﻿ 船用电动伺服舵机性能仿真研究
 舰船科学技术  2016, Vol. 38 Issue (6): 118-121 PDF

Simulation research on shipboard electro-servo rudder actuator performance
XIAO Qing, XIE Jun-chao, HUA Jing
China Ship Development and Design Center, Wuhan 430064, China
Abstract: To reduce the traditional hydraulic steering noise and improve the maintainability of the ships, an electroservo rudder actuator program which mainly includes a DC torque electric motor and a harmonic gear was presented. The model of this actuator was established and the performance was simulated using MATLAB. The main factors which affected the performance of the rudder actuator were analyzed. The simulation results show the performance of this electro-servo rudder actuator can meet the steering requirements of the ship. The research results can be used to support the application of the electro-servo rudder actuator on ships.
Key words: electro-servo     rudder actuator     simulation
0 前 言

1 船用电动舵机方案

 图 1 电动伺服舵机示意图 Fig. 1 Schematic of the electro-servo rudder actuator

 图 2 电动伺服舵机控制框图 Fig. 2 Control diagram of the electro-servo rudder actuator
2 电动舵机性能仿真 2.1 仿真模型 2.1.1 伺服电机模型

 ${U_{{a}}} = R{I_{{a}}} + L\frac{{{\text{d}}{I_{{a}}}}}{{{\text{d}}t}} + E\text{，}$ (1)
 $E = {C_{{e}}}n\text{，}$ (2)
 ${T_{{{em}}}} - {T_{{L}}} = \frac{{G{D^2}{\text{d}}n}}{{375{\text{d}}t}}\text{，}$ (3)
 ${T_{{{em}}}} = {C_{{T}}}{I_{{a}}}\text{。}$ (4)
 图 3 伺服电机等效电路 Fig. 3 Equivalent circuit of the servo electric motor

TlTm 分别表示电气惯性与机械惯性的影响。代入式（1）~ 式（4）整理可得式（5）和式（6）：

 ${U_{{a}}} - E = R({I_{{a}}} + {T_{\text{l}}}\frac{{{\text{d}}{I_{{a}}}}}{{{\text{d}}t}})\text{，}$ (5)
 ${I_{{a}}} - {I_{{{aL}}}} = \frac{{{T_{{m}}}}}{R}\frac{{{\text{d}}E}}{{{\text{d}}t}}\text{，}$ (6)

 ${I_{{{aL}}}} = \frac{{{T_{{L}}}}}{{{C_{{T}}}}}\text{。}$ (7)

 $\frac{{{I_{{a}}}\left( {\text{s}} \right)}}{{U\left( {\text{s}} \right) - E\left( {\text{s}} \right)}} = \frac{{1/R}}{{{T_1}{\text{s}} + 1}}\text{，}$ (8)

 $\frac{{E\left( {\text{s}} \right)}}{{{I_a}\left( {\text{s}} \right) - {I_{{{aL}}}}\left( {\text{s}} \right)}} = \frac{R}{{{T_{{m}}}{\text{s}}}}\text{。}$ (9)

 图 4 伺服电机动态模型 Fig. 4 Dynamic model of the servo electric motor

 图 5 伺服电机简化模型 Fig. 5 Simplified model of the servo electric motor
2.1.2 减速器模型

 图 6 谐波齿轮动态模型 Fig. 6 Dynamic model of the harmonic gear

 ${J_{{a}}} = {{\rm{J}}_{{x}}} + \frac{{{J_1}}}{{j_1^2}} + \frac{{{J_L}}}{{j_L^2}} + m\frac{{{{\rm{v}}^2}}}{{{\rm{\omega }}_{{x}}^2}}\text{。}$ (10)

2.1.3 负载模型

 图 7 负载等效模型 Fig. 7 Load equivalent model
2.2 仿真结果 2.2.1 仿真界面

 图 8 仿真界面 Fig. 8 Simulation interface

2.2.2 仿真结果

 图 9 带负载增益控制下的系统响应 Fig. 9 System response with load under gain control

1）影响系统稳定性的因素主要有阻尼、刚度等参数，在电动伺服舵机中，选用常用的直流力矩电机和谐波齿轮，系统的幅值裕度可达到 5 dB，相位裕度可达到 45°，满足稳定性的条件。

2）对于电动伺服舵机，影响精度的主要因素有伺服电机、谐波齿轮的刚度系数等，当刚度系数越大时，稳态误差越小，精度越高，对于直流力矩电机和谐波齿轮构成的电动伺服舵机，操舵舵角的稳态误差可控制在 0.2°（对应齿条直线位移为 0.2 mm），可满足舵系统这个大惯性系统的操作要求。

3）响应快是电动伺服系统的特点之一，影响其频响的主要因素有电机的电磁时间常数、机电时间常数、转动惯量、谐波齿轮的转动惯量等，根据本系统选择的元件类型，舵机的频响可大于 10 Hz。而负载为大惯性系统，其固有频率小于 1 Hz，因此电动伺服舵机的相应性能可满足操舵的需求。

3 结 语

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