﻿ 船用三相异步电机转速分段PI控制的仿真研究
 舰船科学技术  2018, Vol. 40 Issue (4): 82-87 PDF

Simulation study on speed segment PI control of marine three-phase asynchronous motor
WEN Qiang, LIU Yong-bao, HE Xing, LIANG Qian-chao
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Based on the synchronous rotating coordinate system, the mathematical model of the marine three-phase asynchronous motor is analyzed and meanwhile its rotor flux orientation vector control strategy is studied. In order to achieve fast response and improve the dynamic and static performance of the system, a new method of outer Speed segment PI control is presented based on traditional speed and torque dual closed loop. The Matlab simulation model is established to compare the difference between speed segment PI control and traditional one-parameter PI control in motor performance control. The simulation results show the accuracy of the proposed motor control model. The proposed speed segment PI control method has a better control accuracy and dynamic and static speed control performance, can adapt to various complex operating conditions of ships and enhance system robustness.
Key words: AC three-phase asynchronous     vector control     speed segment PI control     Matlab simulation
0 引　言

1 船用三相异步电机数学模型

1）忽略空间谐波，设三相绕组对称，在空间互差 $2\pi /3$ 电角度，所产生的磁动势沿气隙按正弦规律分布；

2）忽略磁路饱和，各绕组的自感和互感都恒定；

3）忽略铁心损耗；

4）不考虑频率变化和温度变化对绕组电阻的影响。

 $\left[ {\begin{array}{*{20}{l}}{{\psi _{{{sd}}}}}\\{{\psi _{{{sq}}}}}\\{{\psi _{{{rd}}}}}\\{{\psi _{{{rq}}}}}\end{array}} \right] = \left[ {\begin{array}{*{20}{l}}{{L_{{s}}}}&0&{{L_{{m}}}}&0\\0&{{L_{{s}}}}&0&{{L_{{m}}}}\\{{L_{{m}}}}&0&{{L_{{r}}}}&0\\0&{{L_{{m}}}}&0&{{L_{{r}}}}\end{array}} \right]\left[ {\begin{array}{*{20}{l}}{{i_{{{sd}}}}}\\{{i_{{{sq}}}}}\\{{i_{{{rd}}}}}\\{{i_{{{rq}}}}}\end{array}} \right]\text{，}$ (1)

 $\begin{split}\left[ {\begin{array}{*{20}{l}} {{u_{{{sd}}}}}\\{{u_{{{sq}}}}}\\{{u_{{{rd}}}}}\\{{u_{{{rq}}}}}\end{array}} \right] \!= &\!\! \left[ {\begin{array}{*{20}{l}}{{R_{{s}}} + {L_{{s}}}p}\!\!&\!\!{ - {\omega _1}{L_{{s}}}}\!\!&\!\!{{L_{{m}}}p}\!\!&\!\!{ - {\omega _1}{L_{{m}}}}\\{{\omega _1}{L_{{s}}}}\!\!&\!\!{{R_{{s}}} + {L_{{s}}}p}\!\!&\!\!{{\omega _1}{L_{{m}}}}\!\!&\!\!{{L_{{m}}}p}\\{{L_{{m}}}p}\!\!&\!\!{ - {\omega _{{s}}}{L_{{m}}}}\!\!&\!\!{{R_{{r}}} + {L_{{r}}}p}\!\!&\!\!{ - {\omega _{{s}}}{L_{{r}}}}\\{{\omega _{{s}}}{L_{{m}}}}\!\!&\!\!{{L_{{m}}}p}\!\!&\!\!{{\omega _{{s}}}{L_{{r}}}}\!\!&\!\!{{R_{{r}}} + {L_{{r}}}p}\end{array}} \right] \left[ {\begin{array}{*{20}{l}}{{i_{{{sd}}}}}\\{{i_{{{sq}}}}}\\{{i_{{{rd}}}}}\\{{i_{{{rq}}}}}\end{array}} \right]\text{，}\end{split}$ (2)

 ${T_{{e}}} = {n_p}{L_{{m}}}\left( {{i_{{{sq}}}}{i_{{{rd}}}} - {i_{{{sd}}}}{i_{{{rq}}}}} \right)\text{，}$ (3)

 $p\omega = \frac{{{n_p}}}{J}({T_e} - T{}_L)\text{。}$ (4)

 ${T_e} = {n_p}{L_m}({i_{sq}}{i_{rd}} - {i_{sd}}{i_{rq}}) = {n_p}{L_m}{i_{sq}}{i_r} = {n_p}\frac{{{L_m}}}{{{L_r}}}{\psi _r}{i_{sq}}\text{，}$ (5)

