Reduced-order modeling of commensurate fractional-order systems

This paper proposes a new method of finding reduced-order model of a commensurate fractional-order (FO) system. The FO system is first converted to integer-order (IO) and then a mixed method of model-order reduction (MOR) scheme is applied. In this scheme, the denominator is obtained using time-moment matching method and the numerator is determined using the recently developed big bang-big crunch (BB-BC) optimization algorithm. This formulated reduced-order model is reconverted into its commensurate form of FO model. Three examples are presented to validate and illustrate the efficacy of the proposed approach.

[1]  Yogesh V. Hote,et al.  Fractional-order PI control of DC servo system using the stability boundary locus approach , 2015, 2015 IEEE 10th International Conference on Industrial and Information Systems (ICIIS).

[2]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[3]  Ahmed S Elwakil,et al.  Fractional-order circuits and systems: An emerging interdisciplinary research area , 2010, IEEE Circuits and Systems Magazine.

[4]  Duarte Valério,et al.  Introduction to single-input, single-output fractional control , 2011 .

[5]  H. V. D. Vorst,et al.  Model Order Reduction: Theory, Research Aspects and Applications , 2008 .

[6]  Yogesh V. Hote,et al.  Load Frequency Control in Power Systems via Internal Model Control Scheme and Model-Order Reduction , 2013, IEEE Transactions on Power Systems.

[7]  Mehmet Önder Efe,et al.  Fractional Order Systems in Industrial Automation—A Survey , 2011, IEEE Transactions on Industrial Informatics.

[8]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[9]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[10]  Majeed Mohamed,et al.  Model simplification methods for a reduced order system of flexible aircraft , 2015, 2015 International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT).

[11]  Xavier Moreau,et al.  Stability and resonance conditions of elementary fractional transfer functions , 2011, Autom..

[12]  M. Ortigueira.  An introduction to the fractional continuous-time linear systems: the 21st century systems , 2008, IEEE Circuits and Systems Magazine.

[13]  Javad Mohammadpour,et al.  Efficient modeling and control of large-scale systems , 2010 .

[14]  Y. V. Hote,et al.  Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method , 2016 .

[15]  Karabi Biswas,et al.  Reduced Order Approximation of MIMO Fractional Order Systems , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[16]  Ali Kaveh,et al.  Advances in Metaheuristic Algorithms for Optimal Design of Structures , 2014 .

[17]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[18]  M. Haeri,et al.  Model reduction in commensurate fractional-order linear systems , 2009 .

[19]  Yogesh V. Hote,et al.  Dimensionality reduction based IMC-PI tuning for DC servomotor , 2016, 2016 Indian Control Conference (ICC).

[20]  V. Zakian,et al.  Simplification of linear time-invariant systems by moment approximants † , 1973 .

[21]  Suman Saha,et al.  Design of a Fractional Order Phase Shaper for Iso-Damped Control of a PHWR Under Step-Back Condition , 2010, IEEE Transactions on Nuclear Science.

[22]  I. Petráš.  Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[23]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .