A bridge from stability to robust performance design of PID controllers in the frequency domain

Abstract

A graphical technique for finding proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time-delay has been solved. In this research, a method is introduced for finding all achievable PID controllers that also satisfy an H sensitivity, complementary sensitivity, weighted sensitivity, robust stability, or robust performance constraint. These problems can be solved by finding all PID controllers that simultaneously stabilize the closedloop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. There are several key advantages of this procedure. It does not require the plant transfer function model, but depends only on the frequency response. The ability to include the timedelay in the nominal model of the system will often allow for designs with reduced conservativeness in plant uncertainty and an increase in size of the set of all PID controllers that robustly stabilize the system and meet the performance requirements.