阅读说明：本技术 一种永磁同步电机的有限集模型预测直接速度控制方法 (Finite set model prediction direct speed control method of permanent magnet synchronous motor ) 是由 王慧敏 刘伟 周湛清 耿强 郭丽艳 于 2020-03-13 设计创作，主要内容包括：本发明涉及一种永磁同步电机的有限集模型预测直接速度控制方法,采用一种应用泰勒级数的预测直接速度控制器,所述的应用泰勒级数的预测直接速度控制器由应用泰勒级数的FCS-MPDSC方法的延时补偿模型、应用泰勒级数的FCS-MPDSC方法的预测模型和二次型价值函数构成；建应用泰勒级数的FCS-MPDSC方法的延时补偿模型,所得到的电流d、q轴分量补偿值和电角速度补偿值作为预测模型的控制变量初值；其次,采用应用泰勒级数的FCS-MPDSC方法的预测模型,获得各组基本电压矢量作用下的电流d、q轴分量预测值和电角速度预测值；获得最优基本电压矢量,实现对永磁同步电机的预测控制。(The invention relates to a finite set model prediction direct speed control method of a permanent magnet synchronous motor, which adopts a prediction direct speed controller applying Taylor series, wherein the prediction direct speed controller applying the Taylor series is composed of a delay compensation model of an FCS-MPDSC method applying the Taylor series, a prediction model of the FCS-MPDSC method applying the Taylor series and a quadratic value function; establishing a delay compensation model of an FCS-MPDSC method applying Taylor series, and taking the obtained current d and q axis component compensation values and electric angular velocity compensation values as initial control variable values of a prediction model; secondly, obtaining predicted values of components of current d and q axes and predicted values of electrical angular velocity under the action of each group of basic voltage vectors by adopting a prediction model of an FCS-MPDSC method applying Taylor series; and obtaining an optimal basic voltage vector to realize the predictive control of the permanent magnet synchronous motor.)

1. A finite set model prediction direct speed control method of a permanent magnet synchronous motor is characterized in that a prediction direct speed controller applying a Taylor series is adopted in the control method, and the prediction direct speed controller applying the Taylor series comprises a delay compensation model applying an FCS-MPDSC method of the Taylor series, a prediction model applying the FCS-MPDSC method of the Taylor series and a quadratic value function; firstly, performing delay compensation on current d and q axis components and an electric angular velocity at the current moment obtained by sampling conversion by adopting a delay compensation model of an FCS-MPDSC method applying Taylor series, and taking the obtained compensation values of the current d and q axis components and the electric angular velocity as initial control variable values of a prediction model of the FCS-MPDSC method applying the Taylor series so as to solve the problem of one-step delay caused by digital control; secondly, constructing a current candidate basic voltage vector set, and obtaining predicted values of components of current d and q axes and predicted values of electrical angular velocity under the action of each group of basic voltage vectors in the current candidate basic voltage vector set by adopting a prediction model of an FCS-MPDSC method applying Taylor series; and finally, constructing a quadratic value function, comparing the quadratic value function values obtained by calculating the current d and q axis component predicted values and the electric angular velocity predicted values under the action of each group of basic voltage vectors, selecting a group of basic voltage vectors with the minimum quadratic value function value as the optimal basic voltage vector at the current moment, and acting the switching state corresponding to the optimal basic voltage vector on the voltage source type two-level inverter to realize the predictive control of the permanent magnet synchronous motor.

2. The method of claim 1, wherein the delay compensation model of the FCS-MPDSC method using taylor series is:

in the formula i_d ^C(k +1) is a compensation value of a d-axis component of the current at the moment of k + 1; i.e. i_q ^C(k +1) is a compensation value of the q-axis component of the current at the moment of k + 1; omega_e ^C(k +1) is an electric angular velocity compensation value at the moment of k + 1; u. of_d ^L(k) D-axis component of the optimal basic voltage vector at the moment of k-1; u. of_q ^L(k) The q-axis component of the optimal basic voltage vector at the moment k-1; i.e. i_d(k) Is the d-axis component of the current at time k; i.e. i_q(k) Is the q-axis component of the current at time k; omega_e(k) Is the electrical angular velocity at time k; t is_sIs a control period; r_sFor the stator resistance of the motor；L_sIs a motor inductor; psi_fIs a motor magnetic linkage; p is the number of pole pairs of the motor; j. the design is a square_mIs the rotational inertia of the motor; t is_L(k) Is the load torque.

3. The method of claim 1, wherein the prediction model of the FCS-MPDSC method using taylor series is:

in the formula i_d ^P(k +2) is a predicted value of d-axis component of current at the moment of k + 2; i.e. i_q ^P(k +2) is a predicted value of the current q-axis component at the moment of k + 2; omega_e ^P(k +2) is a predicted value of the electrical angular velocity at the moment of k + 2; u. of_d(k) Is the d-axis component of the basic voltage vector at the moment k; u. of_q(k) The q-axis component of the base voltage vector at time k.

4. The method of claim 1, wherein the quadratic cost function is:

G(k)＝^T(k+2)W(k+2)

wherein W is a weight coefficient matrix of 3 x 3, and W is W^T，W＝[w₁₁00；0w₂₂0；00w₃₃]^T(ii) a (k +2) is a variable error column vector consisting of a current d-axis component variable error, a current q-axis component variable error and an electric angular velocity variable error, and (k +2) [ i ]_d ^*-i_d ^P(k+2)i_q ^*-i_q ^P(k+2)ω_e ^*-ω_e ^P(k+2)]^TWherein i is_d ^*Given value of current d-axis component, i_q ^*For setting the value of q-component of current, omega_e ^*The electrical angular velocity is given.

5. Method according to claim 1, characterized in that the position signal θ discrete at time k is obtained in real time by means of an encoder mounted on the permanent magnet synchronous machine_e(k) The DC bus voltage U is obtained by sampling with a voltage sensor_dcAnd a position signal theta discrete at time k_e(k) And constructing the current candidate basic voltage vector set.

6. Method according to claim 1, characterized in that the kalman filter based load observer is a discrete position signal θ in time k_e(k) And the q-axis component i of the current at the time k_q(k) As a load observer input quantity based on Kalman filtering, observing the k-moment electrical angular velocity omega in real time_e(k) And the load torque T at the time k_L(k)。

7. Method according to claim 1, characterized in that the d-axis component of the current is used to set the value i_d ^*The load torque T at the time k is observed according to the control mode of 0_L(k) Obtaining a given value i of the q-axis component of the current_q ^*。

Technical Field

The invention belongs to the technical field of permanent magnet synchronous motors, and relates to a finite set model prediction direct speed control method of a permanent magnet synchronous motor.

Background

Because the permanent magnet synchronous motor has the advantages of simple structure, small volume, high power factor, high power density, large torque-current ratio, low moment of inertia, large air gap, easy heat dissipation, easy maintenance and the like, the permanent magnet synchronous motor is widely applied to industrial occasions with higher control precision requirements, such as numerical control machines, industrial robots, electric automobiles, intelligent factories and the like. Meanwhile, in order to ensure a sufficiently high Control performance of the permanent magnet synchronous motor, researchers have developed many advanced Control methods, one of which is a Model Predictive Control (MPC) method. With respect to the function of the MPC controller, most concepts previously proposed have focused on current, torque and flux linkage control, which are based on a double closed loop architecture (outer speed loop and inner current/torque loop). However, the cascade topology limits the dynamic behavior of the system. In particular, the speed regulation performance will be gentler due to the low bandwidth of the internal current or torque control loop. For highly dynamic performance demanding applications (especially servo systems), the conventional dual closed-loop MPC scheme needs to be improved. In order to overcome the limitation of the cascade Control structure, Preindl and Bolognani firstly propose a Finite Set Model prediction Direct speed Control (FCS-MPDSC) method^[1]. In the conventional FCS-MPDSC method, the prediction model is composed of two parts: current loop portion and speed loop portion^[2]. Wherein, the model input quantity of the current loop part is the basic voltage vector d and the q-axis component u at the moment k_d(k)、u_q(k) And the model output quantity is predicted value i of current d and q-axis component at the moment of k +1_d ^P(k+1)、i_q ^P(k + 1); model input quantity of a speed ring part is a current q-axis component i at the moment k +1_q(k +1), the electric angular velocity predicted value omega at the moment when the model output quantity is k +2_e ^P(k + 2). Therefore, for the conventional FCS-MPDSC method, the basic voltage at the moment when the model input amount is unified to k isComponent u of vector d, q axis_d(k)、u_q(k) In the meantime, the predicted values of the components of the d and q axes as the output quantities of the model are not at the same time as the predicted value of the electrical angular velocity, resulting in that the electrical angular velocity is one control period slower than the current. Meanwhile, in the FCS-MPDSC method, the cost function includes variable errors of current d, q-axis components and electrical angular velocity, and since unit dimensions of the three are different, a weight coefficient is required to allocate a weight of each variable error in the cost function. The traditional FCS-MPDSC method generally adopts a weighted summation type cost function, adopts an empirical setting mode for the distribution of weight coefficients, and performs data fitting through a large amount of simulation to approximately obtain relatively ideal weight coefficients.

