船舶纵向运动多输入多输出不稳定系统的非线性反馈控制

doi:10.16183/j.cnki.jsjtu.2022.076

上海交通大学学报 ›› 2023, Vol. 57 ›› Issue (8): 972-980.doi: 10.16183/j.cnki.jsjtu.2022.076

船舶纵向运动多输入多输出不稳定系统的非线性反馈控制

曹添, 张显库()

大连海事大学航海学院,辽宁大连 116026

收稿日期:2022-03-22 修回日期:2022-07-23 接受日期:2022-07-27 出版日期:2023-08-28 发布日期:2023-08-31
通讯作者: 张显库,教授,博士生导师,电话(Tel.): 0411-84729572;E-mail:zhangxk@dlmu.edu.com.
作者简介:曹添(1997-),硕士生,主要从事船舶运动控制方面的研究.
基金资助:
国家自然科学基金资助项目(51679024);大连市重点领域创新团队支持计划(2020RT08);中央高校基本科研业务费专项资金资助项目(3132021139)

Nonlinear Feedback Control of MIMO Unstable System for Ship Longitudinal Motion

CAO Tian, ZHANG Xianku()

Navigation College, Dalian Maritime University, Dalian 116026, Liaoning, China

Received:2022-03-22 Revised:2022-07-23 Accepted:2022-07-27 Online:2023-08-28 Published:2023-08-31

摘要/Abstract

摘要：

为了提高多输入多输出(MIMO)不稳定系统控制器的鲁棒性与节能效果,以大连海事大学教学实习船“育鲲”轮在波浪上纵摇和升沉运动的数学模型为研究对象,将数学模型的分子分母具有不稳定零极点过程使用根轨迹成形技术以及引用数学工具加权矩阵将其根轨迹拉到左半平面.之后运用闭环增益成形算法设计控制器的思路,以成形后的模型用一阶闭环增益成形算法设计鲁棒控制器,再引入双极性S函数驱动的非线性反馈代替原有的误差线性反馈.从仿真结果可以看出,在模型产生摄动时,非线性反馈控制改进了升沉和纵摇,控制能量大幅减少,对模型干扰具有鲁棒性能.该方案求解过程简单,并且整个系统控制器与被控对象物理意义明确,设计所得的控制器阶次较低,且补充完善了MIMO不稳定系统的控制器设计方法.

关键词: 多输入多输出不稳定系统, 根轨迹成形, 非线性反馈, 鲁棒控制器, 减纵摇

Abstract:

In order to improve the robustness and energy saving of the controller for multiple input multiple output (MIMO) unstable systems, the mathematical model of pitching and the heave motion of the scientific ship “YUKUN” of Dalian Maritime University is taken as the research plant, and the root locus of the transfer function mathematical model with unstable zero-pole and zero-pole processes is pulled to the left half plane by using the root locus shaping technique and weighting matrix. The first-order closed-loop gain shaping algorithm is used to design the robust controller, and the nonlinear feedback driven by the bi-polar S function is introduced to replace the original error linear feedback. The simulation results show that the nonlinear feedback control improves heave and pitching when the model is perturbed, greatly reduces the control energy, and is robust to model disturbance. The solution process of the scheme is simple, and the physical significance of the controller and the controlled object of the whole system is clear. The order of the controller design is low, and the controller design method of the MIMO unstable system is supplemented and perfected.

Key words: multiple input multiple output (MIMO) unstable system, root locus shaping, nonlinear feedback, robust controller, reduction of pitch

中图分类号:

U664.82

曹添, 张显库. 船舶纵向运动多输入多输出不稳定系统的非线性反馈控制[J]. 上海交通大学学报, 2023, 57(8): 972-980.

CAO Tian, ZHANG Xianku. Nonlinear Feedback Control of MIMO Unstable System for Ship Longitudinal Motion[J]. Journal of Shanghai Jiao Tong University, 2023, 57(8): 972-980.

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参数	满载取值	参数	满载取值
两柱间长L/m	105	航速v/kn	16.7
船宽B/m	18	排水体积Δ/m³	5735.5
重心距船舯距离x_c	-0.51	船舯吃水d_M/m	5.2
舵叶面积A_R/m²	11.46	方形系数C_b	0.5595

控制方法	θ_max/(°)	h_max/m	e_TDDE	e_TPAE
被控之前	5.21	3.94	11.72	15.48
加入鲁棒控制器	2.43	0.33	1.44	9.73
非线性反馈改进鲁棒控制器	1.09	0.16	0.78	4.35

船舶纵向运动多输入多输出不稳定系统的非线性反馈控制

Nonlinear Feedback Control of MIMO Unstable System for Ship Longitudinal Motion

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