鲁棒控制理论在船舶摇摆台系统中的应用研究
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摘要
H_∞控制理论是分析和设计不确定系统的一种强有力的工具，主要解决对象建模中的误差和在一定范围内因模型摄动而引起控制品质恶化的控制难题。本文对H_∞控制理论在船舶水舱摇摆台位置系统的应用进行了分析，在详细分析和研究系统数学模型的基础上，首次应用H_∞控制理论对船舶水舱摇摆台控制系统进行了混合灵敏度的优化设计研究，获得了满意的结果。
水舱试验摇摆台是研究和设计减摇水舱的重要试验设备，该试验装置是一种专用综合系统，目前在国内还没有如此功能规模的装置。利用它可以模拟船在海浪中的横摇和横荡运动，从而通过摇摆台试验为减摇水舱的设计提供依据。
水舱试验摇摆台是按照船的摇摆模型和相似关系建立起来的，本文以摇摆台为基础，对摇摆台的控制系统进行了设计。
本文建立了船舶—水舱运动的数学模型以及摇摆台横摇和横荡位置系统数学模型，选取了油缸、电液伺服阀的型号以及传感器的型号。并计算选取了数学模型中的各个参数。同时针对建立的数学模型，采用基本PID控制器对系统进行了校正，并进行了仿真研究。仿真表明，经典的PID控制可以在一定的程度上获得满意的响应特性，但由于系统中存在的参数不确定性以及干扰的作用，当参数摄动时，使得经典的PID控制的位置系统精度开始变差，为了提高系统的鲁棒性、鲁棒性能，引进H_∞控制理论，通过对系统不确定性的分析，合理的选择了加权函数，为系统设计了鲁棒控制器。最后，又对系统进行仿真研究，通过和PID控制器作用下的仿真对比，发现鲁棒控制器作用下的系统在参数摄动时仍能保持很好的稳定性，而且提高了系统的跟随精度，增加了系统在存在外界干扰的鲁棒性，明显改善了系统的性能。
H_∞control theory is a kind of powerful tool of analyzing and designing uncertain system, which can solve mainly control problems of control quality worsening due to the error of object modeling and model perturbation within a certain range. This paper makes analysis on the application of H_∞control theory in the position system of ship anti-rolling tank test swing bench. It is the first time to use H_∞control theory in designing ship anti-rolling tank swing bench control system with the method of mixed sensitivity optimization on base of analyzing and researching into the mathematical model, and a satisfied result is obtained.
The test swing bench of anti-rolling tank is an important experiment facility to research and design anti-rolling tank. The device is a kind of special synthetical system. So far China has no such test equipments in so large scale. The bench can simulate factual movement of the ship rolling and swaging in the wave, and it can also afford experimental verification for the design of anti-rolling tank through bench test.
The test swing bench of anti-rolling tank is based on the rolling and swaying model and conform connection of ship. This paper designs the ship anti-rolling tank swing bench control system on the basis of the bench. The mathematical model of ship-tank and the mathematical model of rolling and swaying position system were founded. Parts of an apparatus and parameters were calculated in this paper. On the basis of the founded mathematical model the system were emended and simulated by adopting classical PID controller. It is showed that classical PID controller can obtain satisfied result to some extent. But the parametric uncertainties and disturbances are existence. When it change, the precision of the PID controllers become low. To improve the robustness and robust performances of system, the robust controller based on H_∞mixed sensitivity for the system is proposed through the analysis of uncertainties and weighting function selection. And the robust controller is to improve the interference immunity. Compared with the PID controllers, the robust controller not only can stabilize when parameters are perturbed, but also improve the tracking accuracy of the system, and increase the robustness of disturbances existence, improve the system performance.
