CN114826079A - Current loop control method of permanent magnet synchronous motor based on error feedback model prediction - Google Patents

Abstract

A current loop control method for a permanent magnet synchronous motor based on error feedback model prediction. The switching command of the inverter is obtained by calculating the value, and then applied to the inverter for current loop control. Compared with the traditional model predictive control based on vector control, it has better decoupling effect and faster dynamic response; This application is a deadbeat model predictive control based on SVPWM technology. The idea is to predict the switching signal of the inverter at the next moment according to the mathematical model of the motor and the inverter. The prediction model is calibrated, and the response speed and steady-state accuracy of the system are improved.

Description

Model-predicted current loop control method for permanent magnet synchronous motor based on error feedback

technical field

The invention relates to the technical field of permanent magnet synchronous motor control, in particular to a current loop control method of a permanent magnet synchronous motor based on error feedback model prediction.

Background technique

Since the 1980s, permanent magnet synchronous motors have been widely used in new energy vehicles, robots, aerospace, wind power generation and high-performance medical equipment due to their high power density and high efficiency. Breakthroughs in related supporting technologies such as , power electronics technology, computer technology, etc., make the precise control of permanent magnet synchronous motor assistants simple.

However, in many occasions, the requirements for motor control performance are getting higher and higher, the response speed and overshoot of the classic PI vector control of permanent magnet synchronous motor are mutually restricted, and the problems such as poor anti-interference ability are difficult to meet the control requirements in cutting-edge fields. In order to give full play to the advantages of the permanent magnet synchronous motor and meet the needs of intelligent development, it is necessary to introduce advanced control strategies into the permanent magnet synchronous motor control system. Compared with other control methods, model predictive control has a faster dynamic response speed. , high-precision tracking control and other advantages.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a current loop control method based on error feedback model prediction of the permanent magnet synchronous motor which improves the steady-state performance and bandwidth and reduces the complexity of the controller.

The technical problem to be solved by the present invention is achieved through the following technical solutions. The present invention is a current loop control method based on error feedback model prediction of permanent magnet synchronous motor. Then, according to the voltage value, the switching command of the inverter is obtained, and then applied to the inverter to control the current loop.

The technical problem to be solved by the present invention can also be further realized by the following technical solutions. For the above-mentioned current loop control method of the permanent magnet synchronous motor based on error feedback model prediction, the specific flow of the method is as follows:

(1) Sampling the position, speed and three-phase current of the permanent magnet synchronous motor;

(2) Clarke-Park transformation is performed on the sampled current;

(3) Calculate the dq axis voltage command according to the mathematical model of the permanent magnet synchronous motor;

(4) SVPWM modulation is performed on the obtained dq-axis voltage command to obtain the switch command;

(5) Output switching commands to the inverter.

The technical problem to be solved by the present invention can also be further realized by the following technical solutions. For the above-mentioned current loop control method of the permanent magnet synchronous motor based on error feedback model prediction, the specific operation method of the method is:

(1) Sampling the current value at the kT _s time, and then predict the voltage value that should be applied at the current time according to the current prediction model, so that the current at the (k+1)T _s sampling time can be tracked to the kT _s time without deadbeat. Current given value, namely:

为K时刻d，q坐标系下的d轴参考电流，q轴参考电流；In the formula: i _d (k+1), i _q (k+1) is the d-axis current in the d, q coordinate system at the time of K+1, the q-axis current,

is the d-axis reference current and the q-axis reference current under the q coordinate system at time K at time d;

给定值作为下一时刻的电流指令值i_d(k+1)、i_q(k+1)，并将其与电机当前采样得到的电流实际值i_d(k)、i_q(k)代入步骤(1)中的公式，计算使电机电流精确跟随指令所需作用的电压矢量u_d(k)、u_q(k)；(2) Speed loop output at time kT _s

The given value is used as the current command value _{id (k+1) and i q (} k+1) at the next moment, and it is compared with the current actual value _{id (k) and i q (} k) obtained by the current sampling of the motor. Substitute into the formula in step (1) to calculate the voltage vectors _ud (k) and u _q (k) required to make the motor current follow the command accurately;

