Stability Margins and Digital Implementation of Controllers

Abstract

This chapter is motivated by recent results on the fragility of optimal controllers and investigates the robustness and related behaviour of control systems containing a digital implementation of a designed continuous time controller, mainly through examples. We determine the coefficient stability margin of the digital controller as the sampling time is varied. We also study the stability and inter-sample response of the hybrid system as the sampling period varies. The main general trend indicated by the examples are a) that the stability margin of the digital controller often decreases as the sampling frequency increases and b) that the actual hybrid system may exhibit unstable inter-sample behaviour even though the discrete time stability margin of the digital controller may be large especially at low sampling frequencies. These examples raise a number of issues related to digital implementation of controllers.