Extreme Value Condition of Stabilizing Digital PID Region

Abstract

This paper considers the stability of the digital PID control systems designed for linear time-invariant plants. The bilinear transform equation is adopted to determine the characteristic equation of the closed-loop system in the s domain. The extreme value condition of the stabilizing digital PID region is derived. Using this condition, the admissible range of the integral gain is derived. For a fixed integral gain, the stabilizing PD region is obtained by using the the stability boundary locus method. Numerical examples illustrate the method presented.