INHERENT DESIGN LIMITATIONS FOR LINEAR SAMPLED-DATA FEEDBACK-SYSTEMS

There is a well-developed theory describing inherent design limitation s for linear time invariant feedback systems consisting of an analogue plant and analogue controller. This theory describes limitations on a chievable performance present when the plant has non-minimum phase zer os, unstable poles, and/or time delays. The parallel theory for linear time invariant discrete time systems is less interesting because it d escribes system behaviour only at sampling instants. This paper develo ps a theory of design limitations for sampled-data feedback systems wh erein the response of the analogue system output is considered. This i s done using the fact that the steady-state response of a hybrid feedb ack system to a sinusoidal input consists of a fundamental component a t the frequency of the input together with infinitely many harmonics a t frequencies spaced integer multiples of the sampling frequency away from the fundamental. This fact allows fundamental sensitivity and com plementary sensitivity functions that relate the fundamental component of the response to the input signal to be defined. These sensitivity and complementary sensitivity functions must satisfy integral relation s analogous to the Bode and Poisson integrals for purely analogue syst ems. The relations shaw, for example, that design limitations due to n on-minimum phase zeros of the analogue plant constrain the response of the sampled-data feedback system regardless of whether the discretize d system is minimum phase and independently of the choice of hold func tion.