PD CONTROLLER DESIGN and STABILITY ANALYSIS for SYSTEMS HAVING FRACTIONAL ORDER DELAY

Year 2022, Issue: 050, 254 - 269, 30.09.2022

Münevver Mine Özyetkin

Abstract

Fractional order systems (FOS) are one of the subjects that have been studied extensively. Such systems are difficult and complex structures to be analyzed mathematically. The degree of difficulty is even greater when the system has time delay. Considering the studies on FOS, either the transfer function of the system is of fractional order, or the controller has a fractional order structure. Time delay is common in practical systems. Studies mostly focused on classical time delay term. However, time delay can be of a fractional order. Studies for such systems are quite limited as the mathematical analysis part is complex.

In this study, systems having fractional order delay, are examined. By using the stability boundary locus (SBL) method, the necessary equations for calculating all stable PD controller parameters for such systems are obtained. It is necessary to test whether the parameters selected from the obtained stability region provide stability. However, stability analysis of such systems is very problematic. For this reason, an approximation method previously proposed by the author is used. Thus, the system is transformed to a fractional order structure. Then, the stability analysis of the FOS can be easily done. It is seen that the obtained equations and the approximation method proposed by the author for the stability test provide quite reasonable results.

Keywords

Fractional Order System, Time Delay, PD Controller, Stability Region

Thanks

I would like to thank the Dean of the Faculty of Engineering at Aydın Adnan Menderes University and the Head of the Department of Electrical and Electronics Engineering for the computer support that enabled me to carry out this study.

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