A graphical tuning method of fractional order proportional integral derivative controllers for interval fractional order plant |
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| Affiliation: | 1. Departamento de Ciencia de la Computación e IA. Universidad del País Vasco (UPV/EHU). Apdo. 649. 20080 Donostia-San Sebastián, Spain;2. Departament de Matemàtica Aplicada I. E.T.S. Enginyeria Industrial de Barcelona. UPC Institut d’Organització i Control(IOC) UPC Diagonal 647. 08028 Barcelona, Spain;3. Departamento de Matemática Aplicada y EIO. Universidad del País Vasco (UPV/EHU). Apdo. 644. 48080 Bilbao, Spain;1. Department of Mathematics, University of Stuttgart, Germany;2. Department of Mechanical Eng., Boğazici University, Istanbul, Turkey;1. Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL, CNRS UMR 9189), Université Lille 1 / École Centrale de Lille, 59650 Villeneuve d’Ascq, France;2. Non-A, INRIA Lille-Nord Europe, France;1. Saint Petersburg State University, St. Petersburg, Russia;2. Departamento de Control Automático, Cinvestav, IPN, México D.F., Mexico;1. School of Electrical Engineering, Chungbuk National University, 52 Naesudong-ro, Heungduk-gu, Cheongju 362-763, Republic of Korea;2. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-ro, Kyongsan 712-749, Republic of Korea;3. School of Electronics Engineering, Daegu University, Gyungsan 712-714, Republic of Korea;4. Department of Biomedical Engineering, School of Medicine, Chungbuk National University, 52 Naesudong-ro, Heungduk-gu, Cheongju 362-763, Republic of Korea |
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| Abstract: | In this paper, a novel graphical tuning method of fractional order proportional integral derivative (FOPID) controllers is proposed for a given interval fractional order plant family. Firstly, an approach is presented to solve the problem of robustly stabilizing the interval fractional order plant using FOPID controller. Moreover, some alternative methods are developed to reduce the computational burden of the presented approach. The results obtained here are general and strict proofs are given on these results. Secondly, a new approach is presented to calculate the complete sets of FOPID controller parameters which guarantee the specified H∞-norm constraint for the interval fractional order plant. The developed approach is convenient and flexible. Finally, a unified design framework is proposed. The aim of the unified design is to compute the biggest region which can simultaneously provide internal stability, maintain the classical gain and phase margin and guarantee the modern H∞-norm constraint for the interval fractional order plant. Examples are followed to illustrate the design procedure. |
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| Keywords: | Interval plant Fractional order controllers Graphical tuning method Interval uncertainties |
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