(3) The voltage vector is modulated by SVPWM technology, and the required switching signal is generated to act on the inverter to control the motor. The equation for calculating the voltage vector is as follows:

According to the model predictive control theory, introducing current feedback, we can get:

为K时刻d，q坐标系下的d轴参考电压，q轴参考电压；R_s为转子电阻值；L_d，L_q为d，q坐标系下的d轴电感，q轴电感；ω_r为转子机械角速度；ω_f为是转子永磁体磁链；h为误差反馈比重系数。In the formula: u _d (k), u _q (k) are the d-axis voltage and q-axis voltage in the d, q coordinate system at time K,

is the d-axis reference voltage and q-axis reference voltage in the d, q coordinate system at time K; R _s is the rotor resistance value; L _d , L _q are the d-axis inductance and q-axis inductance in the d, q coordinate system; ω _r is the rotor mechanical angular velocity; ω _f is the rotor permanent magnet flux linkage; h is the error feedback proportion coefficient.

The technical problem to be solved by the present invention can also be further realized by the following technical solutions. For the above-mentioned current loop control method of permanent magnet synchronous motor based on error feedback model prediction, in order to ensure the stability of the system, h should meet the following conditions:

In the formula: L is the phase inductance, T is the use period, R ₀ is the motor phase resistance, and L ₀ is the actual value of the inductance.

The technical problem to be solved by the present invention can be further realized by the following technical solutions. For the above-mentioned current loop control method of permanent magnet synchronous motor based on error feedback model prediction, in order to ensure the stability of the system, the voltage vector should meet the following conditions :

Where: U is the DC bus voltage.

Compared with the prior art, the present invention proposes a current loop control method of a permanent magnet synchronous motor based on error feedback model prediction, so that the permanent magnet synchronous motor current loop is based on SVPWM predictive control, error feedback is introduced, and the prediction model is calibrated. , improve the response speed and steady-state accuracy of the system; and in order to verify the feasibility of the model control algorithm studied, build a simulation in MATLAB/Simulink, through the simulation results under the reference speed and the same disturbance, the PI control method, prediction The control method and predictive control based on error feedback are analyzed and compared, which reflects the advantages of the model predictive control algorithm based on error feedback used in this application to make the permanent magnet synchronous motor in terms of dynamic response and anti-load disturbance, and has better performance. Control performance.

Description of drawings

Fig. 1 is the predictive control flow chart of the present invention;

2 is a schematic diagram of a PWM inverter model of the present invention;

FIG. 3 is a basic voltage space vector distribution diagram of the present invention.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the present invention. examples, but not all examples. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

1 to 3, a current loop control method of a permanent magnet synchronous motor based on error feedback model prediction, the specific scheme is:

1. The establishment of the system model

1.1. Mathematical model of permanent magnet synchronous motor

For the convenience of analysis, the three-phase permanent magnet synchronous motor is regarded as an ideal motor, that is to say, it meets the following assumptions:

(1) There is no damping winding on the rotor; the armature resistance and inductance of each winding in the stator are equal, and the windings of the three-phase stator are distributed in a symmetrical star shape;

(2) Its air-gap magnetic field obeys sinusoidal distribution and each harmonic is ignored, and the induced electromotive force also obeys sinusoidal distribution;

(3) The equivalent excitation current of the permanent magnet does not change; the effects of eddy current, skin effect, motor core saturation and hysteresis loss in the motor are ignored; temperature and frequency do not affect the parameters of the motor;

The mathematical model of permanent magnet synchronous motor includes basic equations such as voltage equation, flux linkage equation, electromagnetic torque equation and motion equation:

(1) Voltage equation in three-phase stationary coordinate system

In the formula, u _A , u _B , and u _C are the instantaneous values of the three-phase voltages of the stator windings A, B, and C, respectively, i _A , i _B , and i _C are the instantaneous values of the phase currents of the three-phase stator windings, respectively, and R is the phase resistance. ;

