Two-Stage Multirate Feedback Control Design Using Observer

This chapter addresses the limitations of single-rate sampling in designing discrete-time state feedback-based controllers for two-time-scale systems. It proposes a multirate state feedback (MRSF) control approach, i.e. sampling slow and fast states at different rates. The method involves constructing a block-triangular form of the continuous two-time-scale system, discretizing with a smaller sampling period for the fast subsystem, and block-diagonalizing for the slow subsystem. A derived MRSF control stabilizes the full-order system, employing a two-stage observer to estimate slow and fast states. Simulation results demonstrate computational savings without compromising closed-loop performance compared to the single-rate sampling method.