﻿ 基于滑模控制的船舶电力推进调速系统仿真
 舰船科学技术  2018, Vol. 40 Issue (1): 104-107 PDF

Propulsion control system simulation based sliding mode control of ship electric
GAO Jian, WU Xiang-rui
School of Electrical and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: Ship electric propulsion, propulsion motor is to convert electrical energy into mechanical energy of the core element. With the increasing development of science and technology, high-power permanent magnet synchronous motor has been widely used in electric propulsion systems. Due to ship large disturbance outside the system, will restructure some AC drive system have a great impact. Variable structure control by a small external disturbance factors, rapid response, this paper is applied to the synovial VSC AC drive system, the establishment of ship propulsion AC speed control system simulation model. Structure simulation showed that synovial variable structure control AC speed, can accelerate the time of permanent magnet synchronous motor, while reducing the external disturbance influence on the governor, and to meet the marine power motors in dynamic torque response requirements.
Key words: electric propulsion     PMSM     vector control     sliding mode control
0 引　言

1 永磁同步电机数学模型

1）假设转子的永磁场在空间上的分布为正弦波；

2）忽略定子铁心的饱和，将磁路作线性处理，电感参数保持不变；

3）不计铁心涡流和磁滞损耗；

4）转子上没有阻尼绕组。

 $\left[ \begin{array}{l}{u_d}\\{u_q}\end{array} \right] = \left[ {\begin{array}{*{20}{c}}{{R_s} + {L_d}p} & { - {\omega _e}{L_q}}\\{{\omega _e}{L_d}} & {{R_s} + {L_q}p}\end{array}} \right]\left[ \begin{array}{l}{i_d}\\{i_q}\end{array} \right] + {\omega _e}\left[ \begin{array}{l}0\\{\psi _r}\end{array} \right],$ (1)

 ${T_e} = \frac{3}{2}{n_p}[{\psi _r}{i_q} + ({L_d} - {L_q}){i_d}{i_q}],$ (2)

 ${T_e} = \frac{3}{2}{n_p}{\psi _r}{i_q}{\text{。}}$ (3)

 ${T_e} - {T_L} - B\omega = J\frac{{{\rm d}{\omega _m}}}{{{\rm d}t}}\text{。}$ (4)

2 控制器的设计 2.1 滑模面的设计

 $\left\{ \begin{array}{l}{\omega _1} = {\omega ^*} - \omega, \\{\omega _2} = \int_0^t {\omega _1}{\rm d}t =\int_0^t ({\omega ^*} - \omega ){\rm d}t{\text{。}}\end{array} \right.$ (5)

 $L = \int_{- \infty}^0 {\omega _2}{\rm d}t = - {\omega _2}(0),$ (6)

 $s(t) = {\omega _1} + c\int_0^t {\omega _1}{\rm d}t + L{\text{。}}$ (7)

t=0时，s=0，即系统开始在滑模面运动。

2.2 控制率的求取

 ${s'} = {\omega _1}' + c{\omega _1} = - \frac{{3{n_p}{\psi _r}}}{{2J}}{i_q} + \frac{B}{J}\omega + \frac{1}{J}{T_L} + c{\omega _1}{\text{。}}$ (8)

 ${s'} = - \varepsilon \left| {{\omega _1}} \right|{\mathop{\rm sgn}} (s) - ks\text{。}$ (9)

 $\frac{{3{n_p}{\psi _r}}}{{2J}}{i_q} - {\rm{c}}{\omega _{\rm{1}}} = \varepsilon \left| {{\omega _1}} \right|{\mathop{\rm sgn}} (s) + ks + \frac{B}{J}\omega + \frac{1}{J}{T_L},$ (10)

 ${i_q} = \frac{{2J}}{{3{n_p}{\psi _r}}}\left[ {\varepsilon \left| {{\omega _1}} \right|{\mathop{\rm sgn}} (s) + ks + \frac{B}{J}\omega + \frac{1}{J}{T_L} + c{\omega _1}} \right],$ (11)

 ${U_{smc}} = {i_q} = \frac{{2J}}{{3{n_p}{\psi _r}}}\left[ \begin{array}{l}\varepsilon \left| {{\omega _1}} \right|{\mathop{\rm sgn}} (s) + ks + \displaystyle\frac{B}{J}\omega \\ + \displaystyle\frac{1}{J}{T_L} + c{\omega _1}\end{array} \right]\text{。}$ (12)

2.3 稳定性分析

 $\mathop {\lim }\limits_{s \to 0} s{s'} < 0{\text{。}}$ (13)

 $\begin{split}{V'} = &s{s'}=\\ &s[ - \varepsilon \left| {{\omega _1}} \right|{\mathop{\rm sgn}} (s) - ks]=\\ & - \varepsilon \left| {{\omega _1}} \right|s \cdot {\mathop{\rm sgn}} (s) - k{s^2}=\\ & - \varepsilon \left| {{\omega _1}} \right| \cdot \left| s \right| - k{s^2} < 0{\text{。}}\end{split}$ (14)

3 仿真研究

 图 1 PMSM矢量控制系统 Fig. 1 PMSM servo control systerm

1）忽略负载转矩。如图2所示，常规滑模控制响应迅速，但有大约11.5 r/min的超调。图3中，本文设计的的积分变指数滑模控制响应最快，且无超调。

 图 2 常规滑模控制 Fig. 2 Conventional sliding mode control

 图 3 积分变指数滑模控制 Fig. 3 Integral variable index sliding mode control

2）突增10 N·m负载。如图4所示，常规滑模控制存在10 r/min左右的扰动，并经过大约0.03 s恢复到稳态值，且超调一直存在，滑模抖振较大。图5中，本文设计的积分变指数滑模控制，扰动只有3 r/min，在0.01 s内快速恢复到稳定状态。

 图 4 常规滑模控制 Fig. 4 Conventionalsliding mode control

 图 5 积分变指数滑模控制 Fig. 5 Integral variable index sliding mode control

3）突卸10 N·m负载。如图6所示，常规滑模控制存在5 r/min左右的扰动，在大约0.03 s恢复稳定。图7中，本文设计的积分变指数滑模控制，扰动有5 r/min，在0.01 s内快速恢复到稳定状态。

 图 6 常规滑模控制 Fig. 6 Conventional sliding mode control

 图 7 积分变指数滑模控制 Fig. 7 Integral variable index sliding mode control

4 结　语

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