A Laboratory Setup for an Introduction to Fractional Order Systems

Abstract In this paper we propose the use of a simple laboratory setup, which consists of a Peltier cell system, to introduce students to fractional-order systems. The setup can be built by using simple and low-cost components and can be used, by simply evaluating a step response, to show the need of using fractional-order models to accurately describe some real-world physical systems. A possible extension of the system is also described. In addition to fractional systems modeling, also the implementation of fractional control systems can be considered for a more advanced treatment of the topic.

[1]  Manuel Duarte Ortigueira,et al.  A coherent approach to non-integer order derivatives , 2006, Signal Process..

[2]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..

[3]  Fernando Morilla,et al.  Virtual and remote control labs using Java: a qualitative approach , 2002 .

[4]  Antonio Visioli,et al.  The generalised isodamping approach for robust fractional PID controllers design , 2017, Int. J. Control.

[5]  Antonio Visioli,et al.  Inversion-based feedforward and reference signal design for fractional constrained control systems , 2014, Autom..

[6]  Xavier Moreau,et al.  The CRONE Suspension , 1996 .

[7]  YangQuan Chen,et al.  Tuning and auto-tuning of fractional order controllers for industry applications , 2008 .

[8]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[9]  Ramon Vilanova,et al.  Tuning rules for robust FOPID controllers based on multi-objective optimization with FOPDT models. , 2017, ISA transactions.

[10]  Yangquan Chen,et al.  Two direct Tustin discretization methods for fractional-order differentiator/integrator , 2003, J. Frankl. Inst..

[11]  Antonio Visioli,et al.  On the fragility of fractional-order PID controllers for IPDT processes , 2017, 2017 25th Mediterranean Conference on Control and Automation (MED).

[12]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[13]  S. Westerlund,et al.  Capacitor theory , 1994 .

[14]  I. Petras,et al.  The fractional - order controllers: Methods for their synthesis and application , 2000, math/0004064.