Synthesis of H PID controllers

Abstract

This paper considers the problem of synthesizing proportional-integral-derivative (PIC) controllers for which the closed-loop system is internally stable and the H norm of a related transfer function is less than a prescribed level for a given single-input single output plant. In our approach, in this paper, this problem is formulated by virtue of the bounded real lemma, as a feasibility problem involving a bilinear matrix inequality (BMI) and solved by means of a sequence of easier auxiliary quadratic optimization problem. The optimal controller is determined through a line search on the non negative real axis.