Permanent magnet synchronous motor sensorless flux linkage estimation method based on nonlinear observer

Abstract

According to the permanent magnet synchronous motor sensorless flux linkage estimation method based on the non-linear observer, the stator flux linkage can be accurately estimated by applying the non-linear expansion state observer and the effective flux linkage method in the sensorless mode of the motor. By applying a voltage and current hybrid model, adaptive switching of a voltage model and a current model is realized, and the problems of direct current bias, integral saturation and the like existing in first-order integral of the voltage model are solved; and estimating and compensating noise and disturbance existing in the voltage model by applying a non-linear extended state observer, accurately obtaining a stator flux linkage during operation of the motor, and finally estimating a rotor angle and a rotating speed by using a phase-locked loop. According to the method, the estimated values of the rotor angle and the rotating speed are more accurate, and the sensorless control performance of the permanent magnet synchronous motor is improved.

Description

Technical Field

[0001] The invention belongs to the field of permanent magnet synchronous motor control and relates to a position sensorless control method of a permanent magnet synchronous motor, and in particular to estimating stator flux linkage by means of a nonlinear extended state observer, so as to accurately calculate the angle and rotation speed of a rotor. Background Art

[0002] At present, permanent magnet synchronous motors are widely used due to their high efficiency, high energy density, high reliability, simple control, high efficiency, good dynamic and steady-state performance, etc. In general, rotor position detection is achieved by installing mechanical position sensors such as photoelectric encoders or rotary transformers in the system. Both sensors can obtain accurate rotor positions. Although the direct use of sensors can stably detect the rotor position, the use of sensors is often affected by environmental factors. In some harsh environments, the reliability of sensors will be reduced or even fail. At the same time, it will increase the size and cost of the system. Therefore, the study of sensorless control technology of permanent magnet synchronous motors has great theoretical and practical significance.

[0003] For the position sensorless control of permanent magnet synchronous motors, the voltage and current of the motor can be used to construct a flux observer based on the motor mathematical model to obtain the stator flux, and then calculate the rotor flux, and finally obtain information such as angle and speed. However, due to the nonlinearity of the inverter, a certain harmonic component will be mixed into the sampled signal, which will affect the estimation accuracy and even cause the model to diverge. Therefore, it is necessary to improve the traditional voltage and current model.

[0004] The sensorless flux estimation method of permanent magnet synchronous motor based on nonlinear observer can eliminate the DC bias and integral saturation problems caused by harmonics in the calculation of stator flux according to the hybrid model of voltage and current. It can also filter out the disturbance variables of high-order harmonics caused by resistance, inductance parameters and inverter dead zone based on nonlinear extended state observer observation, thereby improving the estimation accuracy of stator flux. Summary of the invention

[0005] The purpose of the present invention is to calculate the stator voltage and stator current of a permanent magnet synchronous motor, apply a voltage-current hybrid model and a nonlinear extended state observer, first estimate the stator flux, and then further estimate the angle and speed of the rotor, so as to achieve the requirement of precise control.

[0006] To achieve the above purpose, the technical solution of the present invention is:

[0007] The stator current of the motor is collected through the current sampling module, and the modulated voltage is used. The voltage-current hybrid model and the nonlinear extended state observer are used to estimate the stator flux, and all software algorithms are performed using a microcontroller. The angle and speed of the rotor are calculated through the effective flux, and the estimated speed and the reference speed are used to form a speed loop. After PI adjustment, the reference current is obtained. The reference current and the current collected by the current acquisition module form a current loop, and the pre-modulated voltage is obtained through PI adjustment. After SVPWM calculation, the required motor voltage is converted into a duty cycle signal, and the inverter power device (IGBT) is controlled to be turned on and off to obtain the desired motor terminal voltage vector (essentially frequency and amplitude), thereby controlling the rotation of the motor.

[0008] A sensorless flux estimation method for a permanent magnet synchronous motor based on a nonlinear observer specifically comprises the following steps:

[0009] Step (1): Sample the three-phase current i of the permanent magnet synchronous motor through the current sampling module a 、i b and i c , which is converted into the α-axis current i in the stationary coordinate system through the Clark transformation module α and the β-axis current i β .

[0010]

[0011] The Park transformation module is used to transform the current i in the stationary coordinate system α 、i β Transformed into the current i based on the dq axis of the synchronous rotating coordinate system d 、i q . The electric rotor angle θ(k-1) is the angle calculated in the previous sampling period.

