A quasi-LMI approach to computing stabilizing parameter ranges of multi-loop PID controllers

This paper addresses the problem of determining the parameter ranges of multi-loop PID (proportional-integral-derivative) controllers which stabilize a given process. An effective computational scheme is established by converting the considered problem to a quasi-LMI problem connected with robust stability test. The descriptor model approach is employed together with linearly parameter-dependent Lyapunov function method. Examples are given for illustration. The results are believed to facilitate real time tuning of multi-loop PID controllers for practical applications.