Synthesis of Stabilizing PID Controllers for Biomechanical Models

Authors:	Roy Anindo, University of Arkansas at Little Rock, United States Iqbal Kamran, University of Arkansas at Little Rock, United States
Topic:	2.1 Control Design
Session:	PID Stabilization and Control
Keywords:	Biomedical systems, PID control, Stability analysis, Feedback systems,Hurwitz polynomial.

Abstract

A framework for synthesis of stabilizing PID controllers for linear time-invariant systems using Hermite-Biehler theorem is presented. The approach is based on the analytical characterization of the roots of the characteristic polynomial. Generalized Hermite-Biehler theorem from functional analysis is used to derive stability results, leading to necessary and sufficient conditions for the existence of stabilizing PID controllers. An algorithm for the selection of stabilizing feedback gains using root locus techniques and Linear Matrix Inequalities (LMI) is presented.