Root-locus design of PID controller for an unstable plant

Abstract

Unstable plant considered in the paper consists of an integrator and 1st order component with positive pole. PID controller is used, so the feedback system becomes of 3rd order. Root-locus design method is applied which for such system gives analytic expressions for controller settings. If weak control action is required, the design provides better responses than conventional one. Unstable ships, particularly oil tankers, require weak control.