﻿ 基于分数阶PI<sup><i>λ</i></sup>D<sup><i>μ</i></sup>的船舶航向控制
 舰船科学技术  2016, Vol. 38 Issue (5): 87-90 PDF

1. 海军驻大连426厂军事代表室, 辽宁 大连 116000 ;
2. 东部战区海军装备部信息系统处, 浙江 舟山 316000 ;
3. 中国船舶重工集团公司第七〇七研究所 九江分部, 江西 九江 332007

Marine course control based on fractional-order PIλDμ
ZHANG An-ming1, SUN Jie2, HUANG Jing3, LIU Jian3
1. The Navy Representative Office in No. 426 Shipyard, Dalian 116000, China ;
2. Eastern Theater Naval Armaments Department Information Systems Branch, Zhoushan 316000, China ;
3. Jiujiang Branch of the 707 Research Institute of CSIC, Jiujiang 332007, China
Abstract: The sailing marine vehicles are disturbed by the wind, wave and current on the ocean, which cause the model parameters' uncertainty for ship motion in different sailing velocity. In this paper, the body of ship and the disturbances of wind, wave and ocean are modeled, and a course control algorithm based on Fractional-Order PIλDμ (FOPID) to restrain the disturbance of wind and wave is proposed. The comparing numerical simulation for the dynamic model of some ship is carried out by the sea state of the 6 wind degree and 5 wave degreecompared with the conventional PID control algorithm. The numerical simulation result shows that, the algorithm proposed guarantee pretty nice control quality and robustness for different sailing speeds, and is adaptive to the disturbance of wind and wave, which can be applied to the course control of ship, and is not complicated to apply in engineering.
Key words: ship modeling     course control     fractional-order PIλDμ
0 引言

1 船舶运动模型

 ${T_1}{T_2}\ddot r + ({T_1} + {T_2})\dot r + r = K\delta + K{T_S}\dot \delta .$ (1)

 $T\dot r + r = K\delta ,$ (2)
 $T = {T_1} + {T_2} + {T_3} .$ (3)

 图 1 航速 15 kn 下艏摇运动的 Bode 图 Fig. 1 The yawing Bode diagram for velocity of 15 knots

 图 2 航速 24 kn 下艏摇运动的 Bode 图 Fig. 2 The yawing Bode diagram for velocity of 24 knots

 图 3 舵液压执行机构模型简化方框图 Fig. 3 The simplified block diagram of rudder hydraulic actuator

 $\frac{\alpha }{{{\alpha _d}}} = \frac{1}{{s + 1}} ,$ (4)

 ${N_{\omega d}} = \frac{1}{2}{\rho _a}g{({V_a} + {V_T})^2}L{C_{n\omega }}({\mu _{\omega d}}){A_L} ,$ (5)

 $\begin{array}{l} N = \displaystyle \sum\limits_{i = 1}^n {{k_1}{R_1}} \left[{\frac{{B_m^2\sin {R_2}({R_3}\cos {R_3} - \sin {R_3})}}{{R_3^2}} - } \right.\\ \left. {\displaystyle \frac{{{L_2}\sin {R_3}({R_2}\cos {R_2} - \sin {R_2})}}{{R_2^2}}} \right]{\varsigma _{ai}}\cos ({\omega _{ei}}t + {\varepsilon _{ni}}). \end{array}$ (6)

 ${R_1} =\displaystyle \frac{{\rho g(1 - {e^{ - {k_1}{d_m}}})}}{{{k_1}}},$
 ${R_2} = \displaystyle \frac{{{k_1}L}}{2}\cos {\mu _e},$
 ${R_3} = \displaystyle \frac{{{k_1}{B_m}}}{2}\sin {\mu _e}.$

 ${N_{cd}} = \frac{1}{2}\rho gV_{cd}^2L{C_{nc}}({\mu _{cd}}){A_{Ls}}.$ (7)

2 分数阶 PID 控制器设计方法

 $_aD_t^\alpha = \left\{ {\matrix{ {{{{{\rm{d}}^\alpha }} \over {{\rm{d}}{t^\alpha }}},} & {Re(\alpha ) > 0,} \cr {1,} & {Re(\alpha ) = 0,} \cr {\int\limits_a^t {{{({\rm{d}}\tau )}^{ - \alpha }}} ,} & {Re(\alpha ).} \cr } } \right.$ (8)

 $_{{t_0}}^CD_t^\alpha f(t){ = _{{t_0}}}D_t^{ - (n - \alpha )}[\frac{{{{\rm d}^n}}}{{{\rm d}{t^n}}}f(t)],$ (9)

 $L{\{ _0}D_t^pf(t);s\} = {s^p}F(s) - \sum\limits_{k = 0}^{n - 1} {{s^k}{{{[_0}D_t^{p - k - 1}f(t)]}_{t = 0}}} ,$ (10)

 $u(t) = {K_p}e(t) + \sum\limits_{i = 1}^k {{K_{Di}}D_{ti}^\mu e(t) + \sum\limits_{j = 1}^n {{K_{Ij}}D_{tj}^{ - \lambda }e(t)} } ,$ (11)

 ${G_c}(s) = {K_p} + \sum\limits_{i = 1}^k {{K_{Di}}{s^\mu } + \sum\limits_{j = 1}^n {{K_{Ij}}{s^{ - \lambda }}} } .$ (12)
3 分数阶 PID 控制器设计

 图 4 航速 15 kn 下闭环系统 Bode 图 Fig. 4 The Bode diagram of closed loop system for velocity of 15 knots

 图 5 航速 24 kn 下艏摇运动的 Bode 图 Fig. 5 The Bode diagram of closed loop system for velocity of 24 knots

4 仿真试验与数据分析

 图 6 航速 15 kn 下航向保持回路仿真响应曲线图 Fig. 6 The simulating response curves of heading-hold loop for velocity of 15 knots

 图 7 航速 24 kn 下航向保持回路仿真响应曲线图 Fig. 7 The simulating response curves of heading-hold loop for velocity of 24 knots

 图 8 航速 15 kn 下舵角输入曲线图 Fig. 8 The rudder input curves for velocity of 15 knots

 图 9 航速 24 kn 下舵角输入曲线图 Fig. 9 The rudder input curves for velocity of 24 knots
5 结语

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