Output Feedback Control of Two-Time-Scale Nonlinear Systems using High-Gain Observers

Abstract

Two-time-scale models are developed for systems whose state equations can be partitioned into sets of slow and fast dynamics, based on a large relative separation of transient response times. The advantage of two-time-scale modeling is the convenience of control design for the system. The state feedback control law for the two-time-scale system consists of two components, designed for reduced-order quasi-steady-state and boundary-layer models of the system. The research presented in this thesis pursues the control design philosophy mentioned above, for a class of two-time-scale nonlinear systems with output feedback. The state feedback control law components based on quasi-steady-state and boundary-layer models employ estimated states through two high-gain observers, one each for the reduced-order quasi-steady-state and boundary-layer models. The advantage of high-gain observers is their well-established robustness to modeling uncertainties of nonlinear systems. The thesis consists of two parts. The first part discusses the design and convergence analysis of high-gain observer based output feedback, closed-loop two-time-scale nonlinear system. Transformation of observer states into state estimation error reveals that the overall closed-loop system becomes three-time-scale. The slow dynamics evolve in the first timescale, the fast system dynamics and estimation error for slow dynamics evolve in second timescale, whereas estimation error for fast system dynamics evolves in even faster, third timescale. It is shown that for sufficient timescale separation, the closed-loop system states are bounded, ultimately bounded, and guarantee performance recovery of state feedback control law. The second part of the thesis presents simulation-based applications of proposed output feedback control. The first example system is the control of a permanent magnet DC motor for which the electrical dynamics are in fast timescale and mechanical dynamics are in the slow timescale. The second application example is of an underactuated inverted pendulum on a cart system. In this case, the pendulum dynamics are in fast timescale and cart dynamics are in slow timescale. The third example is the two-time-scale longitudinal dynamics model of a fixed-wing aircraft for which the rotational dynamics are in fast timescale and translational dynamics are in slow timescale. All of the systems are subjected to modeling uncertainties. Simulation results exhibit convergence of output feedback closed-loop systems using proposed high-gain observer.