Matusu, RadekSenol, BilalPekar, Libor2024-08-042024-08-0420220019-05781879-2022https://doi.org/10.1016/j.isatra.2022.04.037https://hdl.handle.net/11616/100644This 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 infinity 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.eninfo:eu-repo/semantics/openAccessRobust controlRobust relative stabilityRobust stabilityRobust performancePID controllersUnstructured uncertaintyH-infinity normArticle1315795973556230610.1016/j.isatra.2022.04.0372-s2.0-85129925443Q1WOS:000904647900001Q1