Reference documents:

[1]Matthias Preindl,Silverio Bolognani.Model Predictive Direct SpeedControl with Finite Control Set of PMSM Drive Systems[J].IEEE Transactions onPower Electronics,2013,28(02):1007-1015.

[2]Chao Gong,Yihua Hu,Kai Ni,Jinglin Liu,Jinqiu Gao.SM Load TorqueObserver-Based FCS-MPDSC With Single Prediction Horizon for High Dynamics ofSurface-Mounted PMSM[J].IEEE Transactions on Power Electronics,2020,35(01):20-24.

[3]Tingna Shi,Zheng Wang,Changliang Xia.Speed Measurement ErrorSuppression for PMSM Control System Using Self-Adaption Kalman Observer[J].IEEE Transactions on Industrial Electronics,2015,62(05):2753-2763.

[4] researching a speed control strategy of a low-speed and high-torque permanent magnet synchronous motor of a man-year-old type [ D ]. Tianjin: tianjin university, 2015.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, and provides an FCS-MPDSC method applying Taylor series in order to solve the problems in the traditional FCS-MPDSC method. Aiming at the problem that predicted values of components of d and q axes and predicted values of electric angular velocity in the traditional FCS-MPDSC method are not synchronous, a prediction model construction method of the FCS-MPDSC method using Taylor series is provided, and model input quantities are unified into a basic voltage vector d and a q axis component u at the moment of k_d(k)、u_q(k) The output quantity of the model is unified into a current predicted value and an electric angular velocity predicted value at the same moment; aiming at the inherent delay problem in digital control, a delay compensation model of an FCS-MPDSC method applying Taylor series is designed; aiming at the problem that the distribution of weight coefficients of a cost function in the traditional FCS-MPDSC method is set by experience, a quadratic cost function is used for replacing a weighted summation type cost function, and a weight coefficient matrix is obtained by off-line solving through Lyapunov stability analysis.

In order to achieve the purpose, the invention adopts the following technical scheme:

the FCS-MPDSC method of the permanent magnet synchronous motor is characterized in that a Taylor series applied direct speed prediction controller is adopted in the control method, and the Taylor series applied direct speed prediction controller is composed of a time delay compensation model of the FCS-MPDSC method applied to the Taylor series, a prediction model of the FCS-MPDSC method applied to the Taylor series and a quadratic value function; firstly, performing delay compensation on current d and q axis components and an electric angular velocity at the current moment obtained by sampling conversion by adopting a delay compensation model of an FCS-MPDSC method applying Taylor series, and taking the obtained compensation values of the current d and q axis components and the electric angular velocity as initial control variable values of a prediction model of the FCS-MPDSC method applying the Taylor series so as to solve the problem of one-step delay caused by digital control; secondly, constructing a current candidate basic voltage vector set, and obtaining predicted values of components of current d and q axes and predicted values of electrical angular velocity under the action of each group of basic voltage vectors in the current candidate basic voltage vector set by adopting a prediction model of an FCS-MPDSC method applying Taylor series; and finally, constructing a quadratic value function, comparing the quadratic value function values obtained by calculating the current d and q axis component predicted values and the electric angular velocity predicted values under the action of each group of basic voltage vectors, selecting a group of basic voltage vectors with the minimum quadratic value function value as the optimal basic voltage vector at the current moment, and acting the switching state corresponding to the optimal basic voltage vector on the voltage source type two-level inverter to realize the predictive control of the permanent magnet synchronous motor.

