Full-Speed Range Sensorless Control Method for Permanent Magnet Linear Motor Used in Launch

Abstract

The present invention discloses a sensorless control method for a permanent magnet linear motor for launching in the full speed range, including: taking a double-three-phase permanent magnet linear synchronous motor for launching as the control object, establishing a control model in a three-phase stationary coordinate system and a control model in a VSD coordinate system; when the mover acceleration command a meets the conditions, the motor is started statically and operates in a low-speed open-loop manner; when the motor runs to a predetermined speed, it switches to an adaptive sensorless closed-loop control strategy, and the position and speed of the motor are estimated through an adaptive LQR-KF observer, ensuring that the motor system operates reliably and stably up to the maximum launch speed; when the motor runs to the maximum launch speed, it quickly enters a deceleration state, and a control strategy of position open-loop and current closed-loop is adopted to ensure that the motor brakes quickly and stably; it not only ensures the estimation accuracy of the position observer, but also provides guidance for the sensorless closed-loop control of the electromagnetic launch motor.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and particularly to a sensorless control method for a permanent magnet linear motor for launching in the full speed range. Background Art

[0002] Electromagnetic launch technology has significant advantages such as high launch kinetic energy, high launch frequency, and fast startup time, and has broad application prospects in both military and civilian fields. Considering factors such as efficiency, power density, and thrust ripple, electromagnetic launch systems generally use permanent magnet synchronous linear motors as the core actuators. Since there is a possibility of collision with both ends when the linear motor moves linearly back and forth, mechanical position sensors are mostly used in engineering to obtain the position signal of the moving element of the launch motor for closed-loop control. However, mechanical position sensors not only increase the system design cost, but also the complex application conditions of high acceleration and strong vibration shock of electromagnetic launch motors will reduce the accuracy of the sensors, thereby reducing the reliability of the system. Therefore, designing a reliable and high-precision sensorless control method to achieve full-speed sensorless closed-loop control of the launch motor has important engineering value.

[0003] At present, the sensorless technology of motors is generally divided into two categories: sensorless control technology in the zero and low speed range and sensorless control technology in the medium and high speed range. Among them, the high-frequency signal injection method can not only realize the identification of the initial position of the moving element, but also shows excellent moving element position observation performance in the low-speed range. Therefore, this method is widely used in sensorless control of motors in the zero and low speed range. On the premise of knowing the initial position, the motor can be directly started and operated at low speed through open-loop control. The main methods include: voltage-frequency ratio V / F control and current-frequency ratio I / F control. The open-loop control strategy has a simple principle and low cost, and can be applied to motor systems with low requirements for startup performance. For sensorless control in the medium and high speed range, sensorless control technology based on closed-loop observation algorithms has received more attention, such as Model reference adaptive system (MRAS), Sliding mode observer (SMO), Extended Kalman filter (EKF), etc.

[0004] Regarding the research on the sensorless control method for the full speed range of motors, the full-range position observation of the motor from startup to braking can be achieved through a composite control algorithm. The composite control algorithm can ensure the stable operation of the sensorless control for the full speed range of the motor, but the additional switching control increases the system complexity while ensuring the smooth switching of the algorithm. To simplify the sensorless control model for the full speed range of the motor and reduce the problem of observed position oscillation caused by frequent switching of different control algorithms, some scholars have carried out research on a unified control model to achieve position observation of the motor from low speed to medium and high speeds. However, this simplified model is still in the theoretical exploration stage and lacks engineering application experience. Summary of the Invention

[0005] The object of the present invention is to overcome the shortcomings of the existing technology. Aiming at the problems that mechanical sensors bring additional costs to the system and have poor reliability under complex working conditions, and traditional sensorless control algorithms are complex to implement and have poor robustness, an adaptive sensorless control method based on linear quadratic regulator and Kalman filter (LQR-KF) is proposed to more accurately and simply perform real-time tracking control of the motor position.

