Collaborative Research: Control of Underactuated Mechanical Systems through Lyapunov Direct Methods

合作研究：通过李亚普诺夫直接法控制欠驱动机械系统

• 批准号: 0600442
• 负责人: Warren White
• 金额: $ 12.69万
• 依托单位: Kansas State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600442&HistoricalAwards=false
• 关键词: Collaborative; Research; Control; Underactuated; Mechanical

AbstractCollaborative Research: Control of Underactuated Mechanical Systems through Lyapunov Direct MethodsThe proposed project involves developing Lyapunov direct methods for designing stabilizing controllers for nonlinear underactuated mechanical systems that render the system into closed loop Lyapunov form as opposed to closed loop Hamiltonian form. A goal is to show that the controller associated with the closed loop Lyapunov form can be implemented through either an analytical or a numerical solution (done in the feedback) of certain linear (partial) differential equations constituting asymptotic stability. The advantage of the proposed methodology is that the class of systems in Hamiltonian form is a strict subset of the class of systems in Lyapunov form thus yielding a larger class of stabilizing controllers that could offer improvements in system performance. It is further expected that the proposed research will provide a basis on which to treat problems that are intractable using other methods, while also leading to a unifying framework for methods utilizing controlled Lagrangians and controlled Hamiltonians. Another significant result is that the obtained controller is linear with respect to the velocities, whereas existing energy based nonlinear controllers are quadratic in the velocities. Comparisons between control laws designed through the proposed method and those designed through controlled Lagrangian, lambda, and IDA-PBC methods will be made.The primary thrust of the proposed activity is to analyze and further develop a new strategy, Lyapunov direct methods, for designing stabilizing controllers for underactuated mechanical systems, systems characterized by having fewer drives than degrees of freedom such as a robot where one or more joints are not powered. Examples of such systems are spacecraft, underwater vehicles, satellites, hovercraft and cargo cranes for container ships. The proposed method offers an improvement over the current art in that better performance is achieved while not suffering some common problems of existing methods. It is expected that there are systems that can be treated by the proposed techniques that cannot be treated by current techniques. The analysis will include comparisons of control laws produced by Lyapunov direct methods and current published methods. Undergraduate students in both mathematics and engineering will be encouraged to participate in the project through employment and course credit. Some students will help with development of an REU program at KSU. To facilitate participation of underrepresented groups, the KSU Minority Engineering Program and Women in Engineering and Science Program offices have committed to help in student recruitment, an activity that dovetails with their NSF funded STEP program.

摘要调查研究：通过Lyapunov Direct方法控制不足的机械系统，所提出的项目涉及开发Lyapunov的直接方法，用于设计非线性稳定控制器的非线性机械系统稳定控制器，该方法使该系统与封闭的Loop loop loop hamiltonian形式相反。 一个目标是证明与闭环lyapunov形式关联的控制器可以通过某些线性（反馈中完成）的分析或数值解（在反馈中完成）来实现，构成渐近稳定性的某些线性（部分）微分方程。 提出的方法的优点是，以哈密顿形式的系统类别是Lyapunov形式的系统类别的一个子集，因此产生了更大的稳定控制器，可以改善系统性能。 进一步预计，拟议的研究将为治疗使用其他方法棘手的问题提供基础，同时还为使用受控的拉格朗日人和受控的哈密顿人提供了统一的框架。 另一个重要的结果是，获得的控制器相对于速度是线性的，而现有的基于能量的非线性控制器在速度中是二次的。 Comparisons between control laws designed through the proposed method and those designed through controlled Lagrangian, lambda, and IDA-PBC methods will be made.The primary thrust of the proposed activity is to analyze and further develop a new strategy, Lyapunov direct methods, for designing stabilizing controllers for underactuated mechanical systems, systems characterized by having fewer drives than degrees of freedom such as a robot where one or more joints are not powered. 此类系统的例子是航天器，水下车辆，卫星，气垫船和货运船的货物。 提出的方法对当前艺术有所改善，因为可以实现更好的性能，同时又不遇到现有方法的一些常见问题。 预计会有一些系统可以通过所提出的技术来处理，而当前技术无法处理。 该分析将包括由Lyapunov直接方法和当前已发布方法产生的控制定律的比较。 鼓励数学和工程学的本科生通过就业和课程学分参加该项目。 一些学生将帮助在KSU开发REU计划。 为了促进代表性不足的群体的参与，KSU少数民族工程计划和工程和科学计划办公室的妇女致力于帮助学生招聘，这项活动与他们的NSF资助的步骤计划相吻合。