突变控制方法及其在船舶运动中的应用研究
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摘要
随着社会的进步、科学技术的发展,人们在实际工程中所面对的控制对象的特性也变化各异、形态万千。尤其在航空航海工程、电力大系统等复杂生产过程中出现的可能影响系统正常运行的突变现象,迫切需要对其进行描述、分析以及控制。突变理论的创立使其成为可能,但是要进行符合人们意识的控制,则需要结合控制理论,形成新的理论方法。本论文将致力于探索如何将突变理论同控制技术相结合,形成突变控制的方法论,探讨其理论体系框架,并试探性地应用到航海工程——船舶运动及稳定性控制中去。
突变控制理论体系的初步建立过程是在综合和总结现有研究成果的基础上进行的,体系框架主要包括突变的定义、突变控制的提出、突变控制系统模型、突变特性分析方法、突变控制方法、突变控制系统设计等若干方面的内容,旨在为突变控制的应用提供一定的指导。
突变控制作为一个理论体系,固然包含正反两个主要目标：一是在保持系统原有平衡点不变的条件下,为系统建立有益的突变,称为突变控制；二是消除或抑制系统中的有害突变,称为反突变控制。本文以此为主要线索,分别研究了突变建立方法和突变抑制方法,并成功应用于船舶航行过程中的多种运动状态。
突变建立控制的目的是在系统指定位置处通过控制输入建立需要的突变特性,主要包括静态突变特性和动态突变特性。针对静态突变的主要形式,提出了静态突变控制器的设计方法。这种方法结合静态分叉突变的判别条件,使用待定系数法,可以设计出各种类型的静态突变,且控制器简单易行。而对于动态突变,由于其维数的影响,分别提出了基于经典判据的低维突变控制器和基于隐式判据的高维突变控制器,极大限度地扩展了控制技术的应用范围。
工程实践中大部分系统需要抑制可能出现的各种突变形态,主要原因是由于这些突变现象可能使系统失稳,无法工作在正常状态下。本文对典型的静态突变、动态突变以及分支突变现象进行分析和研究,在船舶运动模型中加以具体分析,设计控制律,以保证抑制突变现象的发生。
首先,对潜艇近水面波浪力扰动下操纵运动系统中的静态跨临界分叉突变现象进行了定性和定量地讨论,并结合基于精确反馈线性化的滑模变结构控制方法设计了抑制静态突变的控制器。
其次,讨论了船舶非线性横摇运动中的Hopf动态分叉突变现象,提出线性状态反馈控制器的设计方法,给出了不同参数取值下的控制效果。
最后,研究了船舶二自由度横纵摇耦合运动中存在的双页尖点型突变和力幅分支突变特性,利用耦合状态反馈法设计的控制器可以有效抑制系统中出现的突变。
With the development of social economy and science and technology, the characteristic of control object in practical engineering becomes more variety of form. Especially in some complex manufacture process such as aeronautic and marine engineering, and electric system, catastrophe phenomena would appear which may affect normal state. So, to describe and analysis and control these catastrophe phenomena would be urgent for discussion. The found of catastrophe theory make this possible. But to control these catastrophes in accordance with peoples' intention, a new theoretical method would be formed based on the combination of control theory. This thesis devotes to establish catastrophe control methodology by combining with control theory, to investigate its theoretical framework, and to apply this theory to ship motion and stability control system.
The proceeding of preliminary catastrophe control theory establishment is based on the comprehension and summary of existing research results. The theoretical framework includes many aspects:catastrophe definition, the content of catastrophe control, catastrophe control system model, catastrophe analysis method, catastrophe control method, and catastrophe control system design and so on, which purport is to provide programmatic guidance for catastrophe control applications.
As a theoretical system, it contains two main positive and negative aims:one is to create new beneficial catastrophe while preserve all initial equilibriums, named catastrophe control; the other is to eliminate or restrain harmful catastrophe, called averse-catastrophe. For this study clue, this paper studies the catastrophe creation or restraining control arithmetic respectively, and succeeds to apply them in various navigational ship motions.
The purpose of catastrophe creation control is to establish requisite catastrophe which includes static catastrophe characteristic and dynamic catastrophe characteristic at a desired location by inputting control law. For the main form of static one, the static catastrophe control method is put forward. Combining with static bifurcation distinguish conditions, many kinds of static catastrophe can be designed. And the control law is very easy and convenient. For dynamic catastrophe, tow controllers respectively in the low dimension based on transversality condition and high dimension on implicit criterion are given, which extends the application of control technology.
In engineering, a majority of systems need restrain the entire catastrophe phenomena which would make system couldn't work in normal state and lose stability. In this paper, the three typical catastrophes as static, dynamic and embranchment types are investigated. In ship motion models, these three catastrophe characteristics are concretely analyzed. The control arithmetic are schemed out to restrain different catastrophes respectively.
The static transcritical bifurcation catastrophe in submersible near-surface motion under wave disturbance force is discussed by qualitative and quantitative methods. The variable structure controller based on feedback linearization is designed to eliminate the static catastrophe phenomena.
In analysis of the ship nonlinear rolling equation the Hopf dynamic bifurcation catastrophe is described. So the linear state feedback controller is employed to control this dynamic catastrophe. The influence of control parameters with different values are also presented to prove the control effects.