[0006] To achieve the above object, the technical solution adopted by the present invention is: A sensorless control method for the full speed range of a permanent magnet linear motor for launch, characterized by including the following steps:

[0007] Step 1: Taking a dual three-phase permanent magnet linear synchronous motor (DTP-PMLSM) for launch as the control object, establishing a control model of the DTP-PMLSM in the three-phase stationary coordinate system, and establishing a control model of the DTP-PMLSM in the VSD coordinate system through the vector space decoupling (VSD) coordinate transformation method;

[0008] Step 2: Adopting the I / F open-loop control strategy, when the mover acceleration command a meets the conditions, completing the stationary startup of the DTP-PMLSM and running in low-speed open-loop;

[0009] Step 3: When the DTP-PMLSM runs to the predetermined speed, switching to the adaptive sensorless closed-loop control strategy, and realizing the position and speed estimation of the motor through the adaptive LQR-KF observer to ensure the reliable and stable operation of the motor system to the highest launch speed;

[0010] Step 4: When the DTP-PMLSM runs to the highest launch speed, quickly entering the deceleration state, and adopting the control strategy of position open-loop and current closed-loop to ensure the quick and stable braking of the motor;

[0011] Step 5: Building (through Matlab / Simulink software) the adaptive sensorless control model of the DTP-PMLSM, and analyzing the effectiveness of the control method through simulation.

[0012] Furthermore, the control model of the DTP-PMLSM established in the three-phase static coordinate system in Step 1 is as follows:

[0013]

[0014] In the above formula, u 6s =[u a u b u c u u u v u w T is the stator phase voltage, and the subscripts a, b, c, u, v, w are the stator winding labels. It is the resistance coefficient matrix, and R 6s =diag[R s R s R s R s R s R s , and R s is the resistance i 6s =[i a i b i c i u i v i w T is the stator phase current, is the magnetic flux per phase of the stator, and L 6s is the inductance coefficient matrix, and θ e is the electrical angle;

[0015] Furthermore, in Step 1, by using the vector space decoupling (VSD) coordinate transformation method, the control model of the DTP-PMLSM in the VSD coordinate system is established. By using the vector space decoupling (VSD) coordinate transformation method, each variable of the DTP-PMLSM is mapped into 3 mutually orthogonal subspaces, namely the d-q subspace, the x-y subspace, and the zero-sequence subspace; the mathematical model of the DTP-PMLSM in the VSD coordinate system is as follows:

[0016]

[0017] In the above formula, u d , u q , u x , u y are the stator voltages of the d-q subspace and the x-y subspace, and i d , i q , i x , i y are the stator voltages of the d-q subspace and the x-y subspace, and L​​d , L q is the inductance in the d-q subspace, L x , L y is the leakage inductance, R s is the stator resistance, ω e is the electrical angular velocity, is the permanent magnet flux linkage.

[0018] The motor torque equation is:

[0019]

[0020] Among them, F e is the electromagnetic force output by the motor; τ e is the pole pitch of the motor.

[0021] The motor mechanical motion equation is:

[0022]

[0023] Among them, F f is the interference quantity during motor operation, M is the total mass, v e is the motor operating speed, satisfying v e = ω e τ e / π.

[0024] Furthermore, the specific method of the second step is: in the I / F open-loop control system, a q-axis current is given, and the motor starts and operates; when a frequency is given, the corresponding electrical angular velocity command can be obtained, and its integral is used to obtain the virtual mover position information; the given mover acceleration command a needs to satisfy:

[0025]

[0026] Among them, I qref is the starting q-axis current, F fmax is the maximum external disturbing force of the motor.

[0027] Furthermore, in the third step, the adaptive LQR-KF observer includes two parts: a current state LQR-KF estimation model based on the linear quadratic regulator LQR and the Kalman filter KF, and a speed adaptive parameter.

[0028] The construction method of the LQR-KF estimation model is as follows:

[0029] 1) The KF-based observation system considering random noise can be expressed as:

[0030]

[0031] Wherein, the superscript '^' represents the estimated value of the variable, K is the feedback matrix related to the output error in the KF observer, and A, B, and C are the system matrix, input matrix, and output matrix of the observation system, respectively;

[0032] For the KF algorithm, the optimal state observation objective can be achieved by minimizing the expectation of the observation error. Through derivation, the expectation of the estimation error e(t) can be expressed in the following form:

[0033]

[0034] Wherein, Ψ and Γ are the covariance matrices of the system noise η and the measurement noise λ, respectively, β is the integration variable, and η and λ satisfy:

[0035]

[0036] In the formula, δ is the Dirac function.