[0012]

[0013] Step (2): The stator flux is based on the dq-axis components of the synchronous rotating coordinate system The expression is:

[0014]

[0015] In the above formula, the stator inductance in the synchronous rotating coordinate system is represented by L d and L q express. It is the flux linkage generated by the permanent magnet of the motor.

[0016] According to the torque equation definition is the effective flux, where p is the number of pole pairs of the motor.

[0017] The current model expression of the stator flux is:

[0018]

[0019] The voltage model expression of the stator flux is:

[0020]

[0021] In the above formula, u s =(u α ,u β ) T 、i s =(i α ,i β ) T Respectively represent the stator voltage vector and stator current vector based on the stationary coordinate system. s is the stator resistance, is the stator flux based on the stationary coordinate system.

[0022] Step (3): Substituting into the current model of stator flux, the stator flux can also be expressed by effective flux:

[0023]

[0024]

[0025] In the above formula It is the expression of the effective magnetic flux on the α-β axis of the stationary coordinate system, and contains the position information of the rotor.

[0026] Step (4): The voltage model can be rewritten from step (3) as follows:

[0027]

[0028] Step (5): Since the back EMF of the voltage model is small at low speed, the stator resistance voltage is large, and the back EMF estimation accuracy is low, the calculated stator flux is not accurate enough. The current model does not have the above problem and is not affected by the stator resistance voltage. The low-speed estimation accuracy is high, but the current model is greatly affected by the inductance parameters. Therefore, the advantages of the voltage model and the current model should be combined to realize the adaptive switching of the voltage model and the current model according to the different rotor speeds.

[0029] Adaptive switching method between voltage model and current model: Calculate stator flux based on voltage model Will Substitute it into the current model and then inversely solve Components acting on the dq axes of the synchronously rotating coordinate system through the current model

[0030]

[0031] The current sampled by the current sampling module is converted into i by Clark and Park transformation. d ,and Combination, get the effective flux in the current model

[0032]

[0033] The effective flux obtained by the current model is transformed to the α-β axis of the stationary coordinate system:

[0034]

[0035] In the above formula represents the effective flux on the α-β axis in the voltage model, represents the effective flux on the α-β axis in the current model, It represents the expression of the stator flux in the current model on the dq axis. It represents the expression of the effective magnetic flux in the current model on the dq axis.

[0036] Step (6): By using the deviation of the effective flux in the voltage model and the current model, the voltage model is compensated, and the adaptive switching in the voltage-current hybrid model is completed, thereby improving the estimation accuracy of the stator flux:

[0037]

[0038] Where V comp It represents the compensation of the effective flux deviation produced by the same stator flux in the voltage model and the current model respectively.

[0039] Step (7): The above steps can handle the problems of DC bias and integral saturation in the first-order integral of the voltage model. However, the third harmonics generated by the changes in the resistance and inductance parameters, and the fifth and seventh harmonics generated by the inverter dead zone cannot be handled by the voltage-current hybrid model. Therefore, a nonlinear extended state observer is used to observe the system disturbance variables, and the observed disturbance variables are compensated to the voltage model to obtain accurate stator flux.

[0040] For the voltage model, the expression for the stator flux can be regarded as a first-order single-input single-output system:

[0041]

[0042] Where x is the state variable of the stator flux, u s For system input, -R s is is the system dynamic response, w u System disturbance variable.

[0043] The system disturbance variable w u Expanded into a new state variable x2, the system about the stator flux is expanded into a new linear control system:

[0044]

[0045] Where x1 is the state variable of the stator flux.

[0046] If x2=d(t), define And |h(t)|≤h0. h0 is the boundary of h(t). By selecting appropriate parameters β1 and β2, a nonlinear extended state observer can be established, which can estimate the state x1 of the object and the extended state x2 in real time. Establish a state observer for the extended system:

[0047]

[0048] Where z1 and z2 are the estimated state variables and disturbance variables, respectively. e1 is the observation error, and β1 and β2 are the gains of the nonlinear extended state observer. are the first-order derivatives of z1 and z2 respectively.

[0049] Step (8): Based on the above steps, the voltage model can be expressed as:

[0050]

[0051] In the above formula, V comp represents the compensation for the DC bias and integral saturation problems in the first-order integral of the voltage model, w u The disturbance variables such as the third harmonic generated by the change of resistance and inductance parameters, and the fifth and seventh harmonics generated by the inverter dead zone are estimated by the nonlinear extended state observer, and then the estimated disturbance variables are substituted into the voltage model, subtracted from the disturbance variables, and the stator flux linkage when the motor is running can be accurately estimated.

[0052] Step (9): From step (3), it can be seen that the stator flux estimated in the current sampling period contains information about the rotor position:

[0053]

[0054]

[0055] Where θ(k) is the rotor angle calculated in the current sampling period.

[0056] Step (10): The software algorithm of step (1) to step (9) is completed by the microcontroller, and the estimated rotor angular velocity is output. Feedback to reference speed ω e , forming a speed loop, after PI adjustment, outputting the reference current. The current collected by the current acquisition module is fed back to the reference current by Clark and Park transformation to form a current loop, which is adjusted by PI. The pre-modulated voltage is obtained, and after SVPWM calculation, the required motor voltage is converted into a duty cycle signal, and the inverter power device (IGBT) is controlled to be turned on and off to obtain the desired motor terminal voltage vector, thereby controlling the operation of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a block diagram of the permanent magnet synchronous motor control system of the present invention.

[0058] Figure 2 This is a design diagram of the voltage-current mixed model of the present invention.

[0059] Figure 3 This is a design diagram of the estimation method based on the nonlinear extended state observer of the present invention.

[0060] Figure 4 The present invention is used to detect a second-order system for estimating the rotor angle and speed. DETAILED DESCRIPTION

[0061] In order to describe the technical solution of the present invention more clearly, it will be further described below with reference to the accompanying drawings.

[0062] like Figure 1 As shown, the present invention provides a sensorless flux estimation method for a permanent magnet synchronous motor based on a nonlinear observer, and obtains the angle and speed of the rotor through the estimated flux. The feasibility of the invention is further explained in combination with the control system of the permanent magnet synchronous motor.

[0063] The control system of the permanent magnet synchronous motor includes a current sampling module, a Clark transformation module, a Park transformation module, a nonlinear extended state observer, an angle and speed calculation module, a voltage and current hybrid module for calculating the stator flux, a microcontroller, a three-phase inverter and a permanent magnet synchronous motor, wherein:

[0064] The present invention aims to use the collected signals, process the signals through a microcontroller through a software algorithm, calculate the estimated stator flux, obtain the estimated rotor angle and speed, and replace the position sensor.

[0065] Step (1): Subtract the estimated rotor angular velocity from the reference angular velocity and form a speed loop through PI regulation. The output of the speed PI regulator is the reference current.

[0066] Step (2): The three-phase current collected by the current acquisition module is passed through the Clark and Park conversion modules to obtain the actual current of the motor, and the actual current is subtracted from the reference current to form a current loop through PI regulation. The output of the current PI regulator is the dq axis pre-modulation voltage, which is passed through the inverse Park transformation module to obtain the α-β axis pre-modulation voltage.

[0067] Step (3): The inverter technology based on SVPWM has small torque fluctuation and high DC voltage utilization. The voltage vector in the plane can be synthesized by superposition of 6 basic voltage space vectors and zero voltage space vector according to different action times, so as to avoid harmonic components caused by the switching times of the switch tube as much as possible. When the vector pre-modulation voltage passes through the SVPWM module, it needs to go through three steps: first, the judgment of the sector, second, the determination of the action time of the adjacent space voltage vector, and third, the determination of the switching sequence and the switching time of the voltage space vector, so as to minimize the switching times and switching losses of the switch tube.

[0068] Step (4): The SVPWM module controls the three-phase inverter to provide voltage to the permanent magnet synchronous motor, generating a rotating circular magnetic field in the internal space of the permanent magnet synchronous motor, thereby generating a stable electromagnetic torque to ensure smooth operation of the motor.

