CAREER: Robustness Analysis in the Design of Nonlinear Feedback

职业：非线性反馈设计中的鲁棒性分析

• 批准号: 9624885
• 负责人: Alexandre Megretski
• 金额: $ 18万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9624885&HistoricalAwards=false
• 关键词: CAREER; Robustness; Analysis; Design; Nonlinear

9624885 Megretski The proposed research will concentrate on rigorous analysis of special classes of essentially nonlinear feedback design with application in self-tuning, delta-sigma modulators, anti-reset windup, and computer simulated locomotion. One major objective of the research is to demonstrate how the local analysis of robustness can be used in the global analysis of essentially nonlinear feedback systems, to produce results not matched by any other approach. Another general objective is to propose new solutions, and analyze the known "ad-hoc" solution to several well-known nonlinear feedback problems. Analysis of relay feedback systems. Feedback interconnection of a relay feedback with a linear time-variant plant will be considered. The situation in which such interconnection induces self-oscillation (a limit cycle) will be of most interest. Sufficient conditions for the global stability of such limit cycles will be derived, and the sensitivity of the oscillations in the presence of external inputs will be estimated. In particular, analysis of relay-based self-tunning of PID feedback will be done. Another application will be the analysis of delta- sigma modulators. In general, this part of the research project is aimed to compensate for the lack of methods suitable for rigorous analysis of piecewise linear systems. Feedback control with magnitude and rate constraints. The problem of control of linear and mildly nonlinear systems with constraints imposed on control signal rate and magnitude will be considered. The prime objective will be to improve the speed and efficiency of the control response, expressed in terms of induced norms and other parameters characterizing the transient behavior. Another objective is to provide a rigorous basis for a comparative study of different anti-reset windup designs. Feedback control of computer animation. This part of the project involves research on the feasibility of real-time dynamically simulate d computer animation of an open-loop unstable object. The "object" will be a three-dimensional system on joints, normally having at any time one or two joint ends touching the ground, and maintaining stability by changing the angles between the joints in a coordinated manner. Ultimately, the object will have most of the dynamical features of a human body, through the initial models will have less degrees of freedom. The goal is to teach the object to "walk" in the presence of the gravity force. It is most likely that the stability of the human body motion is ensured by several feedback loops governed by the autonomic nervous system. However, the actual control laws defining these feedbacks are not known. The main objective of the proposed research is to show that, using an advanced nonlinear feedback control methodology, it is possible to find algorithms for real- time stabilization of the open-loop locomotion, at least in the case of a simplified model. The research will also be aimed at studying the algorithms for stabilization of repetitive open-loop unstable motion. Integrated educational software. The educational component of the proposal is aimed at the development of an integrated software package and special methodology for the undergraduate class in "Systems and signals", to provide a tool for state-of- the-art, learning based, and practice-oriented education. The system will provide (a) computer-assisted multimedia-based presentations of course concepts; (b) student self-training using random generators of drill problems; (c) automatic problem generation and evaluation programs for official testing; (d) an open architecture allowing further accumulation of the knowledge. Ultimately, the proposed development should facilitate a major change in the forms of the university education. ***

小行星9624885 拟议的研究将集中在严格的分析，基本上是非线性反馈设计的特殊类与应用程序中的自调整，delta-sigma调制器，抗复位windup，和计算机模拟运动。 研究的一个主要目标是证明如何本地分析的鲁棒性可以用于基本上是非线性反馈系统的全局分析，产生的结果不匹配的任何其他方法。 另一个总体目标是提出新的解决方案，并分析几个著名的非线性反馈问题的已知的“ad-hoc”解决方案。 继电反馈系统分析。 将考虑继电器反馈与线性时变设备的反馈互连。 这种互连引起自振荡（极限环）的情况将是最感兴趣的。 这种极限环的全局稳定性的充分条件将被导出，并在外部输入的存在下的振荡的灵敏度将被估计。 特别是，基于继电自整定PID反馈的分析将完成。 另一个应用将是三角积分调制器的分析。 总的来说，这部分研究项目的目的是弥补缺乏适合于严格分析分段线性系统的方法。 具有幅值和速率约束的反馈控制。 将考虑线性和轻度非线性系统的控制问题，控制信号的速率和幅度施加约束。 主要目标将是提高控制响应的速度和效率，以诱导范数和表征瞬态行为的其他参数表示。 另一个目标是提供一个严格的基础，不同的抗复位饱和设计的比较研究。 计算机动画的反馈控制。 这部分的项目涉及研究开环不稳定物体的实时动态仿真计算机动画的可行性。 该“物体”将是一个三维系统的关节，通常在任何时候有一个或两个关节端接触地面，并保持稳定性，通过改变关节之间的角度，以协调的方式。 最终，对象将具有人体的大部分动力学特征，通过初始模型将具有较少的自由度。 目标是教物体在重力存在的情况下“行走”。 最有可能的是，人体运动的稳定性是由自主神经系统控制的几个反馈回路来确保的。 然而，定义这些反馈的实际控制律是未知的。 所提出的研究的主要目的是表明，使用先进的非线性反馈控制方法，它是可能的，找到算法的开环运动的真实的时间稳定，至少在一个简化的模型的情况下。 本研究亦将针对重复开环不稳定运动的稳定化算法进行研究。 集成教育软件。 该提案的教育部分旨在为“系统与信号”本科课程开发一个综合软件包和特殊方法，为最先进的、基于学习的和以实践为导向的教育提供一个工具。 该系统将提供 (a)以计算机辅助的多媒体方式介绍课程概念; (b)学生自我训练使用随机生成器的演习问题; (c)用于正式测试的自动问题生成和评估程序; (d)一个开放的体系结构，允许进一步积累知识。 最终，拟议的发展应有助于大学教育形式的重大变革。 ***