[0037] It is known that the objective of the KF observer is to minimize the error expectation, so as to ensure the optimal estimation performance of the observer;

[0038] Furthermore, since it is relatively complex to directly solve the error expectation; therefore, the K is equivalently calculated by the LQR algorithm, so as to minimize the error expectation. The method for equivalently calculating the minimized error expectation using the LQR algorithm is as follows:

[0039] 2) According to the LQR theory, for a linear time-invariant system with feedback control u m = Lx m The closed-loop system can be expressed as:

[0040] dx m / dt = (A m + B m L)x m

[0041] Wherein, L is the system feedback gain matrix, and x m represents the system state variable, and A m , B m are the system matrix and the input matrix, respectively;

[0042] Assume that at time τ, an optimal control law u m (t) is found such that the cost function J is minimized, and J can be calculated as:

[0043]

[0044] In the formula, Q and R represent the weights of the state variable x m and the input quantity u m respectively, and are diagonal matrices;

[0045] 3) Comparing the equation of the cost function \(J\) in LQR with the expression of the expected value of the estimation error \(E[e(t)e(t) T of the KF algorithm, starting from the principle of duality, the following equivalent formula can be obtained:

[0046]

[0047] Therefore, by solving \(L\) through the LQR algorithm, \(K\) in the KF algorithm can be equivalently obtained.

[0048] Furthermore, in the third step, the adaptive LQR-KF observer further includes a speed adaptive parameter.

[0049] The speed adaptive parameter in the adaptive LQR-KF observer is designed according to the Popov hyperstability theory; it can be known from the Popov hyperstability theory that the necessary and sufficient condition for the asymptotic stability of a standard nonlinear time-varying feedback system is:

[0050] 1) The transfer matrix of the linear forward path must be a strictly positive real matrix;

[0051] 2) The nonlinear feedback channel satisfies the Popov integral inequality.

[0052] Based on the Popov hyperstability theory, the speed adaptive law is designed in a proportional-integral form:

[0053]

[0054] where \(k\) p and \(k\) i are adaptive gains, is the estimated value of the electrical angular velocity of the motor. Since the studied motor is a surface-mounted motor, \(L\) s is numerically equal to the d-q axis inductance.

[0055] Furthermore, the adaptive positionless control model of DTP-PMLSM in the fifth step is composed as follows:

[0056] 1) LQR-KF current observation model

[0057]

[0058] where \(u\) dl and \(u\) ql satisfy:

[0059]

[0060] In the formula, \(\theta\) e is the electrical angle, which is a necessary item to ensure the observability and controllability of the observation system.

[0061] 2) Speed Adaptive Model

[0062] Among them, the input of the positionless control model is the current, voltage, and motor body parameters in the d-q subspace, and the outputs are the observed values of the motor speed and displacement respectively.

[0063] Furthermore, when the dual three-phase permanent magnet linear synchronous motor decelerates, a braking control strategy with position open-loop and current closed-loop is adopted, a reverse braking electromagnetic force is set, and the q-axis reference value of the current closed-loop is calculated to ensure that the motor can stably decelerate to zero within a limited distance.

[0064] The beneficial effects and features of the present invention are as follows:

[0065] (1) The sensorless control method for the permanent magnet linear motor for launch in the full speed range of the present invention proposes a sensorless closed-loop control method for the permanent magnet linear motor for launch in the full speed range. When the motor operates in the zero low-speed range, I / F open-loop control is adopted; when the motor operates in the medium and high-speed ranges, an adaptive observer based on the linear quadratic regulator LQR and Kalman filter KF algorithms is proposed; during the braking phase of the motor, reverse electromagnetic force position open-loop control is adopted, thereby realizing sensorless closed-loop control of the electromagnetic launch motor in the full speed range.

[0066] (2) The sensorless control method for the permanent magnet linear motor for launch in the full speed range of the present invention designs an adaptive LQR-KF position observer using the LQR optimal control theory and KF optimal observation idea, and at the same time designs a speed adaptation rate according to the stability theorem, and adapts to the changes of external disturbances through the dynamic adjustment of the adaptive module. Compared with the prior art, this sensorless control method in the full speed range not only ensures the estimation accuracy of the position observer, but also enables the observation system to have a certain anti-interference ability, providing guidance for the sensorless closed-loop control of the electromagnetic launch motor. Description of the Drawings

[0067] Figure 1 It is the topology structure diagram of the launch motor in the preferred embodiment of the present invention;

[0068] Figure 2 It is the sensorless closed-loop control block diagram of the launch motor in the preferred embodiment of the present invention;

[0069] Figure 3 It is the principle block diagram of the I / F open-loop control in the preferred embodiment of the present invention (where (a) is the forward starting stage of the motor; (b) is the forward running stage of the motor);

[0070] Figure 4 It is the control block diagram of the adaptive position observer in the preferred embodiment of the present invention;

