CN109167547A - Based on the PMSM method for controlling position-less sensor for improving sliding mode observer - Google Patents

Abstract

The invention discloses a PMSM sensorless control method based on an improved sliding mode observer. The sigmoid function with variable boundary layer thickness is used to replace the sign function, and a back electromotive force observer is constructed to separate back electromotive force signals, eliminating low-pass filtering. At the same time, the gain of the observer can be dynamically adjusted with the speed, which effectively suppresses the chattering phenomenon of the sliding mode observer and obtains the ideal observation accuracy in a wide speed regulation range. The online identification of stator resistance and torque observation are added to the improved sliding mode observer, which improves the robustness of the system to changes in internal and external parameters.

Description

Position Sensorless Control Method for PMSM Based on Improved Sliding Mode Observer

technical field

The invention belongs to the technical field of motor position sensorless control, and in particular relates to a PMSM position sensorless control method based on an improved sliding mode observer.

Background technique

Permanent magnet synchronous machines (PMSM) have the advantages of high power density, high efficiency and simple structure, so they have been widely used in the industrial field.

In order to accurately control the permanent magnet synchronous motor, the position information and speed information of the rotor are required, so it is necessary to install a position sensor on the motor shaft. But it will increase the cost and complexity of the system and reduce the reliability of the system. Therefore, the sensorless control of permanent magnet synchronous motor has become a research hotspot.

At present, the sensorless control strategies of PMSM can be mainly divided into two categories: one is the estimation strategy based on the observer; the other is the high-frequency signal injection method using the salient pole characteristics of the motor. The estimation strategies based on the observer mainly include the model reference adaptive method and the extended Kalman filter method. Such methods rely on the accuracy of the motor model, which affects the estimation performance. The high-frequency signal injection method does not depend on the motor model, but it will bring noise and require the motor rotor to have a certain saliency, so the scope of application is limited. In view of the above problems, the Sliding Mode Observer (SMO) is widely used in AC motor control because of its simple structure and strong robustness, making up for the dependence of the observer on the mathematical model of the motor to a certain extent. system.

The discontinuous switching control is used in the sliding mode observer, so chattering is an inherent feature of the sliding mode variable structure system. In order to reduce buffeting, low-pass filtering and rotor angle compensation are required for the observation results, which in turn depends on the rotor speed, which increases the complexity of the system and cannot meet the control requirements of high-performance applications.

Using the sigmoid function as the control function can reduce the chattering phenomenon, but it will reduce the robustness of the sliding mode observer.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a PMSM sensorless control method based on an improved sliding mode observer. Based on the improved sliding mode observer, the external torque disturbance and the change of internal resistance parameters are simultaneously identified, which solves the problem of the existing sliding mode observation method. The observed signal chattering phenomenon in the device is large, which requires low-pass filtering and rotor angle compensation, and the system is not robust.

The technical solution adopted by the present invention, a PMSM sensorless control method based on an improved sliding mode observer, includes the following steps:

Step 1. Calculate the observed value of the stator current of the permanent magnet synchronous motor in the two-phase stationary coordinate system and the observed value of the back EMF Then, the observation error of the stator current is used as the sliding mode surface, and the improved sliding mode current observer equation is constructed, and the feedback gain k of the sigmoid function is changed according to the rotation speed;

Step 2, use the back EMF observations obtained in step 1 Build the mathematical model of the back EMF observer and calculate the speed estimate Then estimate the rotor position through the phase-locked loop;

Step 3, using the observed value of the stator current Construct the Lyapunov function with the actual values i _α and i _β , and analyze the stability of the back EMF observer in step 2;

Step 4, carry out stability analysis on the improved sliding mode observer, and calculate the observed value of stator resistance;

Step 5, the rotational speed observed by the improved sliding mode observer The permanent magnet flux linkage Ψ _f and the torque current component i _q of the permanent magnet synchronous motor in the two-phase rotating coordinate system construct the torque observer equation, and the observed torque change and the torque current given i _q ^* phase Add, as a new q-axis current given, that is, to complete the sensorless control of the permanent magnet synchronous motor.

The technical feature of the present invention is also that,

Wherein, the step 1 includes the following steps:

Step 1.1, using the sigmoid function, the phase currents i _α and i _β of the permanent magnet synchronous motor in the two-phase static coordinate system are used as input values to calculate the observed value of the stator current in the two-phase static coordinate system. and The sigmoid function formula is as follows:

Among them, a is an adjustable parameter;

Step 1.2, using the sigmoid function, respectively use the observation error value of the stator current of the permanent magnet synchronous motor in the two-phase stationary coordinate system As the input value, the observed value of the back EMF in the two-phase stationary coordinate system is calculated and

Step 1.3, construct the sliding mode current observer equation based on the sigmoid function as the control function, the expression is as follows:

Among them, R _s is the stator phase resistance, L _s is the stator phase inductance, u _α and u _β are the phase voltage components in the two-phase stationary coordinate system, respectively, and k is the feedback gain of the observer.

