﻿ 内模控制及逆系统算法在船舶运动控制中的仿真研究
 舰船科学技术  2016, Vol. 38 Issue (11): 111-115, 119 PDF

Research on internal model control and inverse system theory in the simulation of ship motion control
LIU Yun
Automation College, Guangdong University of Technology, Guangzhou 510006, China
Abstract: We proposed an internal model control based on the inverse system theory to solve the ship movement problems such as multivariable coupling, linearity, hysteresis, limiting and so on It uses the inverse system theory to change the ship's non-linear model into linear pseudomode and uses the internal model to control the linear pseudomode. At the same time, we also proposed the method which combine the internal model control with other control strategies such as PID. The simulation results show the internal model control is not only highly efficient control, but also has a high precision, the robustness is good and it is very convenience to alter the parameter.
Key words: vessels     internal model control     inverse system     nonlinear
0 引言

1 船舶运动的非线性模型

 图 1 船舶运动坐标系 Fig. 1 Vessels moving coordinate system

 $\dot \eta = \boldsymbol{R}(\psi )\nu {\rm{, }}$ (1)

 $\left\{ {\begin{array}{*{20}{l}} {u = \dot y\sin \phi + \dot x\cos \phi }\text{，}\\ {v = \dot y\cos \phi - \dot x\sin \phi }\text{，}\\ {r = \dot \phi }\text{，} \end{array}} \right.$

 $\boldsymbol{R}(\psi ) = \left[{\begin{array}{*{20}{c}} {\cos \psi }&{-\sin \psi }&0\\ {\sin \psi }&{\cos \psi }&0\\ 0&0&1 \end{array}} \right]{\rm{.}}$ (3)

 $\boldsymbol{M}\dot v + \boldsymbol{D}v = \tau + {R^{\rm{T}}}\left( \psi \right)b.$ (4)

 $\begin{array}{l} \boldsymbol{M} = \left[{\begin{array}{*{20}{c}} {m-{X_{\dot u}}}&0&0\\ 0&{m-{Y_{\dot \nu }}}&{m{x_g}-{Y_{\dot r}}}\\ 0&{m{x_g} - {N_{\dot \nu }}}&{{I_z} - {N_{\dot r}}} \end{array}} \right], \\ \boldsymbol{D} = \left[{\begin{array}{*{20}{c}} {-{X_u}}&0&0\\ 0&{-{Y_\nu }}&{-{Y_r}}\\ 0&{ - {N_\nu }}&{ - {N_r}} \end{array}} \right]{\rm{, }} \end{array}$ (5)
 $\tau = {\tau _e} + {\tau _c}{\rm{, }}$ (6)
 ${\boldsymbol{\tau _e}} = \left[{\begin{array}{*{20}{c}} {{X_e}}\\ {{Y_e}}\\ {{N_e}} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} {{X_{wind}} + {X_{wave}} + {X_{current}}}\\ {{Y_{wind}} + {Y_{wave}} + {Y_{current}}}\\ {{N_{wind}} + {N_{wave}} + {N_{current}}} \end{array}} \right].$ (7)

2 基于逆系统方法的内模控制设计 2.1 内模控制原理及结构

 $\frac{{Y(s)}}{{R(s)}} = \frac{{{G_{IMC}}(s) \cdot {G_p}(s)}}{{1 + {G_{IMC}}(s) \cdot [{G_P}(s)-{{\hat G}_p}(s)]}}{\rm{, }}$ (8)
 ${G_{IMC}}(s) = \frac{1}{{{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over G} }_P}(s)}}f\left( s \right).$ (12)
 图 2 IMC结构框图 Fig. 2 IMC structure diagram

 $\begin{array}{l} Y(s) = \frac{{{G_{IMC}}(s) \cdot {G_p}(s)}}{{1 + {G_{IMC}}(s) \cdot [{G_P}(s)-{{\hat G}_p}(s)]}} \cdot R(s) + \\ \;\;\;\;\;\;\;\;\;\;\frac{{1 - {G_{IMC}}(s) \cdot {{\hat G}_p}(s)}}{{1 + {G_{IMC}}(s) \cdot [{G_P}(s)-{{\hat G}_p}(s)]}} \cdot D(s){\rm{;}} \end{array}$ (10)

 $\hat D(s) = [{G_P}(s)-{{\hat G}_p}(s)] \cdot U(s) + D(s){\rm{.}}$ (11)

2.2 内模控制器设计

 ${G_{IMC}}(s) = \frac{1}{{{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over G} }_p} - (s)}}f(s).$ (12)

1）确定被控模型${{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over G} }_p}$

2）考虑有无滞后环节

3）滤波器设计

2.3 非线性系统控制器设计

 图 3 基于α阶逆系统的解耦线性化及α阶伪线性系统 Fig. 3 Based on the α-integral inverse system decoupling linearization and α-integral pseudo-linear system

 图 4 伪线性系统下内模控制 Fig. 4 Internal model control under the pseudo-linear system

3 仿真实验及结果分析 3.1 仿真对象

 $\left\{ {\begin{array}{*{20}{l}} {(m - {X_{\dot u}}) \cdot \dot u - {X_u} \cdot u \cdot \left| u \right| = {F_u}{\rm{, }}}\\ {\begin{array}{*{20}{l}} {(m - {Y_{\dot v}})\dot v - {Y_v} \cdot {v^3} + [(m \cdot {X_g}-{Y_{\dot r}})\dot r{\rm{, }}}\\ {-{Y_r} \cdot r] \cdot {\rm{sgn}}(v) = {F_v}{\rm{, }}} \end{array}}\\ {({I_z} - {N_{\dot r}})\dot r - {N_r} \cdot r = {F_r}{\rm{, }}} \end{array}} \right.$ (13)

3.2 仿真参数

 $\begin{array}{*{20}{l}} {m - {X_{\dot u}} = 223.7, \;{X_u} = - 46.4, \;m - {Y_{\dot v}} = 90, }\\ {{Y_v} = - 450, \;m \cdot {X_g} - {Y_{\dot r}} = 75, \;{Y_r} = - 40, }\\ {{I_z} - {N_{\dot r}} = 150, \;{N_r} = - 45.} \end{array}$ (14)
3.3 有无逆系统控制效果对比

 图 5 引入逆系统系统响应 Fig. 5 Response of Introducing the inverse system

 图 6 无逆系统系统响应 Fig. 6 Response without the inverse system

3.4 控制器限幅下船舶运动仿真

 图 7 有限幅环节系统响应 Fig. 7 Response of controlled variable limitation

 图 8 限幅前控制器力的输出 Fig. 8 The force before control limitation

 图 9 限福后控制器力的输出 Fig. 9 The force after control limitation

3.5 引入其他控制方法仿真效果对比

PID控制器由于用途广泛、使用灵活。本文考虑在控制中引入PID控制[12]。船舶纵向运动双环控制均采用PID控制响应如图 10所示，内环控制采用PID控制且外环采用内模控制后响应如图 11所示。

 图 10 双环pid响应仿真图 Fig. 10 Response of double-loop PID

 图 11 内环pid外环内模系统响应仿真图 Fig. 11 Response of PID and IMC

 图 12 限福后控制器力的输出 Fig. 12 The force after control limitation

3.6 船舶运动仿真效果

 图 13 基于逆系统和内模算法的动力定位控制器响应仿真图 Fig. 13 Response of controller based on inverse system and IMC
4 结语

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