Control of Nonlinear Dynamical Systems with Time-Periodic Coefficients

Auburn University, Auburn AL

Investigators

Abstract

Project Abstract: Modeling of many mechanical systems leads to a set of nonlinear differential equations with periodic coefficients. The dynamics and control of these systems is a very significant issue due to its impact on reliability, capability of operating under high speeds and longevity. In most instances, the linearized equations are used to design the controllers, which by no means is an efficient or a practical solution. Further, in the case when a system has linearly uncontrollable modes then a linear controller cannot be designed and one must resort to a nonlinear controller. In this study a set of practical and efficient techniques are developed that can be applied to a wide class of control problems encountered in nonlinear systems with periodically varying parameters. The main approach is based on the application of Lyapunov-Floquet transformation and time-dependent normal form theory. For linearly uncontrollable critical cases, bifurcation control is suggested through an application of the center manifold theory. Backstepping and Lyapunov's second methods are also employed to synthesize controllers. The practical significance of this study is demonstrated through applications (via computer simulations) to some typical problems including the controller designs for an asymmetric magnetic rotor-baring system, helicopter blades and structures subjected to periodic loads. As an application to cardiac dynamics, a control system is designed to change an irregular heat beat to a desired periodic rhythm.