Posicast control of a class of fractional-order processes

• Authors: Emmanuel Gonzalez , John Hung , Lubomir Dorcak , Jan Terpak , Ivo Petras
• Languages of publication: EN

Abstracts

EN

The number of studies on the control of fractional-order processes-processes having dynamics described by differential equations of arbitrary order-has been increasing in the past two decades and it is now ubiquitous. Various methods have emerged and have been proven to effectively control such processes-usually resulting in fractional-order controllers similar to their conventional integer-order counterparts, which include, but are not limited to fractional PID and fractional lead-lag controllers. However, such methods require a lot of computational effort and fractional-order controllers could be challenging when it comes to their synthesis and implementation. In this paper, we propose a simple yet effective delay-based controller with the use of the Posicast control methodology in controlling the overshoot of a fractional-order process of the class $$\mathcal{P}:\left\{ {P\left( s \right) = {1 \mathord{\left/
{\vphantom {1 {\left( {as^\alpha + b} \right)}}} \right.
\kern-\nulldelimiterspace} {\left( {as^\alpha + b} \right)}}} \right\}$$ having orders 1 < α < 2. Such controllers have proven to be easy to implement because they only require delays and summers. In this paper, the Posicast control methodology introduced in the past few years is modified to minimize the overshoot of the processes step response to a level that is acceptable in control engineering and automation practices. Furthermore, proof of the existence of overshoot for such class of processes, as well as the determination of the peak-time of the open-loop response of a fractional-order process of the class P is presented. Validation through numerical simulations for a class of fractional-order processes are presented in this paper.

Keywords

EN

fractional calculus; fractional-order processes; Posicast; Mittag-Leffler function

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 6
• Pages: 868-880

Dates

published

1 - 6 - 2013

online

9 - 10 - 2013

Contributors

author

Emmanuel Gonzalez

• Department of Computer Technology, College of Computer Studies, De La Salle University Manila, 2401 Taft Ave., Malate Manila, 1004, Philippines

author

John Hung

• Electrical & Computer Engineering Department, Auburn University, Auburn, AL, USA

author

Lubomir Dorcak

• Institute of Control and Informatization of Production Processes, B.E.R.G. Faculty, Technical University of Kosice, B. Nemcovej 3, 042 00, Kosice, Slovak Republic

author

Jan Terpak

• Institute of Control and Informatization of Production Processes, B.E.R.G. Faculty, Technical University of Kosice, B. Nemcovej 3, 042 00, Kosice, Slovak Republic

author

Ivo Petras

• Institute of Control and Informatization of Production Processes, B.E.R.G. Faculty, Technical University of Kosice, B. Nemcovej 3, 042 00, Kosice, Slovak Republic

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Identifiers

DOI

10.2478/s11534-013-0284-3