APPLICATION OF KHARITONOV THEOREM TO MECHANICAL SYSTEMS

In this note, we apply Kharitonov's theorem to derive a robust stabili ty condition for PID controlled multi-degree-of-freedom mechanical sys tems. The characteristic equation of such a system is given as a deter minant of a third-order polynomial with matrix coefficients from which a scalar interval polynomial is obtained. We describe a simple proced ure for designing PID controllers for these mechanical systems and pro ve a new Kharitonov-like result which states roughly that a controller designed for an upper bounding inertia matrix results in stable set-p oint regulation for all other inertias.