﻿ 磁通切换型定子永磁电机的建模与线性自抗扰控制
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 智能系统学报  2018, Vol. 13 Issue (3): 339-345  DOI: 10.11992/tis.201707028 0

### 引用本文

WANG Kelei, CHEN Zengqiang, SUN Mingwei, et al. Modeling and linear active-disturbance-rejection control of flux-switching stator permanent magnet motor[J]. CAAI Transactions on Intelligent Systems, 2018, 13(3): 339-345. DOI: 10.11992/tis.201707028.

### 文章历史

Modeling and linear active-disturbance-rejection control of flux-switching stator permanent magnet motor
WANG Kelei, CHEN Zengqiang, SUN Mingwei, SUN Qinglin
College of Computer and Control Engineering, Nankai University, Tianjin 300350, China
Abstract: Flux-switching permanent magnet (FSPM) motor is a new type of stator permanent magnet brushless motor. It has good prospects for application in the manufacturing industry and navigation. However, it is very difficult to realize high-performance control of FSPM motors. In this study, based on an analysis of the working principle of this type of motor, mathematical models are established for the stator coordinate system and the rotor rotating coordinate system. The current-hysteresis PWM control strategy is adopted, and the linear active-disturbance-rejection controller (LADRC) is introduced into the speed control system of this paper. The steady-state and dynamic-state simulation results show that the FSPM with LADRC has better starting characteristics than the PI-controlled speed regulation system. In addition, the proposed system is more robust to mutation of rotation speed and sudden exertion of load disturbance.
Key words: flux-switching    stator permanent magnet motor    linear active-disturbance-rejection controller    speed regulation system    current hysteresis comparison    PWM control    robustness

1 数学模型

 $\left[ \begin{array}{l}{u_a}\\{u_b}\\{u_c}\end{array} \right] = {R_{ph}}\left[ \begin{array}{l}{i_a}\\{i_b}\\{i_c}\end{array} \right] + {L_1}\frac{{\rm{d}}}{{{\rm{d}}t}}\left[ \begin{array}{l}{i_a}\\{i_b}\\{i_c}\end{array} \right] + \frac{{\rm{d}}}{{{\rm{d}}t}}\left[ \begin{array}{l}{\psi _a}\\{\psi _b}\\{\psi _c}\end{array} \right] + \left[ \begin{array}{l}{e_{ma}}\\{e_{mb}}\\{e_{mc}}\end{array} \right]$ (1)

 ${T_{em}} = \frac{{{P_{em}}}}{{{\omega _r}}} = {T_{pm}} + {T_r} + {T_{cog}}$ (2)

FSPM电机的机械运动方程可以表示为

 ${T_{em}} = J\frac{{{\rm{d}}{\omega _r}}}{{{\rm{d}}t}} + {T_L} + {B_v}{\omega _r}$ (3)
 ${\omega _r} = \frac{{{\rm{d}}{\theta _r}}}{{{\rm{d}}t}}$ (4)

FSPM电机的反电动势和电流均为正弦波波形，因此其在转子旋转坐标系下(d-q 轴)的模型和正弦波永磁同步电机类似。忽略铁芯饱和，经过Park变换后的 FSPM模型为

 $\left[ \begin{array}{l}\!\!\!\! {u_d} \!\!\!\! \\\!\!\!\! {u_q} \!\!\!\! \\\!\!\!\! {u_0} \!\!\!\! \end{array} \right] = \frac{{\rm{d}}}{{{\rm{d}}t}}\left[ \begin{array}{l}\!\!\!\! {\psi _d} \!\!\!\! \\\!\!\!\! {\psi _q} \!\!\!\! \\\!\!\!\! {\psi _0} \!\!\!\! \end{array} \right] + \left[ {\begin{array}{*{20}{c}}\!\!\!\! {{R_{ph}}} & 0 & 0 \!\!\!\! \\\!\!\!\! 0 & {{R_{ph}}} & 0 \!\!\!\! \\\!\!\!\! 0 & 0 & {{R_{ph}}} \!\!\!\! \end{array}} \right]\left[ \begin{array}{l}\!\!\!\! {i_d} \!\!\!\! \\\!\!\!\! {i_q} \!\!\!\! \\\!\!\!\! {i_0} \!\!\!\! \end{array} \right] + \left[ {\begin{array}{*{20}{c}}\!\!\!\! { - {\omega _e}{\psi _q}} \!\!\!\! \\\!\!\!\! {{\omega _e}{\psi _d}} \!\!\!\! \\\!\!\!\! 0 \!\!\!\! \end{array}} \right]$ (5)
 ${T_{em}} = \frac{3}{2}\frac{{{P_{em}}}}{{{\omega _r}}}{\rm{ = }}\frac{3}{2}{P_r}\left[ {{\psi _m}{i_q} + \left( {{L_d} - {L_q}} \right){i_d}{i_q}} \right] + {T_{cog}}$ (6)

