LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

Abstract

Use of 2‐rate controllers for robust control via zero‐placement is a topic of interest in current literature. This paper proposes a 2‐degree‐of‐freedom, 2‐rate, dynamic, output feedback controller to compensate single‐input single‐output (SISO), unstable, non‐minimum phase (NMP), discrete, linear time‐invariant (LTI) plants of relative degree unity; and achieves exactly the same loop and input‐output properties as can be achieved by a linear quadratic regulator (LQR) for the equivalent lifted LTI plant using state feedback. Such LQR‐like loop and input‐output properties, it may be noted, cannot be attained by LTI or even the existing 2‐rate output feedback controllers for plants with NMP zeros. Examples presented illustrate the efficacy of the proposed controller with respect to the existing ones.