[0071] Figure 5It is the speed observation curve and observation error curve of the full-speed range operation of the launch motor in the preferred embodiment of the present invention (where: (a) I / F open-loop start speed waveform; (b) Adaptive sensorless control speed waveform; (c) Back electromagnetic force braking stage speed waveform; (d) Full-speed range speed waveform; (e) Full-speed range position waveform). Detailed implementation manners

[0072] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0073] Please refer to Figure 1 、 Figure 2 An embodiment of the present invention relates to a sensorless control method for a full-speed range of a permanent magnet linear motor for launch, including the following steps:

[0074] The first step: Taking a double three-phase permanent magnet linear synchronous motor (DTP-PMLSM) for launch as the control object, deriving the mathematical model of DTP-PMLSM, and building a closed-loop control system for the motor system;

[0075] The second step: Adopting an I / F open-loop control strategy to complete the static start of DTP-PMLSM and operate at low speed in open loop;

[0076] The third step: When DTP-PMLSM runs to a predetermined speed, switch to an adaptive sensorless closed-loop control strategy, and realize the position and speed estimation of the motor through an adaptive LQR-KF observer to ensure the reliable and stable operation of the motor system to the highest launch speed;

[0077] The fourth step: When DTP-PMLSM runs to the highest launch speed, quickly enter the deceleration state, and adopt a control strategy of position open loop and current closed loop to ensure the quick and stable braking of the motor;

[0078] The fifth step: Build a closed-loop control model for the full-speed range sensorless of the launch motor (for example, through Matlab / Simulink software), and analyze the effectiveness of the control method through simulation.

[0079] The mathematical model of the DTP-PMLSM in the three-phase static coordinate system is as follows:

[0080]

[0081] In the above formula, u 6s =[u a u b uc u u u v u w T is the stator phase voltage, and the subscripts a, b, c, u, v, w are the labels of the stator windings. 6s = diag[R s R s R s R s R s R s , R s is the resistance i 6s = [i a i b i c i u i v i w T is the stator phase current, is the magnetic flux per phase of the stator, L 6s is the inductance coefficient matrix, θ e is the electrical angle.

[0082] Based on the above, the vector space decoupling (VSD) coordinate transformation method is adopted. VSD is to convert the six-phase current from abc to dq, xy, 0, and map the various variables of DTP-PMLSM to 3 mutually orthogonal subspaces respectively, namely the d-q subspace, the x-y subspace, and the zero-sequence subspace. Therefore, the mathematical model of DTP-PMLSM in the VSD coordinate system is:

[0083]

[0084] In the above formula, u d , u q , u x , u y are the stator voltages of the d-q subspace and the x-y subspace, i d , i q , i x , i y are the stator voltages of the d-q subspace and the x-y subspace, L d , L q are the inductances of the d-q subspace, L x , L y are the leakage inductances, R s is the stator resistance, ω e is the electrical angular velocity.

[0085] The motor torque equation is:

[0086] ​​

[0087] Among them, F e is the electromagnetic force output by the motor; τ e is the pole pitch.

[0088] The mechanical motion equation of the motor is:

[0089]

[0090] Among them, F f is the disturbance quantity during motor operation, M is the total mass, and v e is the motor speed, satisfying v e = ω e τ e / π.

[0091] The I / F open-loop control described is a control method with speed open-loop and current closed-loop. By setting a certain current amplitude and combining the thrust power angle self-balancing principle, it has a certain load-carrying capacity and anti-load disturbance ability in the low-speed region.

[0092] Under open-loop control, the maximum electromagnetic thrust F emax output by the motor is:

[0093]

[0094] In the system, the q-axis current is set for motor starting and operation; by setting the frequency, the corresponding electrical angular velocity command can be obtained, and its integral is used to obtain the virtual mover position information. The design of the given mover acceleration command a needs to satisfy:

[0095]

[0096] Among them, I qref is the starting q-axis current, and F fmax is the maximum external disturbance force of the motor.

[0097] The described adaptive positionless closed-loop control mainly includes two parts: a current state estimation model based on the linear quadratic regulator LQR and the Kalman filter KF, and a speed adaptive parameter. Among them, the LQR-KF estimation model is constructed as follows:

[0098] 1) The KF-based observer considering random noise can be expressed as:

[0099]

[0100] Among them, the superscript '^' represents the estimated value of the variable, K is the feedback matrix related to the output error in the KF observer, and A, B, and C are the system matrix, input matrix, and output matrix of the observation system respectively.

