minimization process of the LQR performance index function, so as to construct the dual three-phase permanent magnet linear synchronous motor (DTP-PMLSM) speed observer model to realize the position-free control of the motor; the linear motor system closed-loop controller in the present invention selects the current loop as the inner loop to adjust the six-phase current of the motor; the outer loop adjusts the speed and position errors through the PI controller, and the output is used as the input of the current inner loop; compared with the prior art, this position-free control method is a system optimal state observation in the sense of minimum variance, which greatly reduces the complexity of the algorithm while realizing the optimal observation of the motor speed, and is conducive to hardware implementation.

[0080] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. A method for position-free control of a permanent magnet linear synchronous motor. It is characterized in that The steps include: Step 1: Take the dual three-phase permanent magnet linear synchronous motor as the control object and build a linear motor closed-loop control mathematical model; Step 2: Use i d =0 control mode to perform motor closed-loop control, calculate the motor control quantity based on the linear motor closed-loop control mathematical model built in step 1, and provide twelve control signals for the drive module through the space vector pulse width modulation algorithm. i d is the motor d-axis current; Step 3: Establish an LQR-KF speed observer model based on a linear quadratic regulator LQR and a Kalman filter KF for a dual three-phase permanent magnet linear synchronous motor; Step 4: Conduct simulation test. Both the inner and outer loops of the motor are controlled by PI control. The actual speed and displacement signals of the outer loop come from the LQR-KF speed observer model. Step 5: Analyze the stability of the LQR-KF speed observer model; set the motor stator resistance and inductance to change within the set range, use the mismatched motor parameters, and use the characteristic root locus analysis method to study the effect of parameter changes on the stability of the speed observer model; The linear motor closed-loop control mathematical model in step 1 also includes a mathematical model in a VSD coordinate system, and the mathematical model in the VSD coordinate system is: The vector space decoupling transformation coordinate transformation method is used to map the various variables of DTP-PMLSM to three mutually orthogonal subspaces, namely, dq subspace, xy subspace and zero-sequence subspace; therefore, the mathematical model of DTP-PMLSM in the VSD coordinate system is: , In the formula, u d 、u q are the motor d-axis and q-axis voltages, u x 、u y are the voltages on the α-axis and β-axis of the motor, is the mechanical angular velocity of the motor, φ f is the permanent magnet flux of the motor; for surface-mount motors, the d-axis inductance L d Equal to the q-axis inductance L q , use L s Indicates that the x-axis inductance is equal to the y-axis inductance, expressed as L z Indicates; R is resistance; i d and i q They are the motor d-axis and q-axis currents respectively, i x , i y are the currents on the α-axis and β-axis of the motor respectively; The method of step 3 specifically includes: (1) From the LQR theory, we know that for a linear steady-state system with feedback control input u = Kx, the closed-loop system can be expressed as: , Among them, K represents the gain matrix of the state feedback controller, A is the state transfer matrix of the system, B is the control input matrix of the system, x represents the system state quantity, is the first-order derivative of x; At time t, find an optimal control law u(t) to minimize the performance index function J. The performance index function J is calculated as: , in, Q and R Represents the state variables x and input u The weights are diagonal matrices; (2) According to the KF algorithm, assuming that there is noise in both the state equation and the output equation of the system, the linear steady-state system can be expressed as: , Among them, y is the output of the system, A, B, C and D are the state transfer matrix, control input matrix, output matrix and dynamic feedback matrix of the system respectively; by adjusting D, the output of the system is adjusted to improve the performance of the system. and is an uncorrelated, zero-mean, Gaussian white noise random vector; Therefore, under the premise of knowing the random characteristics of the noise, the system state observer is written in the following form: , in, is an estimate of the system state x, is the estimated value of the system output y, K e is the Kalman gain matrix, which is obtained by matrix recursion and update operations in the KF algorithm; For the KF algorithm, the goal of optimal state observation is achieved by minimizing the expectation of observation error; by derivation, the observation error The expectation can be expressed as follows: , and Γ represent the covariance matrices of system noise and measurement noise, respectively. β 0 is the time parameter; (3) Compare the equation of the performance index function J in LQR with the expected error of the KF algorithm Based on the duality principle, we get the following equivalent formula: , Therefore, solving K through the LQR algorithm is equivalent to solving Ke in the KF algorithm; finally, combined with the system state observer, the optimal observation of the system can be achieved.

2. The method for position-free control of a permanent magnet linear synchronous motor according to claim 1, It is characterized in that The linear motor closed-loop control mathematical model in step 1 includes a mathematical model of the dual three-phase permanent magnet linear synchronous motor in a three-phase stationary coordinate system. The mathematical model of the dual three-phase permanent magnet linear synchronous motor in a three-phase stationary coordinate system is as follows: , In the above formula, is the stator phase voltage, and the subscripts a, b, c, u, v, and w are the stator winding numbers. is the resistivity matrix, R s is the resistance, is the stator phase current, is the stator flux per phase, is the inductance matrix, is the electrical angle; The torque equation of this motor is: , Among them, F e is the electromagnetic force output by the motor; τ is the motor pole pitch; i d 、i q are the motor d-axis and q-axis currents, L q is the quadrature-axis inductance, L d is the direct-axis inductance, φ f is the permanent magnet flux of the motor.

3. The position-free control method of the permanent magnet linear synchronous motor according to claim 1, It is characterized in that The step 2 adopts i d =0 control method for closed-loop control of the motor includes: the d-axis component id of the stator current is zero, that is, id is not controlled, so that id remains zero, and only the q-axis component iq of the stator current is controlled to make the motor maintain a constant torque during operation.

4. The position-free control method of the permanent magnet linear synchronous motor according to claim 1, It is characterized in that The method of providing twelve control signals to the driving module through the space vector pulse width modulation algorithm in step 2 is: Calculate multiple sine wave voltages and multiple cosine wave voltages of the dual three-phase permanent magnet linear synchronous motor and multiple corresponding sector numbers through the SVPWM algorithm; According to the sector number and the control amount of the motor, the power tubes that need to be turned on and off are calculated to generate the SVPWM waveform; The SVPWM waveform is input into the drive module to drive the dual three-phase permanent magnet linear synchronous motor to operate.

5. The method for position-free control of a permanent magnet linear synchronous motor according to claim 1, It is characterized in that The LQR_KF speed observer model is finally expressed as: , in, B v is the damping coefficient, M is the load mass, i d 、i q They are the motor d-axis and q-axis currents respectively, i x , i y are the currents on the α-axis and β-axis of the motor respectively, L x , L y are the inductances on the α-axis and β-axis of the motor respectively; τ is the motor pole pitch, φ f is the permanent magnet flux of the motor; , is the control voltage, and u d , u q There is the following relationship, is the electrical angle, is the mechanical angular velocity of the motor, Rs is the resistance value: , Among them, with superscript The parameters of represent the observed values ​​of the corresponding parameters.

6. The method for position-free control of a permanent magnet linear synchronous motor according to claim 1, It is characterized in that The method of studying the influence of parameter changes on the stability of the speed observer model by characteristic root locus analysis is as follows: performing LQR-KF speed observation stability analysis, and comparing the difference between the actual system and the observed system state quantity. Whether it diverges, analyze the stability of the LQR-KF reduced-order observer; According to automatic control theory: if all the real parts of the characteristic roots of the state matrix A are negative, then the system described is stable, that is, the error It will eventually approach zero, and the observer state gradually approaches the actual object state.

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