Observer-Based Sequential Control of a Nonlinear Two-Time-Scale System with Multiple Slow and Fast States

Abstract

Abstract: This paper extends the method of sequential control of a two-time-scale system with multiple slow and fast states from full-state feedback to observer-based feedback. It provides a guideline for the number and role of the observers needed, and proposes a Lyapunov design method for the selection of observer dynamics. The use of lower-order reduced subsystems simplifies the observer design. Using an extension of the existing composite Lyapunov analysis the stability of the full-order system including the controller and the observer in the loop is investigated. The procedure is demonstrated on a nonlinear two-time-scale system which is a combination of two springs, two masses and two dampers. Results in the paper demonstrate that the observer design methodology for a nonlinear system with one slow and one fast state can be extended to a system with multiple slow and fast states. The extended composite Lyapunov analysis is proposed to find an upper bound of the perturbation parameter up to which the full-order closed-loop system including the controller and the observer is stable.