﻿ 基于模型预测静态规划的高速多体船减纵摇控制
 舰船科学技术  2024, Vol. 46 Issue (10): 152-156    DOI: 10.3404/j.issn.1672-7649.2024.10.026 PDF

1. 江苏大学 电气信息工程学院，江苏 镇江 212013;
2. 江苏航空职业技术学院 航空工程学院，江苏 镇江 212134

Anti-pitching control of high-speed multihull based on model predictive static programming
ZHANG Jun1, ZHONG Ming-jie1, YANG Yi-fan2, WEN Hao1
1. School of Electrical Information Engineering, Jiangsu University, Zhenjiang 212013, China;
2. School of Aeronautical Engineering, Jiangsu Aviation Technical College, Zhenjiang 212134, China
Abstract: To solve the problem of vertical stability deterioration of high-speed multihulls under wave disturbance, an anti-pitching control method is proposed based on model prediction static programming. Considering the non-linearity, time-varying parameters, and wave disturbance non-Gaussian characteristics of the multi-hull vertical motion model, a smooth variable structure filter based on noise information and error information is designed, and an on-line estimation of heave velocity and pitch angular is introduced into the anti-pitching control. On this basis, the anti-pitching control of multihulls is proposed based on the model prediction static programming, and the solution method of terminal deviation correction is adopted to iteratively update the control inputs and reduce the computational complexity. Finally, simulation experiments demonstrate the superiority of the proposed method in effectively suppressing excessive heave and pitch motion amplitude, as well as the small computational load of the anti-pitching control.
Key words: high-speed multihull     anti-pitching control     smooth variable structure filter     model predictive static programming
0 引　言

1 高速多体船垂向运动模型

 图 1 有减摇附体的高速多体船示意图 Fig. 1 Schematic diagram of a high-speed multihull with anti-roll appendages

 $\left\{ \begin{array}{l} m(\dot{w}-qu) = 2F_{\text{T - foil}} + F_{\text{flap}} + F_{H} + F_{b}\cos\theta +\\ \qquad\qquad\quad mg\cos\theta+F_{\text{wave}}，\\ I\dot{q}=-2(x_{\text{T - foil}}-x_{\text{G}})F_{\text{T - foil}}-(x_{\text{flap}}-x_{G})\times F_{\text{flap}}-\\ \qquad (x_{H}-x_{G})F_{H}-(x_{b}-x_{G})F_{b}\cos\theta+M_{\text{wave}}。\end{array} \right.$ (1)

2 平滑变结构滤波器

 $\left\{ \begin{split} & \dot {\boldsymbol x} = {\boldsymbol{Ax}} + {\boldsymbol{Bu}} + {\boldsymbol{B}_w}{\boldsymbol d}，\\ & {\boldsymbol y} = {\boldsymbol{Cx}} 。\end{split} \right.$ (2)

 ${{\boldsymbol{K}}_k} = {{\boldsymbol{C}}^ + }{\text{diag}}\left[ {\left( {\left| {{{\boldsymbol{e}}_{k|k - 1}}} \right| + \gamma \left| {{{\boldsymbol{e}}_{k - 1}}} \right|} \right) \circ S} \right]{\text{diag}}{\left( {{{\boldsymbol{e}}_{k|k - 1}}} \right)^{ - 1}}，$ (3)
 $\begin{split} & S=\left[\begin{array}{c}\text{sat}\left({e}_{k|k-1,1}\cdot {\psi }_{11}^{-1}\right)\\ \text{sat}\left({e}_{k|k-1,2}\cdot {\psi }_{22}^{-1}\right)\\ \vdots\\ \text{sat}\left({e}_{k|k-1,{n}_{e}}\cdot {\psi }_{{n}_{e}{n}_{e}}^{-1}\right)\end{array}\right],\\ & \text{sat}\left({e}_{k|k-1,i}\cdot {\psi }_{ii}^{-1}\right)=\left\{\begin{array}{ll} 1,& {e}_{k|k-1,i}\cdot {\psi }_{ii}^{-1}\geqslant 1，\\ {e}_{k|k-1,i}\cdot {\psi }_{ii}^{-1}, &1 > {e}_{k|k-1,i}\cdot {\psi }_{ii}^{-1} > -1\\ -1,& {e}_{k|k-1,i}\cdot {\psi }_{ii}^{-1}\leqslant -1。\end{array} \right. \end{split}$
 ${{\boldsymbol{\hat y}}_{k|k - 1}} = {\boldsymbol{C}}{{\boldsymbol{\hat x}}_{k|k - 1}} \text{，} {{\boldsymbol{\hat y}}_{k|k - 1}} = {\boldsymbol{C}}{{\boldsymbol{\hat x}}_{k|k - 1}} \text{，} {{\boldsymbol{e}}_{k - 1}} = {{\boldsymbol{y}}_{k - 1}} - {{\boldsymbol{\hat y}}_{k - 1}}。$

