Three-Stage Design Using Two-Time-Scale Technique

This chapter introduces a three-stage feedback control design for a three-time-scale system using a two-time-scale approach. Through two-time-scale similarity transformations, the system is converted into a lower triangular form with slow, fast, and very fast subsystems. Feedback controls are then separately designed for these subsystems, employing a two-time-scale methodology. The final feedback control for the full-order system is derived from subsystem controls using state variable transformation matrices. The method is simple and easy to implement. It requires only four linear transformations and minimizes matrix calculations. Also, it significantly reduces computation time compared to regular three-time-scale approaches.