 $\begin{split}\left[ {\begin{array}{*{20}{l}}{{u_{sd}}}\\{{u_{sq}}}\\0\\0\end{array}} \right] \!= &\!\! \left[ {\begin{array}{*{20}{l}}{{R_s} + {L_s}p}\!\!&\!\!{ - {\omega _1}{L_s}}\!\!&\!\!{{L_m}p}\!\!&\!\!{ - {\omega _1}{L_m}}\\{{\omega _1}{L_s}}\!\!&\!\!{{R_s} + {L_s}p}\!\!&\!\!{{\omega _1}{L_m}}\!\!&\!\!{{L_m}p}\\{{L_m}p}\!\!&\!\!0\!\!&\!\!{{R_r} + {L_r}p}\!\!&\!\!0\\{{\omega _s}{L_m}}\!\!&\!\!0\!\!&\!\!{{\omega _s}{L_r}}\!\!&\!\!{{R_r} + {L_r}p}\end{array}} \right]\left[ {\begin{array}{*{20}{l}}{{i_{sd}}}\\{{i_{sq}}}\\{{i_{rd}}}\\{{i_{rq}}}\end{array}} \right]\text{，}\end{split}$ (6)

 ${i_{sd}} = \frac{{{T_r}p + 1}}{{{L_m}}}{\psi _r}\text{，}$ (7)
 ${\omega _1} - \omega = {\omega _s} = \frac{{{L_m}}}{{{T_r}{\psi _r}}}{i_{sq}}\text{。}$ (8)

 ${T_e} = {n_p}\frac{{{L_m}}}{{{L_r}}}{\psi _r}{i_{sq}}\text{，}$ (9)
 ${\psi _r} = \frac{{{L_m}}}{{{T_r}p + 1}}{i_{sd}}\text{，}$ (10)
 $\phi = \int_0^t {({n_p}{\omega _r} + \frac{{L{}_m{i_{sd}}}}{{{T_r}{\psi _r}}})} {\rm d}t\text{。}$ (11)
 图 1 三相异步电机矢量控制结构框图 Fig. 1 Block diagram of vector control for three phase asynchronous motor
2 转速分段PI调节器设计

 $T_e^* = {K_p}(\omega _{ref}^* - {\omega _r}) + {K_i}\int {(\omega _{ref}^* - {\omega _r})} {\rm d}t\text{。}$ (12)

 ${W_s} = \frac{{{k_p}(\tau s + 1)}}{{J\tau {s^2}(T{}_{sum}s + 1)}}\text{，}$ (13)

 ${K_p} = \frac{{J(h + 1)}}{{2h{T_{sum}}}}\text{。}$ (14)
 图 2 电机转速PI闭环控制框图 Fig. 2 Block diagram of motor speed PI closed loop control

 图 3 转速差值 ${\omega _s}$ 变化曲线 Fig. 3 Difference-time curve of speed

 图 4 转速分段PI调节器模块 Fig. 4 Regulator module of speed segment PI
3 船用三相异步电机控制模块的建立 3.1 矢量控制仿真模块

 图 5 矢量控制模块 Fig. 5 Module of Vector control
3.2 Park变换模块

Park变换模块实现静止坐标系定子三相参考相电流 ${i_{abc}}$ d-q旋转坐标系两相参考相电流 ${i_{dq}}$ 的转换。

 $\left[ {\begin{array}{*{20}{l}} {{i_d}}\\ {{i_q}}\\ {{i_0}} \end{array}} \right] = {\rm{ }}\frac{2}{3}\left[ {\begin{array}{*{20}{c}} {\cos \theta }&{\cos \left( {\theta - 120{\rm{^\circ }}} \right)}&{\cos \left( {\theta + 120{\rm{^\circ }}} \right)}\\ { - \sin \theta }&{ - \sin \left( {\theta - 120{\rm{^\circ }}} \right)}&{ - \sin \left( {\theta + 120{\rm{^\circ }}} \right)}\\ {1/2}&{1/2}&{1/2} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{i_a}}\\ {{i_b}}\\ {{i_c}} \end{array}} \right]$ (15)

 图 6 3s/2r模块 Fig. 6 Module of 3s/2r
3.3 电流滞环跟随模块

 图 7 PWM电流滞环模型 Fig. 7 Model of PWM current hysteresis loop
4 仿真结果分析

 图 8 三相异步电机矢量控制系统仿真模型 Fig. 8 Vector control simulation model of three phase asynchronous motor

 图 9 突加60 N·m负载时转速曲线 Fig. 9 Speed-time curve of 60 N·m sudden load