In the step 1.3, a more preferred solution is to use k _va =k·ω _ref to replace the feedback gain k in the original observer, where ω _ref represents the rotor angular velocity.

The expression of the back EMF observer equation in the step 2 is as follows:

where l is the observer gain, l>0, e _α , e _β , are the back-EMF component and the observed value of the electrical angular velocity in the two-phase stationary coordinate system, respectively. The angle information of the rotor is obtained through the phase-locked loop. The estimated value of the rotational speed is expressed as follows:

The Lyapunov function constructed in the step 3 is as follows:

in,

R _s , are the actual and observed values of the stator resistance;

For the change of stator resistance Estimate, according to Lyapunov stability theorem, when , the system is asymptotically stable, satisfying The conditions are:

in, are the observation errors of stator current and stator resistance, respectively;

According to the condition of the asymptotic stability of the system, the observed value of the stator resistance in the step 4 can be obtained:

The value range of the feedback gain k is:

k>max(|e _α |, |e _β |).

The torque observer equation in step 5 is:

Among them, k ₁ , k ₂ are torque observer gain coefficients; Estimate the rotational speed for the sliding mode observer; Estimate the rotational speed for the torque observer; Ψ _f is the permanent magnet flux linkage; is the estimated torque; J is the moment of inertia.

The beneficial effects of the present invention are as follows:

1. The present invention uses the sigmoid function of variable boundary layer thickness to replace the sign function, and constructs a back-EMF observer for separating back-EMF signals, eliminating the low-pass filter and phase compensation links, and effectively suppressing the chattering of the sliding mode observer. phenomenon and obtain ideal observation accuracy over a wide speed range.

2. The present invention adopts the stator resistance online identification link, and uses the Lyapunov function to design the resistance parameter online identification algorithm. Through the online identification of the resistance, the identification model of the sliding mode observer is adjusted in real time, which improves the robustness of the system to changes in internal parameters.

3. The present invention adds a torque observer to perform torque feedforward control, reduces the influence of torque disturbance on the control system of the permanent magnet synchronous motor, and improves the robustness of the system to changes in external parameters.

Description of drawings

1 is a block diagram of a position sensorless vector control system of a permanent magnet synchronous motor based on an improved sliding mode observer of the present invention;

Fig. 2 is the principle block diagram of the sigmoid function with variable boundary layer thickness in the present invention;

Fig. 3 is the phase-locked loop structure diagram based on back electromotive force of the present invention;

Fig. 4 is the principle block diagram of the improved sliding mode observer in the present invention;

Fig. 5 is the principle block diagram of the load torque observer in the present invention;

Fig. 6 is when the motor speed is stepped from 500r/min to 1000r/min in 0.05s, the speed estimated by the observer of the present invention and the speed waveform estimated by the sigmoid function;

Figure 7 is the rotation speed error waveform observed when the motor speed is 1000r/min and the motor torque changes from 5N m to 10N m in 0.03s, using torque feedforward control and not using torque feedforward control.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the present invention is not limited to the specific embodiments.

The PMSM position sensorless control method based on the improved sliding mode observer of the present invention includes the improved sliding mode observer based on the sigmoid function, a stator resistance identification link, a back electromotive force observer and a torque observer.

Referring to FIG. 1 , the improved sliding mode observer of the present invention is applied in the vector control of a permanent magnet synchronous motor. The control method adopts id = 0 control. After the three-phase current and voltage of the permanent magnet synchronous motor are transformed by Clarke, the components i _α , i _β and u _α , u _β in the two _- phase stationary coordinate system are obtained as the components of the improved sliding mode observer. Input, the rotational speed observed by the improved sliding mode observer and the torque component i _q of the motor current are used as the input of the load torque observer, and its output is added to the torque current given as a new q-axis current given, with In the vector control of permanent magnet synchronous motor. Specifically include the following steps:

Step 1, take the phase voltage u _α , u _β and phase current i _α , i _β of the permanent magnet synchronous motor in the two-phase stationary coordinate system as the input of the sliding mode observer based on the sigmoid function, and the output is the observed value of the stator current and Put i _α , i _β with The difference is used as the input of the sigmoid function, and its output is the observed value of the back EMF in the two-phase stationary coordinate system At the same time, the width of the boundary layer of the sigmoid function is changed according to the rotational speed, that is, the feedback gain of the sigmoid function.

