Loop Frequency Response Design for Prescribed Step Response Bounds

Abstract

A loop frequency response design procedure for achieving prescribed closed loop step response bounds is described. This procedure is based on the Horowitz sensitivity criterion which specifically deals with large plant parameter variations and is essentially frequency domain orientated. The variations in the closed loop system frequency response are represented by polygonal plots in the complex plane at a number of frequencies and the overall loop frequency response is adjusted until these plots are seen to lie in or close to corresponding specified polygonal plots which represent bounds on the system step response. The advantages of this technique compared with others using the Horowitz criterion are that it is ideally suited to computer assisted design when use is made of a visual display unit and it provides an effective and natural way of specifying the step response bounds. Any preferred method can be used to construct the required loop frequency response function although that suggested here permits a very rapid initial design since essentially only one parameter need be varied. Thus trade-offs between loop gain-bandwidth and system sensitivity can be quickly established.