 $\left\{ \begin{array}{l}{\psi _{md}} = {\psi _m}\\{\psi _{mq}} = 0\end{array} \right.$ (7)

${i_d} = 0$ 是上述4种电流控制算法中最简单的一种，这种控制方法使得用来调节磁场的直轴电流为0，并根据给定的电磁转矩 ${T^*_{em}}$ 通过计算得到交轴电流 ${i^*_q}$ ，本文采用 ${i_d} = 0$ 控制，则其电磁转矩公式可简化为

 ${T_{em}} = {T_{pm}} + {T_{cog}} = \frac{3}{2}{P_r}{\psi _m}{i_q} + {T_{cog}}$ (8)
2.2 线性自抗扰控制

 $\dot y = - ay + w + bu$ (9)

 $\left\{ \begin{array}{l}{{\dot x}_1} = {x_2} + {b_0}u\\{{\dot x}_2} = \dot f = h\\y = {x_1}\end{array} \right.$ (10)

 $\left\{ \begin{array}{l}{{\dot z}_1} = {z_2} - {\beta _1}\left( {{z_1} - y} \right) + {b_0}u\\{{\dot z}_2} = - {\beta _2}\left( {{z_1} - y} \right) \end{array} \right.$ (11)

 ${z_1}\left( t \right) \to y\left( t \right),{z_2}\left( t \right) \to f$

 $u = \frac{{\left( { - {z_2} + {u_0}} \right)}}{{{b_0}}}$ (12)

 $\dot y = \left( {f - {z_2}} \right) + {u_0} \approx {u_0}$ (13)

 ${u_0} = {k_p}\left( {v - {z_1}} \right)$ (14)

 $\begin{array}{c}{{\dot \omega }_r} = \displaystyle\frac{1}{J}\left( {{T_{{\rm{em}}}} - {T_L} - {B_v}{\omega _r}} \right) = \\a\left( x \right) + bu\end{array}$ (15)

$f = a\left( x \right) + \left( {b - {b_0}} \right)u$ $f$ 为转速环的总扰动。将式(15)转化为如式(16)标准形式：

 $\left\{ \begin{array}{l}{{\dot \omega }_r} = f + {b_0}u\\y = {\omega _r} \end{array} \right.$ (16)

 $\left\{ \begin{array}{l}e = {z_1} - y\\{{\dot z}_1} = {z_2} - {\beta _1}\left( {{z_1} - {\omega _r}} \right) + {b_0}u\\{{\dot z}_2} = - {\beta _2}\left( {{z_1} - {\omega _r}} \right) \end{array} \right.$ (17)

P控制器：

 ${u_0} = {k_{\rm{p}}}\left( {v - {z_1}} \right)$ (18)

 ${\dot \omega _r} = {u_0}$ (19)

 Download: 图 2 FSPM电机矢量控制系统结构图 Fig. 2 Vector control diagram of FSPM machine

3.1 稳态仿真结果

FSPM电机的稳态模型是在给定转速和转矩的前提下建立的，对电机的机械特性进行研究。根据表1设置三相FSPM电机的电磁和电气参数。

3.2 动态仿真结果

1) 空载启动

2) 负载转矩恒定，转速突变

 Download: 图 5 FSPM在转速突变时的仿真结果 Fig. 5 Simulation results of FSPM under speed mutation

3) 转速恒定，负载转矩突变