This example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with multiplicative uncertainty is built on the basis of the second-order plant with three uncertain parameters. The applied graphical method, adopted from the authors' previous work, is grounded in finding the contour that is linked to the pairs of P-I coefficients marginally fulfilling the condition of robust relative stability expressed using the H∞ norm. The illustrative example in the current article emphasizes that the technique itself for plotting the boundary contour of robust relative stability needs to be combined with the precondition of the nominally stable feedback control system and with the line for which the integral parameter equals zero in order to get the final robust relative stability regions. The calculations of the robust relative stability regions for various robust stability margins α are followed by the demonstration of the control behavior for two selected controllers applied to a set of members from the family of plants.

Centre for Security Information and Advanced Technologies Faculty of Applied Informatics Tomas Bata University in Zlín nám T G Masaryka 5555 760 01 Zlín Czech Republic

Department of Automation and Control Engineering Faculty of Applied Informatics Tomas Bata University in Zlín nám T G Masaryka 5555 760 01 Zlín Czech Republic

Department of Technical Studies College of Polytechnics Jihlava Tolstého 1556 586 01 Jihlava Czech Republic

Software Engineering Department Faculty of Engineering Aksaray University Bahçesaray Mahallesi 68100 Aksaray Turkey

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