Flux Equation

In the formula, L _AA , L _BB , and L _CC are the self-inductances of each phase winding of the stator; L _AB =L _BA , L _BC = L _CB , L _AC = L _CA are the mutual inductances of the two-phase windings; ψ _fA , ψ _fB , ψ _fC are the mutual induction flux linkages generated by the permanent magnet magnetic field between each phase winding;

Because the air gap is assumed to be uniform and the windings are symmetrical, the mutual inductance and self-inductance between the windings are constant. Let L _s be the winding self-inductance, then we have:

L _AA =L _BB =L _CC =L _S (2-3)

M can be set as the mutual inductance of the windings, because each phase winding is 120 electrical degrees away from each other in space, and the armature magnetic fields generated by the stator windings are all sinusoidal distributions, there are:

L _AB =L _BC =L _AC =M (2-4)

Since the mutual induction flux linkage generated by the permanent magnet excitation magnetic field in each phase winding is symmetrically distributed, the following relationship is obtained:

Assume that the stator winding of the motor adopts the star-shaped connection mode without neutral line. According to the KCL theorem, it can be known that the three-phase current of the stator satisfies the relationship: i _A + i _B + i _C = 0, and formulas (2-3), (2-4), (2-4), (2-5) Substitute into formula (2-2), the flux linkage equation can be obtained as:

Wherein, L ₀ =L _s -M. Substituting Equation (2-6) into Equation (2-1), the stator voltage can be obtained as:

Where: ω _e is the electrical angular velocity of the rotor and ω _e =Pω _r , where P is the number of pole pairs of the motor, and ω _r is the mechanical angular velocity of the rotor;

It can be seen that the voltage equation of the permanent magnet synchronous motor in the three-phase static coordinates is a set of linear differential equations with variable coefficients, which has the characteristics of multi-variable, time-varying, nonlinear and strong coupling, and it is very difficult to directly solve it. It is also not conducive to the control of the motor;

Therefore, it is necessary to simplify the mathematical model through coordinate transformation, change the AC control to the DC control, and realize the control performance similar to the DC motor. The voltage equation in the rotating coordinate system is:

In the above formula: u _d and u _q are the dq-axis components of the stator voltage vector u _s , respectively, id , _{i q} are the _dq -axis components of the stator current is, respectively, ω _e is the rotor electrical angular velocity and ω _e =Pω _r , where P _n is the number of motor pole pairs, ω _r is the rotor mechanical angular velocity, ψ _f is the rotor permanent magnet flux linkage, J is the motor rotational inertia, T _L is the motor load torque, and B is the motor friction coefficient;

In the case where the control period T _s is short enough, the input voltage u and the back EMF D of the system are considered to remain constant between a control period (kT _s to (k+1)T _s ). (2-13) The discretization solution can obtain the current prediction model:

2. Space vector control SVPWM

The theoretical basis of SVPWM is the principle of mean value equivalence, that is, by combining the basic voltage vectors in one switching cycle to make the mean value equal to the given voltage vector, the main goal of control is to make the output voltage space vector of the inverter. The motion trajectory is close to an ideal circle;

构成三相全桥，电机绕组采用“Y”型连接，途中每个上下桥臂均由IGBT和二极管组成，上下两个桥臂开通与关断由IGBT的状态决定，但是同一桥臂的两个IGBT不能同时导通；并且在任何时刻必须有三个开关管处于导通状态，而另外三个开关管需保持关断状态；二极管的主要作用是为电流提供续流通道，保护IGBT不被击穿；The two-level three-phase inverter widely used in the control system of the permanent magnet synchronous motor is shown in Figure 2. It is actually a discrete system that digitally encodes and outputs the analog signal level. The three-phase voltage The source-to-inverter conversion consists of six switch tubes _Sa , _{Sb, Sc ,}

A three-phase full bridge is formed, and the motor windings are connected in a "Y" type. Each upper and lower bridge arm is composed of IGBTs and diodes. The turn-on and turn-off of the upper and lower bridge arms is determined by the state of the IGBT, but the two The IGBT cannot be turned on at the same time; and at any time, three switches must be in the on state, and the other three switches must be kept off; the main function of the diode is to provide a freewheeling channel for the current to protect the IGBT from breakdown ;

In order to facilitate the analysis, the switch states of the three bridge arms of the inverter are defined as _{SA, S B ,} and S _C. S _A =0 means that the lower arm of phase A is turned on and the upper arm is turned off, and _SA =1 means The upper bridge arm of phase A is turned on and the lower bridge arm is turned off, and S _B and S _C are the same, so there are 2 ³ =8 switching states, including 6 effective voltage output states U ₁ (001), U ₂ (010 ), U ₃ (011), U ₄ (100), U ₅ (101), U ₆ (110), 2 invalid voltage output states U ₀ (000), U ₇ (111), these 8 voltage space vectors is called the fundamental voltage space vector. The phase angles of the adjacent vectors U ₁ to U ₆ are 60° different from each other, and their amplitudes are all 2U _dc /3, where U _dc is the DC side voltage of the inverter. When they act on the motor, they will form a phase with the same in the motor. The corresponding stator flux linkage vector, while U ₀ and U ₇ will not form a flux linkage vector when they act on the motor, it can change the change speed of the flux linkage vector but will not change the shape of the flux linkage track;

One working cycle of the inverter is divided into six regions by six non-zero basic voltage space vectors, these six regions are called sectors, and two zero voltage space vectors are located in the center of the six sectors, as shown in Figure 3, In a control cycle, for any given reference voltage vector U _s , it can be synthesized by the two adjacent basic voltage space vectors of the sector where it is located according to their respective action times. It can be seen from the figure that if the six effective voltages If the vector appears only once, the hexagonal vector trajectory formed is quite different from the circular trajectory. If the amplitude of the voltage vector is constant, the higher the switching frequency, the more vectors are generated in one sinusoidal cycle, and the more the vector trajectory is. Close to a circle, so as to achieve the goal of making the stator flux linkage track approach the ideal flux linkage circle;

3. Current predictive control based on error feedback

3.1. Predictive control algorithm

According to the basic idea of deadbeat current prediction control: sample the current value at the kT _s time, and then predict the voltage value that should be applied at the current time according to the current prediction model, so that the current at the (k+1)T _s sampling time can be free of charge. The beat tracks to the current given value at the moment of kT _s , including:

为第kT_s时刻d、q轴电流给定值；where:

is the given value of the d and q axis currents at the kT _s time;

给定值作为下一时刻的电流指令值i_d(k+1)、i_q(k+1)，并将其与电机当前采样得到的电流实际值i_d(k)、i_q(k)代入式(3-20)，以计算使电机电流精确跟随指令所需作用的电压矢量u_d(k)、u_q(k)；将电压矢量通过SVPWM技术调制，生成所需要的开关信号作用于逆变器，从而对电机进行控制，无差拍电流预测控制计算电压矢量的方程如下所示：Therefore, the velocity loop output at time kT _s

The given value is used as the current command value _{id (k+1) and i q (} k+1) at the next moment, and it is compared with the current actual value _{id (k) and i q (} k) obtained by the current sampling of the motor. Substitute into formula (3-20) to calculate the voltage vectors u _d (k) and u _q (k) required to make the motor current follow the command accurately; the voltage vector is modulated by SVPWM technology to generate the required switching signal to act on the The inverter is used to control the motor, and the equation for calculating the voltage vector for deadbeat current predictive control is as follows:

According to the model predictive control theory, the current feedback is introduced:

Due to the modulation link, the deadbeat predictive control has a fixed switching frequency, and this frequency is the same as the control frequency. Its control structure is very close to the traditional vector control, and it is easy to implement on the basis of the original vector control. The predictive control flow chart is shown in the figure. 1 shown;

The resistance and inductance in the expression are identification values. In order to ensure the stability of the system, h should meet the following conditions:

3.2. Voltage amplitude limit

Since the actual system cannot output excessive voltage, it is necessary to limit the voltage vector calculated by the prediction model to achieve effective voltage output. In the coordinate system with constant amplitude, when the DC bus voltage is U, in the rotating coordinate system The maximum output voltage is 2U/3, when the voltage exceeds 2U/3, use the formula to calculate:

4. System simulation and experiment

The simulation and experiment of the current predictive control based on error feedback proposed in this application are carried out. The motor parameter power is 200W, L _d =L _q =0.0373mH, the rated speed is 3000r/min, the phase resistance is 0.265Ω, the number of pole pairs is 3, and the resolver feedback ;

The simulation environment is MATLAB/Simulink, and the current loop control period of both simulation and experiment is 10KHz;

For the same motor, the current predictive control and PI control based on error feedback are used for comparative testing, and the test results are shown in Table 1;

Table 1

It can be seen from Table 1 that this application improves the response speed and steady-state accuracy of the system, and the response speed is faster!

Claims (5)

1. a current loop control method based on the model prediction of error feedback of permanent magnet synchronous motor, it is characterized in that: this method is by the permanent magnet synchronous motor current, rotating speed and rotor position measured, obtain the current moment should be applied by calculating. voltage value, and then calculate the switching command of the inverter according to the voltage value, and then apply it to the inverter for current loop control. 2. The current loop control method of the permanent magnet synchronous motor based on the model prediction of error feedback according to claim 1, is characterized in that: the concrete flow of this method is: (1) Sampling the position, speed and three-phase current of the permanent magnet synchronous motor; (2) Clarke-Park transformation is performed on the sampled current; (3) Calculate the dq axis voltage command according to the mathematical model of the permanent magnet synchronous motor; (4) SVPWM modulation is performed on the obtained dq-axis voltage command to obtain the switch command; (5) Output switching commands to the inverter. 3. The current loop control method of the permanent magnet synchronous motor based on the model prediction of error feedback according to claim 1 and 2, it is characterized in that: the concrete operation method of this method is: (1) Sampling the current value at the kT _s time, and then predict the voltage value that should be applied at the current time according to the current prediction model, so that the current at the (k+1)T _s sampling time can be tracked to the kT _s time without deadbeat. Current given value, namely:

In the formula: i _d (k+1), i _q (k+1) is the d-axis current in the d, q coordinate system at the time of K+1, the q-axis current,

is the d-axis reference current and the q-axis reference current under the q coordinate system at time K at time d; (2) Speed loop output at time kT _s

The given value is used as the current command value _{id (k+1) and i q (} k+1) at the next moment, and it is compared with the current actual value _{id (k) and i q (} k) obtained by the current sampling of the motor. Substitute into the formula in step (1) to calculate the voltage vectors _ud (k) and u _q (k) required to make the motor current follow the command accurately; (3) The voltage vector is modulated by SVPWM technology, and the required switching signal is generated to act on the inverter to control the motor. The equation for calculating the voltage vector is as follows:

According to the model predictive control theory, introducing current feedback, we can get:

In the formula: u _d (k), u _q (k) are the d-axis voltage and q-axis voltage in the d, q coordinate system at time K,

is the d-axis reference voltage and q-axis reference voltage in the d, q coordinate system at time K; R _s is the rotor resistance value; L _d , L _q are the d-axis inductance and q-axis inductance in the d, q coordinate system; ω _r is the rotor mechanical angular velocity; ω _f is the rotor permanent magnet flux linkage; h is the error feedback proportion coefficient. 4. the current loop control method of the model prediction based on error feedback of permanent magnet synchronous motor according to claim 3, is characterized in that: in order to guarantee system stability, h should satisfy following condition:

In the formula: L is the phase inductance, T is the use period, R ₀ is the motor phase resistance, and L ₀ is the actual value of the inductance. 5. The current loop control method of the model prediction based on error feedback of the permanent magnet synchronous motor according to claim 3, is characterized in that: in order to ensure system stability, the voltage vector should meet the following conditions:

Where: U is the DC bus voltage.

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