Three-Stage Multirate Feedback Control Design Using Observer

This chapter addresses the challenges of designing discrete-time state feedback control for a multi-time-scale system, where lower sampling rates fail to capture information from fast and very fast states, while higher rates significantly increase computation. The proposed solution is a multirate state feedback (MRSF) control for a linear time-invariant three-time-scale system, involving sampling of slow, fast, and very fast states at different periods. The method employs a block-triangular form of the continuous three-time-scale system, successive discretization, and simultaneous feedback control design at various sampling rates to formulate a combined MRSF control, proven to stabilize the full-order system. A sequential three-stage observer is introduced for state estimation, and simulations demonstrate the superiority of the approach over single-rate sampling.