Calculation of robustly relatively stabilizing PID controllers for linear time-invariant systems with unstructured
Radek Matušů1, Bilal Senol2, Libor Pekař3
1Centre for Security, Information and Advanced Technologies (CEBIA-Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01 Zlín, Czech Republic.
Abstract:
This article deals with the calculation of all robustly relatively stabilizing (or robustly stabilizing as a special case) Proportional-Integral-Derivative (PID) controllers for Linear Time-Invariant (LTI) systems with unstructured uncertainty. The presented method is based on plotting the envelope that corresponds to the trios of P-I-D parameters marginally complying with given robust stability or robust relative stability condition formulated by means of the H∞ norm. Thus, this approach enables obtaining the region of robustly stabilizing or robustly relatively stabilizing controllers in a P-I-D space. The applicability of the technique is demonstrated in the illustrative examples, in which the regions of robustly stabilizing and robustly relatively stabilizing PID controllers are obtained for a controlled plant model with unstructured multiplicative uncertainty and unstructured additive uncertainty. Moreover, the method is also verified on the real laboratory model of a hot-air tunnel, for which two representative controllers from the robust relative stability region are selected and implemented.
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