The expression of the sliding mode observer equation based on the sigmoid function constructed in step 1 is as follows:

Among them, R _s is the stator phase resistance, L _s is the stator phase inductance, i _α , i _β , u _α , u _β are the phase current and phase voltage components in the two-phase stationary coordinate system, respectively, is the observed value of the phase current. is the sigmoid function, a is an adjustable parameter, and k is the feedback gain of the observer.

Referring to FIG. 2 , the feedback gain k in the original observer is replaced by k _va =k·ω _ref , and the width of the boundary layer is changed according to the rotation speed, thereby reducing the chattering phenomenon.

Step 2, use the back EMF observations obtained in step 1 and the actual back-EMF components e _α and e _β of the motor to construct a back-EMF observer to obtain the estimated speed Then, the rotor position is obtained through the phase-locked loop in Figure 3, and the mathematical model of the back EMF observer is constructed as follows:

where l is the observer gain, l > 0, are the observed value of back electromotive force and the observed value of electrical angular velocity in the two-phase stationary coordinate system, respectively. The angle information of the rotor is obtained through the phase-locked loop, and the estimated value of the rotational speed is expressed as follows:

Step 3, select the Lyapunov function to analyze the stability of the back-EMF observer constructed in step 2. The error equation of the back-EMF observer is:

in are the observation errors of back EMF and rotational speed, respectively;

The Lyapunov function is selected as:

To ensure system stability, it must meet:

Simplify the above equation according to the error equation of the back EMF, we can get:

Since l>0, so So the back EMF observer is always asymptotically stable.

Step 4, define the Lyapunov function, analyze the stability of the improved sliding mode observer, and design the online identification algorithm of resistance parameters to calculate the observed value of stator resistance

Define the Lyapunov function as:

in the formula For the change of stator resistance estimate;

The mathematical model of the surface-mounted permanent magnet synchronous motor in the two-phase stationary coordinate system is:

In the formula, i _α , i _β , u _α , u _β and e _α , e _β are the phase current, phase voltage and back EMF component in the two-phase stationary coordinate system, R _s is the stator phase resistance, L _s is the stator Phase inductance, Ψ _f is the permanent magnet flux linkage, ω _r is the rotor electrical angular velocity, θ is the rotor position;

According to the mathematical model of the surface-mounted permanent magnet synchronous motor in the two-phase stationary coordinate system and the constructed sliding mode current observer equation based on the sigmoid function, it can be obtained:

in:

According to Lyapunov stability theorem, to ensure the stability of the system, it must satisfy:

Further derivation, the stability condition of the sliding mode can be obtained as:

in are the observation errors of stator current and stator resistance, respectively.

Thus the observed value of the stator resistance described in step 4 is:

The value range of the feedback gain k is:

k＞max(|e _α |,|e _β |)

The resulting block diagram of the improved sliding mode observer (see Figure 4).

Step 5, referring to Fig. 5, the rotational speed observed by the improved sliding mode observer The permanent magnet flux linkage Ψ _f and the torque current component i _q of the permanent magnet synchronous motor in the two-phase rotating coordinate system construct the torque observer equation, and the expression is as follows:

Among them, k ₁ , k ₂ are torque observer gain coefficients; Estimate the rotational speed for the sliding mode observer; Estimate the speed for the torque observer; To estimate the torque, J is the moment of inertia.

Add the observed torque change to the torque current given i _q ^* as a new q-axis current given, that is, to complete the sensorless control of the permanent magnet synchronous motor.

The feasibility of the present invention is verified below with reference to the simulation waveforms in FIGS. 6 to 7 .

Fig. 6 is the comparative simulation diagram of the improved sliding mode observer of the present invention and the sliding mode observer based on the sigmoid function. The simulation time is 0~0.1s, no load, the initial speed of the motor is set to 500r/min, and the given motor speed is 1000r/min at 0.05s. It can be seen from Fig. 6 that the chattering can be reduced by using the sigmoid function, but as the rotation speed increases, the estimation error will become larger, while the improved sliding mode observer of the present invention still has a smaller estimation when the rotation speed is higher error.

Fig. 7 shows the observation of the traditional sliding mode observer without torque feedforward observation and the improved sliding mode observer of the present invention when the rotation speed is 1000r/min, and the load torque changes suddenly from 5N·m to 10N·m at 0.03s As can be seen from Figure 7, when the permanent magnet synchronous motor is subjected to torque disturbance, the torque feedforward observer can feed back the change information of the load torque to the forward channel of the q-axis current loop in real time. , by rapidly increasing the q-axis current given way to speed up the adjustment speed of the current loop, so the speed estimation error has less overshoot and faster convergence speed.

