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

ECS-9875273 Lin该提案提出了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为一大类现有理论无法充分处理的真正非线性系统开发新的、理论上合理且实用的反馈设计方法和技术。 要完成的另一个重要目标是测试和指导理论的发展，通过具有挑战性的基准工程问题的应用。 拟议的研究计划包括理论发展和实验验证。 其目的在于：1.开发一个系统的综合程序，基于输入输出参数或类似的Lyapunov方法，用于设计低增益和低增益和高增益控制器，全局渐近稳定比前馈系统更大的一类非仿射非线性系统，2.发展非最小相位仿射非线性系统控制的设计技术，3.针对不确定最小相位非线性系统，发展鲁棒无源系统理论和全局逆L2增益设计方法，使系统对结构建模不确定性或干扰具有鲁棒性; 4.通过解决一些长期存在的开放性控制问题，证明新的非线性控制策略的有效性和实用性。这项工作将结合非线性控制理论，计算机仿真和物理实验。 在我们的理论方法的一个独特的线程是系统地使用低增益设计技术，利用系统的非线性性质的反馈设计，而不是设计基于线性化的系统（无论是通过第一近似或反馈线性化）的反馈控制。 低增益反馈设计方法在一些非线性控制问题上已经产生了重要的影响，但在非线性控制中还没有得到充分的利用。 该研究计划侧重于几个重要问题，这些问题不仅本身有趣，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，涉及球和梁，倒立摆在车上，和工业级pH试点过程将在控制工程实验室在工程的案例学校进行。拟议的教育计划是一个重要的和不可分割的一部分，这个程序。 它的主要目标是为学生提供参与高级研究项目的机会。 通过这一创新的研究计划，学生在工程的案例学校将不仅开发分析和计算机技能，和科学发现的新方法，而且还丰富了他们的工程知识和实践动手经验，从而更好地为他们准备工程职业生涯在日益全球化，跨学科，和迅速变化的技术气候。 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。 虽然两个博士和硕士研究生将直接参与该计划，该项目也将受益于本科生通过课程开发和高级设计项目相关的这个计划。

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.