﻿ 基于快速终端滑模自抗扰的船舶曲线航迹跟踪控制
 舰船科学技术  2016, Vol. 38 Issue (8): 57-61 PDF

Active disturbance rejection control for curve-path tracking of ship based fast terminal sliding mode
QIN Chao-yu, LI Wei, NING Jun, SUN Jian
Navigation College, Dalian Maritime University, Dalian 116026, China
Abstract: This paper adopts extended states observer in active disturbance rejection controller to estimate and compensate the internal and external disturbances in real time, which is specific to curve-path tracking problem of underactuated surface vessel. Nonsingular fast terminal sliding mode combined with power exponential reaching law are introduced to nonsingular state error feedback to design FTSM-ADRC control law, which improve the convergence speed and steady-state tracking accuracy of the system and reduce the chattering. Finally, designing a dimension reduction equation, the complicated path following is changed to the simple heading stabilization. Simulation results verify that the controller can follow an expected curve-path fast and accurately, and with good effect.
Key words: underactuated vessel     power exponential reaching law     fast terminal sliding mode     active disturbance rejection control     curve-path tracking
0 引言

1 船舶运动数学模型

 $\left\{ \begin{gathered} \dot x = u\cos \varphi -v\sin \varphi\text{，} \\ \dot y = u\sin \varphi + v\cos \varphi\text{，} \\ \dot \varphi = r \text{，} \\ \dot r = f(r) + \omega (t) + b\delta\text{。} \\ \end{gathered} \right.$ (1)

 $\dot \delta = {K_E}({\delta _r}-\delta )/{T_E}\text{。}$

2 FTSM-ADRC控制器设计 2.1 自抗扰控制结构和算法

 $\left\{ \begin{gathered} {\sigma _1}(k + 1) = {\sigma _1}(k) + h{\sigma _2}(k)\text{，} \\ {\sigma _2}(k + 1) = {\sigma _2}(k) + hfh \text{，} \\ fh = fhan({\sigma _1}(k)-\sigma (k),{\sigma _2}(k),r,h)\text{。} \\ \end{gathered} \right.$ (2)

 \left\{ \begin{aligned} \Delta \dot x = & u\cos \Delta \varphi -v\sin \Delta \varphi \text{，} \\ \Delta \dot y = & u\sin \Delta \varphi + v\cos \Delta \varphi \text{，} \\ \Delta \varphi = & {\varphi _d}(t)-{\varphi _p}(t) \\ {\varphi _d}(t) \!\!= & \!\! -{a_2}\!\!\!\int_0^t {\tanh [\Delta \dot y(\delta ) \!\!+\!\! {a_1}\!\!\tanh ({a_0}\Delta y)]d\delta \!\!+\!\! {\varphi _p}(t)} \text{。} \\ \end{aligned} \right. (13)

4 Simulink仿真

 图 2 横向位置 Fig. 2 Horizontal positions

 图 3 舵角 Fig. 3 Rudder angle

 图 4 船首向角 Fig. 4 Heading angle

 图 5 船位 Fig. 5 Position of vessel

 图 6 船首向角误 Fig. 6 Heading angle error
5 结语

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