This 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.
