TY - JOUR

T1 - Design of an integer order proportional–integral/proportional–integral–derivative controller based on model parameters of a certain class of fractional order systems

AU - Yumuk, Erhan

AU - Güzelkaya, Müjde

AU - Eksin, İbrahim

N1 - Publisher Copyright:
© IMechE 2018.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In this study, we deal with systems that can be represented by single fractional order pole models and propose an integer order proportional–integral/proportional–integral–derivative controller design methodology for this class. The basic principle or backbone of the design methodology of the proposed controller relies on using the inverse of the fractional model and then approximating this fractional controller transfer function by a low integer order model using Oustaloup filter. The emerging integer order controller reveals itself either in pre-filtered proportional–integral or proportional–integral–derivative form by emphasizing on the dominancy concept of pole-zero configuration. Parameters of the proposed controllers depend on the parameters of the single fractional order pole model and the only free design parameter left is the overall controller gain. This free design parameter is determined via some approximating functions relying on an optimization procedure. Simulation results show that the proposed controller exhibits either satisfactory or better results with respect to some performance indices and time domain criteria when they are compared to classical integer order proportional–integral–derivative and fractional order proportional–integral–derivative controllers. Moreover, the proposed controller is applied to real-time liquid level control system. The application results show that the proposed controller outperforms the other controllers.

AB - In this study, we deal with systems that can be represented by single fractional order pole models and propose an integer order proportional–integral/proportional–integral–derivative controller design methodology for this class. The basic principle or backbone of the design methodology of the proposed controller relies on using the inverse of the fractional model and then approximating this fractional controller transfer function by a low integer order model using Oustaloup filter. The emerging integer order controller reveals itself either in pre-filtered proportional–integral or proportional–integral–derivative form by emphasizing on the dominancy concept of pole-zero configuration. Parameters of the proposed controllers depend on the parameters of the single fractional order pole model and the only free design parameter left is the overall controller gain. This free design parameter is determined via some approximating functions relying on an optimization procedure. Simulation results show that the proposed controller exhibits either satisfactory or better results with respect to some performance indices and time domain criteria when they are compared to classical integer order proportional–integral–derivative and fractional order proportional–integral–derivative controllers. Moreover, the proposed controller is applied to real-time liquid level control system. The application results show that the proposed controller outperforms the other controllers.

KW - Fractional order model

KW - fractional order proportional–integral–derivative

KW - inverse control

KW - liquid level control system

KW - pre-filtered integer order proportional–integral/proportional–integral controller

UR - http://www.scopus.com/inward/record.url?scp=85052601035&partnerID=8YFLogxK

U2 - 10.1177/0959651818792363

DO - 10.1177/0959651818792363

M3 - Article

AN - SCOPUS:85052601035

SN - 0959-6518

VL - 233

SP - 320

EP - 334

JO - Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

JF - Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

IS - 3

ER -