[0101] For the KF algorithm, the optimal state observation objective can be achieved by minimizing the expectation of the observation error. Through derivation, the expectation of the estimation error e(t) can be expressed in the following form:

[0102]

[0103] where Ψ and Γ are the covariance matrices of the system noise η and the measurement noise λ respectively, β is the integration variable, and η and λ satisfy:

[0104]

[0105] In the formula, δ is the Dirac function.

[0106] It is known that the objective of the KF observer is to minimize the error expectation, so as to ensure the optimal estimation performance of the observer. Since directly solving the error expectation is relatively complex. Therefore, the K is equivalently calculated through the LQR algorithm to minimize the error expectation.

[0107] 2) According to the LQR theory, for a linear time-invariant system with feedback control u m = Lx m , the closed-loop system can be expressed as:

[0108] dx m / dt = (A m + B m L)x m

[0109] where L is the system feedback gain matrix, x m represents the system state variable, and A m , B m are the system matrix and the input matrix respectively.

[0110] Assume that at time τ, an optimal control law u m (t) is found to minimize the cost function J, and J can be calculated as:

[0111]

[0112] In the formula, Q and R represent the weights of the state variable x m and the input u m respectively, and are diagonal matrices.

[0113] 3) Comparing the equation of the cost function J in LQR with the expression of the estimation error expectation E[e(t)e(t) T in the KF algorithm, based on the duality principle, the following equivalent formula can be obtained:

[0114]

[0115] Therefore, by solving for L using the LQR algorithm, K in the KF algorithm can be equivalently obtained.

[0116] In the described adaptive LQR-KF observer, the speed adaptation parameter is designed according to Popov hyperstability theory. According to Popov hyperstability theory, the necessary and sufficient condition for the asymptotic stability of a standard nonlinear time-varying feedback system is:

[0117] 1) The transfer matrix of the linear forward path must be a strictly positive real matrix;

[0118] 2) The nonlinear feedback channel satisfies the Popov integral inequality.

[0119] For the first condition of Popov hyperstability theory, based on the positive real lemma, by selecting C = P = I, the transfer function G of the linear forward path is obtained as:

[0120] G = -(P(A s + K)+(A s + K) T P)

[0121] where I is the identity matrix, C is the linear compensation matrix, P is the positive definite matrix, A s is the state matrix of the system, and K is the feedback gain matrix used to implement feedback control.

[0122] For the second condition of Popov hyperstability theory, the adaptation law of the nonlinear feedback path satisfies the Popov integral inequality:

[0123]

[0124] is an arbitrary positive number, η(0, t0) represents the Popov integral inequality, and y is the output of the nonlinear feedback channel.

[0125] where,

[0126]

[0127] Then, the speed adaptation law is designed in a proportional-integral form:

[0128]

[0129] where, k p 、k i are the adaptation gains, is the estimated value of the electrical angular velocity of the motor. Since the studied motor is a surface-mounted motor, L s is numerically equal to the d-q axis inductance.

[0130] Finally, the adaptive positionless control model of DTP-PMLSM consists of the following:

[0131] 1) LQR-KF current observation model

[0132]

[0133] where, u dl and u ql satisfy:

[0134]

[0135] In the formula, θ e is the electrical angle, which is a necessary item to ensure the observability and controllability of the observation system.

[0136] 2) Speed adaptive law

[0137] where, the inputs of the positionless control model are the currents, voltages and motor body parameters in the d-q subspace, and the outputs are the observed values of the motor speed and displacement.

[0138] The topology structure of the transmitting motor in the specific embodiment of the present invention is as Figure 1 shown, which is a long-primary double-sided permanent magnet linear synchronous motor adopting a double-layer Halbach structure. The primary winding includes a C-type six-phase winding and a support frame, and the winding can effectively reduce high-order harmonics and improve the limit capacity of the motor. The secondary system consists of a permanent magnet array with radially magnetized N poles and S poles alternating and its frame. The air-gap magnetic field of the permanent magnet array presents a flat-top waveform with the least harmonic distortion, and can provide the sine-wave air-gap magnetic field necessary to maintain the normal operation of the motor.

[0139] As Figure 2 shown, the principle block diagram of the positionless control of the dual three-phase permanent magnet linear synchronous motor is provided. The control principle of this linear motor mainly includes the following aspects:

[0140] (1) When the motor starts at zero low speed, the motor adopts the I / F start control strategy with position open loop and current closed loop. By giving the q-axis current and setting the motor start frequency at the same time, the motor can start stably and at low speed.

