CAREER: Taking Advantage of Nonlinearity: New Methods for Nonlinear Feedback Design

本文提出了在非线性控制系统分析和设计领域的研究和教育计划。该提案的主要目标是开发新的，理论上合理的和实际有用的反馈设计方法和技术，用于一大类真正的非线性系统，这些系统不能被现有理论充分处理。另一个要完成的重要目标是通过应用挑战性的基准工程问题来测试和指导理论发展。提出的研究计划包括理论发展和实验验证两个部分。它的目标是：1；开发一个系统的综合程序，基于输入输出参数或李雅普诺夫方法，用于设计低增益和低增益和高增益控制器，这些控制器可以全局渐近地稳定比前馈系统更大的非仿射非线性系统，2。非最小相位仿射非线性系统控制设计技术的发展；3 .针对不确定的最小相位非线性系统，开发了鲁棒无源系统理论和全局逆l2增益设计方案，从而使系统对结构建模不确定性或干扰具有鲁棒性；通过解决一些长期存在的开放控制问题，证明了新的非线性控制策略的有效性和实用性。这项工作将融合非线性控制理论、计算机模拟和物理实验。在我们的理论方法中，一个独特的线索是系统地使用低增益设计技术，在反馈设计中利用系统的非线性特性，而不是基于系统的线性化（通过第一近似或反馈线性化）来设计反馈控制。低增益反馈设计方法已经对一些非线性控制问题产生了重大影响，但在非线性控制方面还没有得到充分的应用。研究计划集中在几个重要的问题上，这些问题不仅本身很有趣，而且对非线性控制理论的发展和应用至关重要。计算机模拟和物理实验将在Case工程学院的控制工程实验室进行，包括球梁、推车上的倒立摆和工业级pH试验过程。提出的教育计划是该计划的重要组成部分。它的主要目标是为学生提供参与高级研究项目的机会。通过这个创新的研究项目，凯斯工程学院的学生不仅可以培养分析和计算机技能，以及科学发现的新方法，还可以丰富他们的工程知识和实践经验，从而更好地为他们在日益全球化，跨学科和快速变化的技术环境中的工程职业做好准备。这一目标将通过重塑课程、开发新的实验室实验和指导学生来实现。虽然博士和硕士研究生将直接参与该项目，但该项目也将通过与该项目相关的课程开发和高级设计项目使本科生受益。

ECS-9875273LinThis proposal presents a research and educational program in the field of analysis and design of nonlinear control systems. The principle goal of the proposal is to develop new, theoretically sound and practically useful feedback design methods and techniques for a large class of genuinely nonlinear systems that cannot be adequately dealt with by existing theory. The other important objective to be accomplished is to test and guide the theoretical development via applications to challenging benchmark engineering problems. The proposed research plan consists of both theoretical development and experimental validation. It aims at: 1. developing a systematic synthesis procedure, based on either the input-output argument or the Lyapunov-like approach, for designing low-gain and low-and-high gain controllers that globally asymptotically stabilize a larger class of non-affine nonlinear systems than feedforward systems, 2. developing design techniques for the control of non-minimum-phase affine nonlinear systems, 3. developing robust passive systems theory and global inverse L2-gain design schemes for uncertain minimumphase nonlinear systems, leading to performance robustness against structural-modeling uncertainties or disturbances, and 4. demonstrating the effectiveness and usefulness of the new nonlinear control strategies, by solving some long-standing open control problems.This effort will merge nonlinear control theory, computer simulation, and physical experiments. A unique thread in our theoretical approach is the systematic use of low-gain design techniques, to take advantage of the nonlinear nature of the system in the feedback design, rather than to design feedback controls based on linearization of the system (either by first approximation or feedback linearization). The low-gain feedback design method has had a significant impact on a few nonlinear control problems, but it has not yet been fully exploited for nonlinear control. The research plan focuses on several important issues that are not only interesting in their own right but also critical to the advancement and application of nonlinear control theory. Computer simulation and physical experiments involving the ball-and-beam, inverted pendulum on a cart, and an industrial-grade pH pilot process will be performed in the control engineering laboratories at The Case School of Engineering.The proposed educational plan is an important and integral part of this program. It's main objective is to provide students with opportunities to participate in advanced research projects. Through this innovative research program, the students in The Case School of Engineering will not only develop analytical and computer skills, and new methods of scientific discovery, but also enrich their engineering knowledge and practical hands-on experience, hence better preparing them for an engineering career in an increasingly global, interdisciplinary, and rapidly changing technical climate. This goal will be achieved by reshaping curriculum, developing new laboratory experiments, and advising students. While both Ph.D. and M.S graduate students will be involved directly in this program, the project will also benefit undergraduate students through curriculum development and senior design projects related to this program.