The invention adopts the sigmoid function of the variable boundary layer thickness to replace the sign function, and constructs a back electromotive force observer for separating the back electromotive force signal, eliminating the low-pass filter and the phase compensation link, and at the same time, the observer gain can be dynamically adjusted with the speed. The chattering phenomenon of the sliding mode observer is effectively suppressed and the ideal observation accuracy in a wide speed regulation range is obtained. The stator resistance online identification and torque observation links are added to the improved sliding mode observer, which improves the robustness of the system to changes in internal and external parameters.

Claims (7)

1. A PMSM (permanent magnet synchronous motor) position sensorless control method based on an improved sliding-mode observer is characterized by comprising the following steps:

step 1, calculating an observed value of stator current of a permanent magnet synchronous motor under a two-phase static coordinate systemAnd observed value of back electromotive forceThen, taking the observation error of the stator current as a sliding mode surface, constructing an improved sliding mode current observer equation, and simultaneously changing the feedback gain k of the sigmoid function according to the rotating speed;

step 2, utilizing the observed value of the back electromotive force obtained in the step 1Constructing a mathematical model of a counter electromotive force observer and calculating a rotating speed estimation valueEstimating the position of the rotor through a phase-locked loop;

step 3, utilizing the observed value of the stator currentAnd the actual value i_α、i_βConstructing a Lyapunov function, and performing stability analysis on the back electromotive force observer in the step 2;

step 4, carrying out stability analysis on the improved sliding mode observer, and calculating a stator resistance observation value;

step 5, utilizing the observed rotating speed of the improved sliding mode observerPermanent magnet flux linkage Ψ_fAnd the torque current component i of the permanent magnet synchronous motor under the two-phase rotating coordinate system_qConstructing a torque observer equation, and giving i to the observed torque variation and the torque current_q ^*And adding, and finishing the control of the permanent magnet synchronous motor without the position sensor as new q-axis current setting.

2. The improved sliding-mode observer based PMSM position sensorless control method according to claim 1, wherein the step 1 comprises the steps of:

step 1.1, adopting sigmoid function, and respectively using phase current i of the permanent magnet synchronous motor in a two-phase static coordinate system_α、i_βAs an input value, an observed value of the stator current in a two-phase stationary coordinate system is calculatedAndthe sigmoid function is as follows:

wherein a is an adjustable parameter;

step 1.2, adopting sigmoid function, and respectively using the observation error values of the stator current of the permanent magnet synchronous motor under the two-phase static coordinate systemAs an input value, an observed value of back electromotive force in a two-phase stationary coordinate system is calculatedAnd

step 1.3, constructing a sliding mode current observer equation based on a sigmoid function as a control function, wherein the expression is as follows:

wherein R is_sIs stator phase resistance, L_sIs a stator phase inductance u_α、u_βThe phase voltage components are respectively under a two-phase static coordinate system, and k is the feedback gain of the observer.

3. The improved sliding-mode observer based PMSM position sensorless control method according to claim 2, characterized in thatIn the step 1.3, it is more preferable to use k_va＝k·ω_refReplacing the feedback gain k, ω in the original observer_refRepresenting the rotor angular velocity.

4. The improved sliding-mode observer-based PMSM position sensorless control method according to claim 1, characterized in that the expression of the back electromotive force observer mathematical model constructed in step 2 is as follows:

where l is the observer gain, l>0，e_α、e_β、The method comprises the following steps of respectively obtaining back electromotive force components and electric angular velocity observed values under a two-phase static coordinate system through a phase-locked loop, wherein the rotation speed estimated value expression is as follows:

5. the improved sliding-mode observer-based PMSM position-sensorless control method according to claim 1, characterized in that the Lyapunov function constructed in step 3 is as follows:

wherein,

R_s、respectively representing an actual value and an observed value of the stator resistance;

for variation of stator resistanceEstimation, according to the Lyapunov theorem of stability whenThe system is gradually stable and meets the requirementsThe conditions of (a) are as follows:

wherein,the observation errors of the stator current and the stator resistance are respectively;

6. the improved sliding-mode observer-based PMSM position sensorless control method according to claim 5, characterized in that according to the condition of system asymptotic stability, the stator resistance observed value in the step 4 can be obtained as follows:

the value range of the feedback gain k is as follows:

k＞max(|e_α|,|e_β|)。

7. the improved sliding-mode observer based PMSM position sensorless control method according to claim 6, wherein the torque observer equation in step 5 is:

wherein k is₁，k₂Is a torque observer gain factor;estimating a rotation speed for the sliding mode observer;estimating a rotational speed for the torque observer;to estimate the torque, J is the moment of inertia.