The established delay compensation model of the FCS-MPDSC method applying the Taylor series is as follows:

in the formula i_d ^C(k +1) is a compensation value of a d-axis component of the current at the moment of k + 1; i.e. i_q ^C(k +1) is a compensation value of the q-axis component of the current at the moment of k + 1; omega_e ^C(k +1) is an electric angular velocity compensation value at the moment of k + 1; u. of_d ^L(k) D-axis component of the optimal basic voltage vector at the moment of k-1; u. of_q ^L(k) The q-axis component of the optimal basic voltage vector at the moment k-1; i.e. i_d(k) Is the d-axis component of the current at time k; i.e. i_q(k) Is the q-axis component of the current at time k; omega_e(k) Is the electrical angular velocity at time k; t is_sIs a control period; r_sL is motor stator resistance_sIs a motor inductor; psi_fIs a motor magnetic linkage; p is the number of pole pairs of the motor; j. the design is a square_mIs the rotational inertia of the motor; t is_LIs the load torque.

The prediction model of the FCS-MPDSC method applying the Taylor series is as follows:

in the formula i_d ^P(k +2) is a predicted value of d-axis component of current at the moment of k + 2; i.e. i_q ^P(k +2) is a predicted value of the current q-axis component at the moment of k + 2; omega_e ^P(k +2) is a predicted value of the electrical angular velocity at the moment of k + 2; u. of_d(k) Is the d-axis component of the basic voltage vector at the moment k; u. of_q(k) The q-axis component of the base voltage vector at time k.

The quadratic cost function used is:

G(k)＝^T(k+2)W(k+2)

wherein W is a weight coefficient matrix of 3 x 3, and W is W^T，W＝[w₁₁0 0；0 w₂₂0；0 0 w₃₃]^T(ii) a (k +2) is a variable error column vector consisting of a current d-axis component variable error, a current q-axis component variable error and an electrical angular velocity variable error,(k+2)＝[i_d ^*-i_d ^P(k+2)i_q ^*-i_q ^P(k+2)ω_e ^*-ω_e ^P(k+2)]^Twherein i is_d ^*Given value of current d-axis component, i_q ^*For setting the value of q-component of current, omega_e ^*The electrical angular velocity is given.

Drawings

FIG. 1 is a system diagram of an FCS-MPDSC method using Taylor series for a permanent magnet synchronous motor;

FIG. 2 is a flow chart of the design steps of a predictive direct speed controller employing a Taylor series;

fig. 3 is an experimental waveform of a permanent magnet synchronous motor by applying a taylor series FCS-MPDSC method, (a) an experimental waveform of an electrical angular velocity of the motor, (b) an experimental waveform of a d-axis component of a motor current, (c) an experimental waveform of a q-axis component of a motor current, (d) an experimental waveform of an a-phase current of the motor, (e) an experimental waveform of an electrical angle of the motor;

fig. 4 is a load observer experimental waveform based on kalman filtering, (a) a motor electrical angular velocity observation experimental waveform (b) a motor load torque observation experimental waveform.

Detailed Description

The invention is further illustrated with reference to the following figures and examples.

FIG. 1 is a block diagram of an FCS-MPDSC method system using Taylor series for a permanent magnet synchronous motor.

The system comprises a permanent magnet synchronous motor, a voltage source type two-level inverter, a current sensor, a voltage sensor, an encoder, a Kalman filtering based load observer, a three-phase static/two-phase static (abc/αβ) coordinate transformation module, a two-phase static/two-phase rotating (αβ/dq) coordinate transformation module and a prediction direct speed controller applying Taylor series, wherein the three-phase current i of a stator of the motor at the moment k is_a(k)、i_b(k)、i_c(k) Measured by a current sensor, and then a three-phase static/two-phase static (abc/αβ) coordinate transformation module and a two-phase static/two-phase rotating (αβ/dq) coordinate transformation module are used for obtaining d and q axis components i at the moment k_d(k)、i_q(k) (ii) a By mounting on permanent magnetsAn encoder on the step motor obtains a position signal theta with discrete k moments in real time_e(k) (ii) a DC bus voltage U obtained by sampling through voltage sensor_dcAnd a position signal theta discrete at time k_e(k) Obtaining a current-time alternative basic voltage vector set V_(0-7)(ii) a Kalman filtering based position signal theta discrete by k time of load observer_e(k) And the q-axis component i of the current at the time k_q(k) As a load observer input quantity based on Kalman filtering, observing the k-moment electrical angular velocity omega in real time_e(k) And the load torque T at the time k_L(k) (ii) a Given value i by using d-axis component of current_d ^*In the control method of 0, the load torque at the observed time k is multiplied byThen obtaining a given value i of the q-axis component of the current_q ^*Setting given value of electrical angular velocity omega_e ^*(ii) a Setting the electrical angular velocity to a given value omega_e ^*D-axis component given value i of current_d ^*Given value of q-axis component of current i_q ^*D-axis component i of current at time k_d(k) Current q-axis component i at time k_q(k) And the electrical angular velocity ω at the time k_e(k) As predicted direct speed controller input using a taylor series; and obtaining the switching state corresponding to the optimal basic voltage vector by applying a Taylor series prediction direct speed controller, and outputting the switching state to a voltage source type two-level inverter to drive the permanent magnet synchronous motor to operate.

