﻿ 基于滑模变结构的船用永磁同步电机直接转矩控制
 舰船科学技术  2017, Vol. 39 Issue (10): 88-91 PDF

1. 江苏科技大学 电子信息学院，江苏 镇江 212003;
2. 江苏吉意信息技术有限公司，江苏 镇江 212003

Direct torque control of permanent magnet synchronous motor for ship based on sliding mode variable structure
GAO Chuan1, FENG You-bing1, CHEN Kun-hua2
1. School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. Jiangsu Ji -Yi Information Technology Co., Ltd. Zhenjiang 212003, China
Abstract: The electric propulsion is used more and more in the ship power system. The simulation of direct torque control of permanent magnet synchronous motor is studied in this paper. The sliding mode variable structure control (SMC) strategy is introduced to solve the problems of large flux and torque ripple in direct torque control of permanent magnet synchronous motor (PMSM). Design two sliding mode controllers of torque and flux linkage to replace the two hysteresis comparators in the conventional direct torque control, and then use the space vector pulse width modulation (SVPWM) to control motor operation. The simulation results show that this control strategy can effectively reduce the existing flux and torque ripple in the conventional direct torque control and keep the inverter switching frequency be constant, and it is strongly robust to system parameter variations and external disturbance.
Key words: permanent magnet synchronous motor     sliding mode variable structure control     direct torque control     space vector pulse width modulation
0 引　言

1 永磁同步电机数学模型

 $\left[ \begin{array}{l}{u_d}\\{u_q}\end{array} \right] = \left[ \begin{array}{l}R + p{L_{d\;}}\;\;\;\;\;\; - {\omega _r}{L_q}\;\\\;\;{\omega _r}{L_d}\;\;\;\;\;\;\;R + p{L_d}\end{array} \right]\left[ \begin{array}{l}{i_d}\\{i_q}\end{array} \right] + \left[ \begin{array}{l}\;\;\;0\\{\omega _r}{\psi _f}\end{array} \right],$ (1)

 $\begin{split}\left[ \begin{array}{l}{u_\alpha }\\{u_\beta }\end{array} \right] = & \left[ \begin{array}{l}R + p{L_d}\;\;\;\;\;\;\;\;\;\;{\omega _r}({L_d} - {L_q})\\ - {\omega _r}({L_d} - {L_q})\;\;\;\;R + p{L_d}\end{array} \right]\left[ \begin{array}{l}{i_\alpha }\\{i_\beta }\end{array} \right] +\\ &\left[ {({L_d} - {L_q})({\omega _r}{i_d} - {{\dot i}_q}) + {\omega _r}{\psi _f}} \right]\;\left[ \begin{array}{l} - \sin {\theta _r}\\\;\cos {\theta _r}\end{array} \right]{\text{。}}\end{split}$ (2)

 $\left[ \begin{array}{l}{e_\alpha }\\{e_\beta }\end{array} \right] = \left[ {({L_d} - {L_q})({\omega _r}{i_d} - {{\dot i}_q}) + {\omega _r}{\psi _f}} \right]\;\left[ \begin{array}{l} - \sin {\theta _r}\\\;\cos {\theta _r}\end{array} \right]{\text{。}}$ (3)

 $\begin{split}\left[ \begin{array}{l}{{\dot i}_\alpha }\\{{\dot i}_\beta }\end{array} \right] = & \left[ \begin{array}{l} - R/{L_d}\;\;\;\;\;\;\;\;\;\;\;\; - {\omega _r}({L_d} - {L_q})/{L_d}\\{\omega _r}({L_d} - {L_q})/{L_d}\;\;\;\;\; - R/{L_d}\end{array} \right]\left[ \begin{array}{l}{i_\alpha }\\{i_\beta }\end{array} \right] - \\ &\left[ \begin{array}{l}1/{L_d}\;\;\;0\\0\;\;\;\;\;\;\;1/{L_d}\end{array} \right]\;\left[ \begin{array}{l}{e_\alpha }\\{e_\beta }\end{array} \right] + \frac{1}{{{L_d}}}\left[ \begin{array}{l}{u_\alpha }\\{u_\beta }\end{array} \right]{\text{。}}\end{split}$ (4)

α-β坐标系下定子磁链方程为：

 $\left\{ \begin{array}{l}{{\dot \psi }_\alpha } = {u_\alpha } - R{i_\alpha },\\{{\dot \psi }_\beta } = {u_\beta } - R{i_\beta }{\text{。}}\end{array} \right.$ (5)

 $T = \frac{{3{p_n}}}{2}({\psi _\alpha }{i_\beta } - {\psi _\beta }{i_\alpha }),$ (6)