[0141] To improve the control performance of the motor, a vector control algorithm under VSD coordinate transformation is adopted for the current inner loop. The current inner loop mainly includes a d-q subspace closed-loop regulator and an x-y harmonic subspace closed-loop regulator. To ensure that the motor has the minimum stator copper loss when outputting the same electromagnetic torque, the given value of the x-y harmonic subspace is set to zero. When the VSD transformation method is adopted, the variables obtained in the x-y subspace are alternating quantities. Due to the gain and bandwidth limitations of the conventional PI regulator, the static error-free regulation of alternating quantities cannot be achieved, so the obtained control result is not the best. To solve the above problems, a proportional-resonant PR control is adopted for the current inner loop, so as to obtain better control performance.

[0142] (2) After the motor starts stably, switch to the adaptive position-free closed-loop control strategy in the medium and high speed range. The closed-loop system adopts a double-loop control, mainly including a current inner loop and a position outer loop. The input of the outer loop control is the motor reference speed V ref , the reference position X ref and the motor observed speed and position signals output by the adaptive LQR-KF observer. The q-axis current i qref output by the outer loop is used as the reference input of the current inner loop. At the same time, the input of the current inner loop also includes the d-axis current reference value i dref and the x-y axis current reference value i xy,ref .

[0143] The adaptive LQR-KF position-free control module takes the measured current and control voltage of the motor as inputs, and outputs the observed speed v ehat and the observed position x ehat for the closed-loop control of the motor. The observed position signal is transformed by a coefficient to obtain an angle for the coordinate transformation of the motor control.

[0144] (3) When the motor accelerates to the maximum launch speed and enters the deceleration and braking stage, a braking control strategy with a position open-loop and a current closed-loop is adopted. By inputting a braking electromagnetic force opposite to the direction of the motor movement, the q-axis reference current of the current inner loop is calculated to ensure that the motor brakes quickly and stably within a short distance.

[0145] (4) In addition, for the inverter control strategy, the voltage output by the motor control is used as the input of the inverter, and the six-phase voltage for the operation of the dual three-phase motor is obtained through the space vector modulation SVPWM algorithm. The main advantages of the SVPWM algorithm are as follows: The SVPWM has a relatively high degree of harmonic optimization, and the harmonic elimination effect is better than that of SPWM. It is easy to implement and can improve the voltage utilization rate; The SVPWM algorithm improves the DC voltage utilization rate of the voltage source inverter and the dynamic response speed of the motor, and at the same time reduces the torque ripple of the motor, etc.; It is more suitable for digital control systems.

[0146] Figure 3It is a block diagram of the I / F open-loop control principle. The q-axis current is used for rotor positioning. To make the electromagnetic torque output at the initial startup moment start from 0, the angle of open-loop driving starts from 270°. As Figure 3 (a) shows, the d-q axes are marked with v to represent the virtual coordinate system d qref where I is located v -q v , d v -q v The coordinate system lags behind the actual d-q coordinate system by 90°, and at this time the electromagnetic thrust is 0. Figure 3 (a), δ = 0, θ L = π / 2.

[0147] Define the angle between the q-axis of the virtual synchronous coordinate system and the d-axis of the actual coordinate system as δ:

[0148]

[0149] Set the electrical angular velocity of the motor to increase ramp-like from 0 to a certain stable value, and the d v -q v coordinate system rotates following the given electrical angular velocity, making δ > 0, thus generating electromagnetic thrust, as Figure 3 (b) shows. Figure 3 (b), in the d v -q v coordinate system lags behind the actual d-q coordinate system by θ L , and the lag angle θ L depends on the projection of I qref on the actual d-q coordinate system, satisfying: i t = I qref cosθ L .

[0150] Project the I v -q v in the coordinate system onto the actual d-q coordinate system, and the electromagnetic thrust of the motor in the IF control can be obtained: qref

[0151]

[0152] When δ = π / 2, the PMLSM outputs the maximum electromagnetic force, but the motor is in a critically stable state. Once there is a slight disturbance, it will cause θ L < 0, and further cause the motor to lose step.

[0153] Figure 4 It is a control block diagram of the adaptive position observer. It can be seen from the figure that the adaptive position observer consists of two parts: a current observation model based on LQR-KF and a speed adaptive model.