A tow-degree-of-freedom ship nonlinear motion was investigated for double page cusp catastrophe and force-response embranchment catastrophe characteristics. By utilize of coupled state feedback method, the controller is derived to retrain these catastrophes.
突变控制理论体系的初步建立过程是在综合和总结现有研究成果的基础上进行的,体系框架主要包括突变的定义、突变控制的提出、突变控制系统模型、突变特性分析方法、突变控制方法、突变控制系统设计等若干方面的内容,旨在为突变控制的应用提供一定的指导。
突变控制作为一个理论体系,固然包含正反两个主要目标：一是在保持系统原有平衡点不变的条件下,为系统建立有益的突变,称为突变控制；二是消除或抑制系统中的有害突变,称为反突变控制。本文以此为主要线索,分别研究了突变建立方法和突变抑制方法,并成功应用于船舶航行过程中的多种运动状态。
突变建立控制的目的是在系统指定位置处通过控制输入建立需要的突变特性,主要包括静态突变特性和动态突变特性。针对静态突变的主要形式,提出了静态突变控制器的设计方法。这种方法结合静态分叉突变的判别条件,使用待定系数法,可以设计出各种类型的静态突变,且控制器简单易行。而对于动态突变,由于其维数的影响,分别提出了基于经典判据的低维突变控制器和基于隐式判据的高维突变控制器,极大限度地扩展了控制技术的应用范围。
工程实践中大部分系统需要抑制可能出现的各种突变形态,主要原因是由于这些突变现象可能使系统失稳,无法工作在正常状态下。本文对典型的静态突变、动态突变以及分支突变现象进行分析和研究,在船舶运动模型中加以具体分析,设计控制律,以保证抑制突变现象的发生。
首先,对潜艇近水面波浪力扰动下操纵运动系统中的静态跨临界分叉突变现象进行了定性和定量地讨论,并结合基于精确反馈线性化的滑模变结构控制方法设计了抑制静态突变的控制器。
其次,讨论了船舶非线性横摇运动中的Hopf动态分叉突变现象,提出线性状态反馈控制器的设计方法,给出了不同参数取值下的控制效果。
最后,研究了船舶二自由度横纵摇耦合运动中存在的双页尖点型突变和力幅分支突变特性,利用耦合状态反馈法设计的控制器可以有效抑制系统中出现的突变。
With the development of social economy and science and technology, the characteristic of control object in practical engineering becomes more variety of form. Especially in some complex manufacture process such as aeronautic and marine engineering, and electric system, catastrophe phenomena would appear which may affect normal state. So, to describe and analysis and control these catastrophe phenomena would be urgent for discussion. The found of catastrophe theory make this possible. But to control these catastrophes in accordance with peoples' intention, a new theoretical method would be formed based on the combination of control theory. This thesis devotes to establish catastrophe control methodology by combining with control theory, to investigate its theoretical framework, and to apply this theory to ship motion and stability control system.
The proceeding of preliminary catastrophe control theory establishment is based on the comprehension and summary of existing research results. The theoretical framework includes many aspects:catastrophe definition, the content of catastrophe control, catastrophe control system model, catastrophe analysis method, catastrophe control method, and catastrophe control system design and so on, which purport is to provide programmatic guidance for catastrophe control applications.
As a theoretical system, it contains two main positive and negative aims:one is to create new beneficial catastrophe while preserve all initial equilibriums, named catastrophe control; the other is to eliminate or restrain harmful catastrophe, called averse-catastrophe. For this study clue, this paper studies the catastrophe creation or restraining control arithmetic respectively, and succeeds to apply them in various navigational ship motions.
The purpose of catastrophe creation control is to establish requisite catastrophe which includes static catastrophe characteristic and dynamic catastrophe characteristic at a desired location by inputting control law. For the main form of static one, the static catastrophe control method is put forward. Combining with static bifurcation distinguish conditions, many kinds of static catastrophe can be designed. And the control law is very easy and convenient. For dynamic catastrophe, tow controllers respectively in the low dimension based on transversality condition and high dimension on implicit criterion are given, which extends the application of control technology.
In engineering, a majority of systems need restrain the entire catastrophe phenomena which would make system couldn't work in normal state and lose stability. In this paper, the three typical catastrophes as static, dynamic and embranchment types are investigated. In ship motion models, these three catastrophe characteristics are concretely analyzed. The control arithmetic are schemed out to restrain different catastrophes respectively.
The static transcritical bifurcation catastrophe in submersible near-surface motion under wave disturbance force is discussed by qualitative and quantitative methods. The variable structure controller based on feedback linearization is designed to eliminate the static catastrophe phenomena.
In analysis of the ship nonlinear rolling equation the Hopf dynamic bifurcation catastrophe is described. So the linear state feedback controller is employed to control this dynamic catastrophe. The influence of control parameters with different values are also presented to prove the control effects.
A tow-degree-of-freedom ship nonlinear motion was investigated for double page cusp catastrophe and force-response embranchment catastrophe characteristics. By utilize of coupled state feedback method, the controller is derived to retrain these catastrophes.
引文
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