 $\psi = \psi _\alpha ^2 + \psi _\beta ^2{\text{。}}$ (7)
2 滑模控制器设计 2.1 确定切换函数

 ${S} = {\left[ {{S_T}\;{S_\psi }} \right]^{\rm T}},$ (8)
 $\left\{ \begin{array}{l}{S_T} = {k_{p{\rm{1}}}}{e_T} + {k_{i{\rm{1}}}}\int_0^t {{e_T}{\rm d}t}, \\[5pt]{S_\psi } = {k_{p{\rm{2}}}}{e_\psi } + {k_{i{\rm{2}}}}\int_0^t {{e_\psi }{\rm d}t}{\text{。}} \end{array} \right.$ (9)

2.2 滑动模态控制率

 $\dot{ S} = {\left[ {{{\dot S}_T}\;{{\dot S}_\psi }} \right]^{\rm T}} = {F} + {DU},$ (10)

 $\left\{ \begin{array}{l}{{\dot S}_T} = {k_{p1}}{{\dot e}_T} + {k_{i1}}{e_T},\\{{\dot S}_\psi } = {k_{p{\rm{2}}}}{{\dot e}_\psi } + {k_{i{\rm{2}}}}{e_\psi }{\text{。}}\end{array} \right.$ (11)
 ${F} = {\left[ {{F_1}\;{F_2}} \right]^{\rm T}}$ (12)
 $\left\{ \begin{split}\!\!\!\!& {F_1} = - \displaystyle\frac{3}{2}{k_{p1}}{p_n}{\rm{\{ }}[{\omega _r}({L_d} - {L_q}){\psi _\alpha }{i_\alpha } - R{\psi _\alpha }{i_\beta } - \\[3pt]& \quad\quad{\psi _\alpha }{e_\beta }]/{L_d} + [{\omega _r}({L_d} \!-\! {L_q}){\psi _\beta }{i_\beta } \!+\! R{\psi _\beta }{i_\alpha } \!+\\[3pt] & \quad\quad{\psi _\beta }{e_\alpha }]/{L_d}{\rm{\} }} \!+{k_{p1}}{\rm{(}}{T^ * } \!-\! T{\rm{)}},\\\!\!\!\!& {F_2} = 2{k_{p2}}(R{\psi _\alpha }{i_\alpha } + R{\psi _\beta }{i_\beta }) + {k_{i2}}({\psi ^ * } - \psi ){\text{。}}\end{split} \right.$ (13)
 ${U} = {\left[ {{u_\alpha }\;{u_\beta }} \right]^{\rm T}},$ (14)
 ${D} = - \left[ \begin{array}{l}\displaystyle\frac{3}{2}{p_n}({i_\beta } - {\psi _\beta }/{L_d})\;\;\;\displaystyle\frac{3}{2}{p_n}({\psi _\alpha }/{L_d} - {i_\alpha })\\\;\;\;\;\;\;\;\;\;\;\;{\rm{2}}{\psi _\alpha }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{2}}{\psi _\beta }\end{array} \right]{\text{。}}$ (15)
2.3 系统稳定性

 $V = \frac{1}{2}{{S}^{\rm T}}{S},$ (16)

 $\dot V = {{S}^{\rm T}}\dot{ S} = {{S}^{\rm T}}({F} + {DU}),$ (17)

 ${U} = - {{D}^{ - 1}}\left[ \begin{array}{l}{F_1} + \;{K_1}{S_T} + \;{K_2}sign({S_T})\\{F_2} + {K_3}{S_\psi } + {K_4}sign({S_\psi })\end{array} \right],$ (18)

 $\begin{split}\dot V = & - {S_T}\left[ {{K_1}{S_T} + {K_2}sign({S_T})} \right] - \\ &{S_\psi }\left[ {{K_3}{S_\psi } + {K_4}sign({S_\psi })} \right]{\text{。}}\end{split}$ (19)

2.4 系统鲁棒性

 $\dot{ S} = {F} + {DU} + {H},$ (20)

 $\begin{split}\dot V = & - {S_T}\left[ {{K_1}{S_T} + {K_2}sign({S_T}) - {H_1}} \right] - \\ &{S_\psi }\left[ {{K_3}{S_\psi } + {K_4}sign({S_\psi }) - {H_2}} \right]{\text{。}}\end{split}$ (21)

3 滑模变结构控制系统仿真与分析

 图 1 基于滑模变结构的永磁同步电机直接转矩控制系统框图 Fig. 1 The DTC system block diagram of PMSM based on sliding mode variable structure

 图 2 传统直接转矩控制和基于滑模变结构直接转矩控制下转速曲线 Fig. 2 The speed curve under two control strategies

 图 3 传统直接转矩控制和基于滑模变结构直接转矩控制下转矩曲线 Fig. 3 The torque curve under two control strategies

 图 4 传统直接转矩控制和基于滑模变结构直接转矩控制下磁链曲线 Fig. 4 The flux linkage curve under two control strategies
4 结　语

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