[0154] Figure 5 The simulation results of sensorless control for the motor over the full speed range are presented. In the simulation, the following settings are made: when \(t = 0s - 2.6s\), the motor adopts the I / F open-loop control strategy, and the motor slowly accelerates from rest to a constant speed of \(0.06m / s\) according to the given speed, as shown in Figure 5 (a). When \(t = 2.6s - 2.875s\), the motor switches from the I / F open-loop control to the adaptive sensorless closed-loop control, and the motor accelerates, with the maximum acceleration being \(20m / s\) 2 . The motor accelerates to \(5m / s\) within \(0.275s\), and the simulation waveforms are as shown in Figure 5 (b). It can be seen from the figure that when \(t>2.875s\), the motor control system switches to the reverse electromagnetic force braking control, and at this time the reverse acceleration is \(-110m / s\) 2 . The motor decelerates until its speed drops to 0, and then the control system is powered off, as shown in Figure 5 (c). In addition, Figure 5 (d) and Figure 5 (e) show the speed waveform and position waveform of the motor over the full speed range. From the Figure 5 simulation results, it can be seen that the sensorless closed-loop control of the launch motor over the full speed range is achieved by the method proposed in the present invention.

[0155] In the embodiment of the present invention, a dual three-phase permanent magnet linear synchronous motor (DTP-PMLSM) is used as the electromagnetic launch motor. First, the motor is started and operated at low speed through I / F open-loop control; secondly, the control strategy is switched from the I / F algorithm to the sensorless algorithm, and an adaptive position observer based on the linear quadratic regulator and Kalman filter (LQR-KF) is designed to achieve the sensorless closed-loop control of the motor. Under this control, the motor runs to the set maximum speed; finally, in the motor deceleration stage, it switches to the position open-loop control, and a reverse braking force is applied through the current inner loop to ensure the fast and stable braking of the motor. Compared with the prior art, this full-speed-range sensorless control method adopts the position open-loop control during the start and braking of the motor, which can simplify the algorithm while ensuring the rapid start and stop of the motor. In the medium and high speed operation region of the motor, the system state estimation model is derived to achieve the optimal state estimation of the launch motor; at the same time, an adaptive module is designed to dynamically estimate the speed of the launch motor, and the adaptive module is dynamically adjusted to cope with the changes of external disturbances, ensuring the anti-disturbance ability of the algorithm.

[0156] Those skilled in the art can easily understand 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 replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A sensorless control method for a permanent magnet linear motor in full speed range for launching, characterized in that It includes the following steps: Step 1: Taking the dual three-phase permanent magnet linear synchronous motor for launch (DTP-PMLSM) as the control object, establish the control model of DTP-PMLSM in the three-phase static coordinate system, and establish the control model of DTP-PMLSM in the VSD coordinate system through the vector space decoupling (VSD) coordinate transformation method; Step 2: Adopt the I / F open-loop control strategy. When the mover acceleration command a meets the conditions, complete the static start of DTP-PMLSM and operate in low-speed open-loop; Step 3: When DTP-PMLSM runs to the predetermined speed, switch to the adaptive positionless closed-loop control strategy. Estimate the position and speed of the motor through the adaptive LQR-KF observer to ensure the reliable and stable operation of the motor system to the maximum launch speed; In the said Step 3, the adaptive LQR-KF observer includes two parts: the current state LQR-KF estimation model based on the linear quadratic regulator (LQR) and the Kalman filter (KF), and the speed adaptive parameter; The construction method of the LQR-KF estimation model is as follows: 1) The observation system based on KF considering random noise is expressed as: where the superscript '^' represents the estimated value of the variable, K is the feedback matrix related to the output error in the KF observer, and A, B, and C are the system matrix, input matrix, and output matrix of the observation system respectively; For the KF algorithm, the optimal state observation can be achieved by minimizing the expectation of the observation error; through derivation, the expectation of the estimation error e(t) can be expressed in the following form: where Ψ and Γ are the covariance matrices of the system noise η and the measurement noise λ respectively, β is the integration variable, and η and λ satisfy: In the formula, δ is the Dirac function; The goal of the KF observer is to minimize the error expectation; Step 4: When DTP-PMLSM runs to the maximum launch speed, quickly enter the deceleration state, and adopt the control strategy of position open-loop and current closed-loop to ensure the rapid and stable braking of the motor; Step 5: Build the adaptive positionless control model of DTP-PMLSM and analyze the effectiveness of the control method through simulation.

