A Unified Approach to Two-time-scale Control Systems Design: a Tutorial

The goal of the tutorial is to give an overview of the newest unified design methodology of continuous-time or discretetime nonlinear control systems which guarantees desired transient performances in the presence of plant parameter variations and unknown external disturbances. The tutorial presents the up-to-date coverage of fundamental issues and recent research developments in design of nonlinear control systems with the highest derivative in feedback. The discussed design methodology allows us to provide effective control of nonlinear systems on the assumption of uncertainty. The approach is based on an application of a dynamical control law with the highest derivative of the output signal in the feedback loop. A distinctive feature of the control systems thus designed is that two-time-scale motions are forced in the closed-loop system. Stability conditions imposed on the fast and slow modes, and a sufficiently large mode separation rate, can ensure that the full-order closed-loop system achieves desired properties: the output transient performances are as desired, and they are insensitive to parameter variations and external disturbances. A general design methodology for control systems with the highest derivative in feedback for continuous-time systems, as well as corresponding discrete-time counterpart, will be presented during this tutorial. The method of singular perturbation is used to analyze the closed-loop system properties throughout.