The permanent magnet synchronous motor, the voltage source type two-level inverter, the encoder, the Kalman filtering based load observer, the three-phase static/two-phase static (abc/αβ) coordinate transformation module, the two-phase static/two-phase rotating (αβ/dq) coordinate transformation module and the like are all the prior art, wherein the Kalman filtering based load observer technology can be seen in a reference document^[3-4]。

The design method of the prediction direct speed controller applying the Taylor series is as follows:

firstly, establishing a permanent magnet synchronous motor state equation considering a coupling term:

in the formula i_dIs the d-axis component of the current; i.e. i_qIs the current q-axis component; omega_eIs the electrical angular velocity; r_sL is motor stator resistance_sIs a motor inductor; psi_fIs a motor magnetic linkage; p is the number of pole pairs of the motor; j. the design is a square_mIs the rotational inertia of the motor; t is_LIs the load torque.

Establishing i according to equation (1)_d、i_qAnd ω_eA first taylor series at time k + 1:

in the formula i_d ^[1]、i_q ^[1]And ω_e ^[1]The current d, q axis components and the first order taylor series coefficients of the electrical angular velocity, respectively.

Setting u_d、u_qAnd T_LConstant which does not change from time k to k + 1. Further extended according to equation (2), i can be established_d、i_qAnd ω_eSecond order Taylor series at time k + 1:

in the formula i_d ^[2]、i_q ^[2]And ω_e ^[2]The second order taylor series coefficients of the d and q axis components of the current and the electrical angular velocity, respectively.

The prediction model of the FCS-MPDSC method using taylor series at the time k +1 based on taylor series obtained from equations (2) and (3) can be expressed as:

the right side of equation (4) is expanded as:

designing a delay compensation model of the FCS-MPDSC method applying Taylor series according to the formula (5):

by compensating the prediction model by equation (6), the prediction model of the FCS-MPDSC method to which the taylor series is applied can be updated as:

and (5) arranging the equation into a space state equation form:

x(k+1)＝Ax(k)+Bu(k)+D (8)

wherein the content of the first and second substances,

x＝[i_di_qω_e]^T；u＝[u_du_q]^T；

assume that when the system is operating to steady state, i.e., x (k +1) ═ x (k) ═ x^*，x^*＝[i_d ^*i_q ^*ω_e ^*]^TThe steady state model of the control system can then be expressed as:

x^*＝Ax^*+Bu(k)+D (9)

a quadratic cost function of the FCS-MPDSC method applying the Taylor series is designed as follows:

G(k)＝^T(k+1)W(k+1) (10)

assuming that the quadratic cost function G (k) is L yapunov function, i.e., the quadratic cost function G (k) is positive and G (k) < G (k-1), the difference between the cost functions at two adjacent time instants can be expressed as:

further, it is possible to obtain:

according to Schur's theorem, the left side of formula (12) is defined as M with respect to W^-1Schur supplement of (1). According to known conditions, it is possible to obtain:

since the weight coefficient matrix W is a diagonal matrix, the quadratic cost function g (k) can be written in the form of a polynomial as follows:

G(k)＝w_{11 1}(k+2)²+w_{22 2}(k+2)²+w_{33 3}(k+2)²(14)

in the formula, w₁₁And w₂₂Respectively, the d-axis component variable error (i)_d ^*-i_d ^P(k+2))²And current q-axis component variable error (i)_q ^*-i_q ^P(k+2))²The coefficient of (a); w is a₃₃As error of electrical angular velocity variation (omega)_e ^*-ω_e ^P(k+2))²The coefficient of (a).

The method comprises the steps of using a L MI functional module of MAT L AB software to realize off-line solving of a weight coefficient matrix W, defining the type of M by using an lmivar function, defining the parameter of M by using an lmiterm function, and solving a minimum solution of M by using a feasp function.