On Applications of Generalized Sampled-data Hold Functions to Robustness Enhancement

Abstract

This paper serves a two-fold purpose. First, a dynamic periodic digital compensator using generalized sampled-data hold functions (GSHF) for continuous-time linear systems is proposed and studied in respect of gain margin improvement. It turns out that with the same sampling period, GSHF controllers can improve the closed-loop gain margin much more significantly than periodic digital controllers proposed in Francis and Georgiou (1988). In addition, it is proved that under a mild condition, the gain margin improvement can be achieved without forcing the sampling period small. The second purpose of the paper is to reveal another important advantage of periodic compensation over time-invariant compensation; namely, periodic controllers can reduce a certain conflict between gain margin and sensitivity for discrete-time systems.