2. The sensorless control method for a permanent magnet linear motor for launch in the full speed range according to claim 1, wherein The control model of DTP-PMLSM established in the said Step 1 in the three-phase static coordinate system is: In the above formula, u 6s = [u a u b u c u u u v u w T is the stator phase voltage, and the subscripts a, b, c, u, v, w are the stator winding labels, R 6s = diag[R s R s R s R s R s R s is the resistance coefficient matrix, i 6s = [i a i b i c i u i v i w T is the stator phase current, is the magnetic flux per phase of the stator, L 6s is the inductance coefficient matrix, is the magnetic flux of the permanent magnet, θ e is the electrical angle.​​ 3. The sensorless control method for the permanent magnet linear motor for launching in the full speed range according to claim 1, wherein The method for establishing the control model of DTP-PMLSM in the VSD coordinate system through the vector space decoupling coordinate transformation method is: adopt the vector space decoupling coordinate transformation method to map each variable of DTP-PMLSM to 3 mutually orthogonal subspaces, namely the d-q subspace, the x-y subspace, and the zero-sequence subspace; the mathematical model of DTP-PMLSM in the VSD coordinate system is: In the above formula, u d , u q , u x , u y are the stator voltages in the d-q subspace and the x-y subspace, i d , i q , i x , i y are the stator voltages in the d-q subspace and the x-y subspace, L d , L q are the inductances in the d-q subspace, L x , L y is the leakage inductance, R s is the stator resistance, ω e is the electrical angular velocity, is the permanent magnet flux linkage; The motor torque equation is: Among them, F e is the electromagnetic force output by the motor; τ e is the pole pitch of the motor; The motor mechanical motion equation is: Among them, F f is the interference amount during motor operation, M is the total mass, and v e is the motor operation speed, satisfying v e = ω e τ e / π.

4. The sensorless control method for a permanent magnet linear motor for launching in the full speed range according to claim 1, wherein The specific method of the said Step 2 is: In the I / F open-loop control system, given the q-axis current, the motor starts and runs; given the frequency, the corresponding electrical angular velocity command can be obtained, and its integral is taken to obtain the virtual mover position information; the given mover acceleration command a needs to satisfy: Among them, I qref is the starting q-axis current, and F fmax is the maximum external disturbing force of the motor.

5. The sensorless control method for a permanent magnet linear motor for launching in the full speed range according to claim 4, characterized in that, The method for equivalently calculating the minimization of the error expectation using the LQR algorithm is as follows: According to the LQR theory, for a linear time-invariant system with feedback control u m = Lx m the closed-loop system is expressed as: dx m / dt = (A m + B m L)x m Among them, L is the system feedback gain matrix, and x m represents the system state variable, A m , B m are the system matrix and the input matrix respectively; Assume that at time τ, an optimal control law u m (t) is sought such that the cost function J is minimized, and J is calculated as: where Q and R respectively represent the weights of the state variable x m and the input quantity u m and are diagonal matrices; 3) Compare the equation of the cost function J in LQR with the expression of the estimated error expectation E[e(t)e(t) T to obtain the following equivalent formula based on the duality principle: Therefore, by solving L using the LQR algorithm, K in the KF algorithm is equivalently obtained.

6. The sensorless control method for a permanent magnet linear motor for launching in the full speed range according to claim 1, wherein In the third step, the adaptive LQR-KF observer further includes a speed adaptive parameter. The speed adaptive parameter in the adaptive LQR-KF observer is designed according to the Popov hyperstability theory. It can be known from the Popov hyperstability theory that the necessary and sufficient condition for the asymptotic stability of a standard nonlinear time-varying feedback system is: 1) The transfer matrix of the linear forward path must be a strictly positive real matrix; 2) The nonlinear feedback channel satisfies the Popov integral inequality; Based on the Popov hyperstability theory, the speed adaptive law is designed in a proportional-integral form: where k p and k i are adaptive gains, is the estimated value of the electrical angular velocity of the motor. Since the studied motor is a surface-mounted motor, L s is numerically equal to the d-q axis inductance.

7. The sensorless control method for full-speed range of a permanent magnet linear motor for launching according to claim 6, wherein The adaptive positionless control model of the DTP-PMLSM in the fifth step is composed of the following: 1) LQR-KF current observation model Among them, the intermediate variables u dl and u ql satisfy the following formula: where θ e is the electrical angle, which is a necessary item to ensure the observability and controllability of the observation system; 2) Speed adaptive model Among them, the inputs of the positionless control model are the currents, voltages, and motor body parameters in the d-q subspace, and the outputs are the observed values of the motor speed and displacement respectively.

8. The sensorless control method for a permanent magnet linear motor for launching in the full speed range according to claim 1, characterized in that When the dual three-phase permanent magnet linear synchronous motor decelerates, a braking control strategy with position open-loop and current closed-loop is adopted, a reverse braking electromagnetic force is set, and the q-axis reference value of the current closed-loop is calculated to ensure that the motor can stably decelerate to zero within a limited distance.

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