Claims

1. A sensorless flux estimation method for a permanent magnet synchronous motor based on a nonlinear observer realizes full-speed range position sensorless control of the permanent magnet synchronous motor. The present invention aims to replace the effect of the position sensor by using a nonlinear extended state observer and an effective flux control method. The control system includes: Current sampling module, Park transformation module, Clark transformation module, three-phase inverter, voltage-current hybrid model calculation module, nonlinear extended state observer module, angle calculation module, phase-locked loop module, permanent magnet synchronous motor, microcontroller, the microcontroller completes all software algorithms; characterized in that the method comprises the following steps: Step (1): Sample the three-phase current i of the permanent magnet synchronous motor through the current sampling module a 、i b and i c , which is converted into the α-axis current i in the stationary coordinate system through the Clark transformation module α and the β-axis current i β . The Park transformation module is used to transform the current i in the stationary coordinate system α 、i β Transformed into the current i based on the dq axis of the synchronous rotating coordinate system d 、i q . The electric rotor angle θ(k-1) is the angle calculated in the previous sampling period. Step (2): The stator flux is based on the dq-axis components of the synchronous rotating coordinate system The expression is: In the above formula, the stator inductance in the synchronous rotating coordinate system is represented by L d and L q express. It is the flux linkage generated by the permanent magnet of the motor. According to the torque equation definition is the effective flux, where p is the number of pole pairs of the motor. The current model expression of the stator flux is: The voltage model expression of the stator flux is: In the above formula, u s =(u α ,u β ) T 、i s =(i α ,i β ) T Respectively represent the stator voltage vector and stator current vector based on the stationary coordinate system. s is the stator resistance, is the stator flux based on the stationary coordinate system. Step (3): Substituting into the current model of stator flux, the stator flux can also be expressed by effective flux: In the above formula It is the expression of the effective magnetic flux on the α-β axis of the stationary coordinate system, and contains the position information of the rotor. Step (4): The voltage model can be rewritten from step (3) as follows: Step (5): Since the back EMF of the voltage model is small at low speed, the stator resistance voltage is large, and the back EMF estimation accuracy is low, the calculated stator flux is not accurate enough. The current model does not have the above problem and is not affected by the stator resistance voltage. The low-speed estimation accuracy is high, but the current model is greatly affected by the inductance parameters. Therefore, the advantages of the voltage model and the current model should be combined to realize the adaptive switching of the voltage model and the current model according to the different rotor speeds. Adaptive switching method between voltage model and current model: Calculate stator flux based on voltage model Will Substitute it into the current model and then inversely solve Components acting on the dq axes of the synchronously rotating coordinate system through the current model The current sampled by the current sampling module is converted into i by Clark and Park transformation. d ,and Combination, get the effective flux in the current model The effective flux obtained by the current model is transformed to the α-β axis of the stationary coordinate system: In the above formula represents the effective flux on the α-β axis in the voltage model, represents the effective flux on the α-β axis in the current model, It represents the expression of the stator flux in the current model on the dq axis. It represents the expression of the effective magnetic flux in the current model on the dq axis. Step (6): By using the deviation of the effective flux in the voltage model and the current model, the voltage model is compensated, and the adaptive switching in the voltage-current hybrid model is completed, thereby improving the estimation accuracy of the stator flux: Where V comp It represents the compensation of the effective flux deviation produced by the same stator flux in the voltage model and the current model respectively. Step (7): The above steps can handle the problems of DC bias and integral saturation in the first-order integral of the voltage model. However, the third harmonics generated by the changes in the resistance and inductance parameters, and the fifth and seventh harmonics generated by the inverter dead zone cannot be handled by the voltage-current hybrid model. Therefore, a nonlinear extended state observer is used to observe the system disturbance variables, and the observed disturbance variables are compensated to the voltage model to obtain accurate stator flux. For the voltage model, the expression for the stator flux can be regarded as a first-order single-input single-output system: Where x is the state variable of the stator flux, u s For system input, -R s i s is the system dynamic response, w u System disturbance variable. The system disturbance variable w u Expanded into a new state variable x2, the system about the stator flux is expanded into a new linear control system: Where x1 is the state variable of the stator flux. If x2=d(t), define h0 is the boundary of h(t). By selecting appropriate parameters β1 and β2, a nonlinear extended state observer can be established, which can estimate the state x1 of the object and the extended state x2 in real time. Establish a state observer for the extended system: Where z1 and z2 are the estimated state variables and disturbance variables, respectively. e1 is the observation error, and β1 and β2 are the gains of the nonlinear extended state observer. are the first-order derivatives of z1 and z2 respectively. Step (8): Based on the above steps, the voltage model can be expressed as: In the above formula, V comp represents the compensation for the DC bias and integral saturation problems in the first-order integral of the voltage model, w u The disturbance variables such as the third harmonic generated by the change of resistance and inductance parameters, and the fifth and seventh harmonics generated by the inverter dead zone are estimated by the nonlinear extended state observer, and then the estimated disturbance variables are substituted into the voltage model, subtracted from the disturbance variables, and the stator flux linkage when the motor is running can be accurately estimated. Step (9): From step (3), it can be seen that the stator flux estimated in the current sampling period contains information about the rotor position: Where θ(k) is the rotor angle calculated in the current sampling period. The effective flux calculated by the voltage model is used to calculate the estimated rotor angle by performing inverse tangent, but if the estimated rotor angle obtained by inverse tangent is directly used for field oriented control, the system will not be able to achieve the expected performance due to high-frequency noise. Therefore, the type 2 system shown in Figure 4 is used to detect the rotor angle and speed. The transfer function of the type 2 system is:

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