 $\begin{split} {{\boldsymbol{\bar \psi }}_k} = \,& \left\{ {{\left[ {{\text{diag}}\left( {\left| {{{\boldsymbol{e}}_{k|k - 1}}} \right| + \gamma \left| {{{\boldsymbol{e}}_{k - 1}}} \right|} \right)} \right]}^{ - 1}}{\boldsymbol{C}}{{\boldsymbol{P}}_{k|k - 1}}{{\boldsymbol{C}}^{\text{T}}}\right.\cdot\\ & \left.{{\left( {{\boldsymbol{C}}{{\boldsymbol{P}}_{k|k - 1}}{{\boldsymbol{C}}^{\text{T}}} + {{\boldsymbol{R}}_{{v}}}} \right)}^{ - 1}} \right\}^{ - 1} 。\end{split}$ (4)

 ${{\boldsymbol{\hat x}}_k} = {{\boldsymbol{\hat x}}_{k|k - 1}} + {{\boldsymbol{K}}_k}{{\boldsymbol{e}}_{k|k - 1}} 。$ (5)

 ${{\boldsymbol{P}}_k} = \left[ {{\boldsymbol{I}} - {{\boldsymbol{K}}_k}{\boldsymbol{C}}} \right]{{\boldsymbol{P}}_{k|k - 1}}{\left[ {{\boldsymbol{I}} - {{\boldsymbol{K}}_k}{\boldsymbol{C}}} \right]^{\text{T}}} + {{\boldsymbol{K}}_k}{\boldsymbol{RK}}_k^{\text{T}} 。$ (6)
3 基于模型静态规划的减纵摇控制

 $\begin{gathered} {\text{ }}\mathop {\min }\limits_u J(k) \\ {\mathrm{s}}.{\mathrm{t}}.\left\{ \begin{gathered} \hat x(k + j + 1) = {A_d}\hat x(k + j) + {B_d}u(k + j),{\text{ }}j = 1,{\text{ }}2,{\text{ }}...,N，\\ \hat x{(k + N)^{\mathrm{T}}}P\hat x(k + N) \leqslant {\sigma _{T}}，\\ \end{gathered} \right. \\ \end{gathered}$ (7)
 $\begin{split} J(k) = \;& \frac{1}{2}\sum\limits_{j = 1}^N {{{(y(k + j) - {y^*})}^{\text{T}}}{\boldsymbol{Q}}} (y(k + j) - {y^*}) + \\ & \;\frac{1}{2}\sum\limits_{j = 1}^N {{{(u(k + j))}^{\text{T}}}{\boldsymbol{R}}(u(k + j))}。\end{split}$

 图 4 多体船的升沉曲线 Fig. 4 Heave displacement of multihull

 图 5 多体船的纵摇角曲线 Fig. 5 Pitch angle of multihull

3）不同预测控制策略的减摇性能对比：将本文所提的模型预测静态规划与文献[8]的传统预测控制进行对比，两者的加权矩阵，预测步长选为相同进行仿真，如图6图7所示，可以看出基于模型预测静态规划的高速多体船减摇控制效果明显优于传统的预测控制。

 图 6 多体船的升沉对比 Fig. 6 Comparison of heave motionl

 图 7 多体船的纵摇角对比 Fig. 7 Comparison of pitch motion
5 结　语

1）采用自适应边界层宽度矩阵的平滑变结构滤波器估计升沉速度、纵摇角速度，对多体船模型不确定性、不符合高斯分布的海浪噪声，具有较好的鲁棒性。

2）基于模型预测静态规划的减纵摇控制策略，通过迭代更新获得预测控制的最优控制量，降低了计算复杂度。

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