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LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Institute of Automotive Mechatronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, 812 19 Bratislava, Slovakia
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Algorithms 2019, 12(8), 167; https://doi.org/10.3390/a12080167
Received: 1 July 2019 / Revised: 2 August 2019 / Accepted: 8 August 2019 / Published: 13 August 2019
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Abstract

Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called “D regions” where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system. View Full-Text
Keywords: robust control; pole placement; LMI regions robust control; pole placement; LMI regions
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Rosinová, D.; Hypiusová, M. LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design. Algorithms 2019, 12, 167.

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