水舱试验摇摆台是研究和设计减摇水舱的重要试验设备，该试验装置是一种专用综合系统，目前在国内还没有如此功能规模的装置。利用它可以模拟船在海浪中的横摇和横荡运动，从而通过摇摆台试验为减摇水舱的设计提供依据。
水舱试验摇摆台是按照船的摇摆模型和相似关系建立起来的，本文以摇摆台为基础，对摇摆台的控制系统进行了设计。
本文建立了船舶—水舱运动的数学模型以及摇摆台横摇和横荡位置系统数学模型，选取了油缸、电液伺服阀的型号以及传感器的型号。并计算选取了数学模型中的各个参数。同时针对建立的数学模型，采用基本PID控制器对系统进行了校正，并进行了仿真研究。仿真表明，经典的PID控制可以在一定的程度上获得满意的响应特性，但由于系统中存在的参数不确定性以及干扰的作用，当参数摄动时，使得经典的PID控制的位置系统精度开始变差，为了提高系统的鲁棒性、鲁棒性能，引进H_∞控制理论，通过对系统不确定性的分析，合理的选择了加权函数，为系统设计了鲁棒控制器。最后，又对系统进行仿真研究，通过和PID控制器作用下的仿真对比，发现鲁棒控制器作用下的系统在参数摄动时仍能保持很好的稳定性，而且提高了系统的跟随精度，增加了系统在存在外界干扰的鲁棒性，明显改善了系统的性能。
H_∞control theory is a kind of powerful tool of analyzing and designing uncertain system, which can solve mainly control problems of control quality worsening due to the error of object modeling and model perturbation within a certain range. This paper makes analysis on the application of H_∞control theory in the position system of ship anti-rolling tank test swing bench. It is the first time to use H_∞control theory in designing ship anti-rolling tank swing bench control system with the method of mixed sensitivity optimization on base of analyzing and researching into the mathematical model, and a satisfied result is obtained.
The test swing bench of anti-rolling tank is an important experiment facility to research and design anti-rolling tank. The device is a kind of special synthetical system. So far China has no such test equipments in so large scale. The bench can simulate factual movement of the ship rolling and swaging in the wave, and it can also afford experimental verification for the design of anti-rolling tank through bench test.
The test swing bench of anti-rolling tank is based on the rolling and swaying model and conform connection of ship. This paper designs the ship anti-rolling tank swing bench control system on the basis of the bench. The mathematical model of ship-tank and the mathematical model of rolling and swaying position system were founded. Parts of an apparatus and parameters were calculated in this paper. On the basis of the founded mathematical model the system were emended and simulated by adopting classical PID controller. It is showed that classical PID controller can obtain satisfied result to some extent. But the parametric uncertainties and disturbances are existence. When it change, the precision of the PID controllers become low. To improve the robustness and robust performances of system, the robust controller based on H_∞mixed sensitivity for the system is proposed through the analysis of uncertainties and weighting function selection. And the robust controller is to improve the interference immunity. Compared with the PID controllers, the robust controller not only can stabilize when parameters are perturbed, but also improve the tracking accuracy of the system, and increase the robustness of disturbances existence, improve the system performance.
引文
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[30] 史忠科等．鲁棒控制理论．北京：国防工业出版社，2003
[31] 郑勇斌．减摇水舱试验台架及横摇和横荡运动实验研究。哈尔滨工程大学硕士学位论文，2003．1
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[38] 郑勇斌等．减摇水舱试验台架系统PID控制算法的研究与实现．自动化与应用第31卷第4期，2002
[39] 刘少昌．减摇水舱试验台架监控系统．自动化技术与应用第22卷第8期，2003
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[2] 金鸿章，李国斌．船舶特种装置控制系统．国防工业出版社，1995
[3] 李积德．船舶耐波性．国防工业出版社，1996
[4] Lee. B. S, Vassalos. D. V. Investigation into the Stabilization. Effects of Anti-roll Tanks with Flow Obstructions. International Shipbuliding Progress, 1996, 43(433): 71～88P
[5] Webster. W. C. Analysis of the Control Activated Anti-rolling Tanks. SNAME Transaction, Vol. 75, 1967: 296～331P
[6] 寺尾裕等．新型被动可控式减摇水舱的系统模拟和海上试验．关西造船协会志．1993(219)：75～88P
[7] Stabilization. Marine Engineers Review, 1995(9): 14～15P
[8] 管小铭主编．船舶电力系统及自动化．大连：大连海事大学出版社， 1999：1～7P，133～145P
[9] 姜长生，孙隆和，吴庆宪，陈文华编著．系统理论与鲁棒控制．北京：航空工业出版社，1998：366～408P
[10] 冯纯伯，田玉平，忻欣．鲁棒控制系统设计．东南大学出版社，1995：1～4P，151～181P．
[11] Doyle, K. Lenz and A. Packard. Design Examples Using μ-Synthesis: Space Shuttle Lateral Axis FCS During Reentry. Proc. of IEEE Conf. On Deci. and Contr., Athens, Greece, 1986
[12] R. Y. Chiang, M. G. Safonov, K. Haiges, K. Madden and J. Tekawy. A Fixed H_∞ Controller for a Supermaneuverable Fighter Performing the Herbst Maneuver. Automatics, 1993, Vol. 29, No. 1, 111～127P
[13] C. D. Yang, H. S. Ju and S. W. Liu. Expermental Design of H_∞ Weighting Functionns for Flight Control Systems. J. of Guidance, Control and Dynamics, 1994, Vol. 17, No. 3, 544～552P
[14] D. J. N. Limebeer and E. Kasenally. H_∞-Optimal Control of a Synchronous Turbo generator. Proc. of IEEE Conf. On Deci. and Contr., Athens, Greece, 1986: 62～65P
[15] W. Hirata, S. Koizumi and R. Takahashi. H_∞ Control of Railroad Vehicle Active Suspension. Automatica, 1995, Vol. 31, No. 1, 13～24P
[16] D. Walker and LPostlethwaite. Discrete Time H_∞ Control Laws for a High Performance Helicopter. Proc. of CDC, 1991: 128～129P
[17] R. A. Hyde and K. Glover. VSTOL AIRCRAFT FLIGHT. CONTROL SYSTEM DESIGN USING H_∞ CONTROLLERS AND A SWITCHING STRATEGY. Proc. of CDC, 1990
[18] K. W. Byun, B. Wie, D. Gelle rand J. Sunkel. Robust H_∞ Control Design for the Space Station with Structured Parameter Uncertainty. J. of Guidance, Control and Dynamics, 1991, Vol. 14, No. 6, 1115～1122P
[19] M. J. Ruth. Robust Control of a Coupled Undersea Vehicle Using μ-Synthesis. Proc. of ACC, 1991: 2375～2379P
[20] 吴旭东．解学书．H_∞鲁棒控制中的加权阵选择．清华大学学报，1997，37(1)
[21] 卢子广，王维亚．电子换向电机伺服系统的二自由度H_∞优化鲁棒控制．自动化学报，1998(5)：37～43P
[22] 杨承恩，贾欣乐，毕英君．一种用于减摇的多变量自动舵控制器．船舶工程，1998(5)：38～41P
[23] Bell. J and Walker. W. P. Activated and Passive Controlled Fluid Tank System for Ship Stabilization. SNAMF Transaction, Vol. 75. 1967: 150～193P
[24] 刘金琨．先进PID控制MATLAB仿真．北京：电子工业出版社，2004
[25] 张虹，梁利华等．横荡对被动式减摇水舱运动的影响．船舶工程第26卷第3期，2004
[26] 王广雄．控制系统设计．哈尔滨工业大学出版社，1991
[27] 郭大勇．减摇水舱台架试验及仿真方法研究．哈尔滨工程大学博士学位论文，2002．3
[28] Doyle J C et al. State-Space Solutions to Standard H_∞Control Problems[J]. IEEE T rans On AC, 1989, 34(8)
[29] 杨鹏．水舱试验摇摆台位置系统控制方法研究．哈尔滨工程大学硕士学位论文，2005．1
[30] 史忠科等．鲁棒控制理论．北京：国防工业出版社，2003
[31] 郑勇斌．减摇水舱试验台架及横摇和横荡运动实验研究。哈尔滨工程大学硕士学位论文，2003．1
[32] 曲家文．船舶减摇水舱试验装置理论及试验研究．哈尔滨工程大学博士学位论文，2003．2
[33] 金鸿章，姚绪梁．船舶控制原理．哈尔滨工程大学出版社，2001
[34] 上海交通大学船模试验池．关于被动式减摇水舱模拟台试验的几个问题．上海交通大学技术资料情报室，1997
[35] Katsuhiko Ogata 著．卢伯英 等译．现代控制工程．电子工业出版社．2003
[36] 翁正新，王广雄等．鲁棒H_∞状态反馈控制．控制理论与应用第11卷第4期，1994
[37] 于立君，王辉等．减摇水舱台架中私服系统的分析与校正．应用科技第31卷第8期，2004
[38] 郑勇斌等．减摇水舱试验台架系统PID控制算法的研究与实现．自动化与应用第31卷第4期，2002
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