Model Order Reduction: a comparison between Fractional and Integer Order Approximation

The paper reports and compare some strategies to reduce high integer order transfer functions, exploiting both integer and non integer order calculus. In particular, the fractional order approach based on the implicit model, a genetic algorithm based procedure and the open loop balanced realization have been compared. Being fractional order system described in terms of pseudo-space, the number of the parameters of the reduced order models and their frequency response errors have been taken as performance indexes.

[1]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[2]  Khaled Salah,et al.  Model order reduction using artificial neural networks , 2016, 2016 IEEE International Conference on Electronics, Circuits and Systems (ICECS).

[3]  Khaled Salah,et al.  A generic model order reduction technique based on Particle Swarm Optimization (PSO) algorithm , 2017, IEEE EUROCON 2017 -17th International Conference on Smart Technologies.

[4]  B. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

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

[6]  Luigi Fortuna,et al.  Optimal and Robust Control : Advanced Topics with MATLAB , 2012 .

[7]  Seema Das,et al.  Model order reduction of high order LTI system using Genetic Algorithm , 2017, 2017 International Conference on Computer, Communications and Electronics (Comptelix).

[8]  Christophe Farges,et al.  Fractional systems state space description: some wrong ideas and proposed solutions , 2014 .

[9]  Devendra Kumar,et al.  Editorial: Fractional Calculus and Its Applications in Physics , 2019, Front. Phys..

[10]  Paul Van Dooren,et al.  A collection of benchmark examples for model reduction of linear time invariant dynamical systems. , 2002 .

[11]  Rachid Mansouri,et al.  Approximation of high order integer systems by fractional order reduced-parameters models , 2010, Math. Comput. Model..

[12]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[13]  S. N. Deepa,et al.  Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique , 2011 .

[14]  Application of fractional order transfer function with zero and pole in approximation of electromechanical systems high order objects , 2018, 2018 XIV-th International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH).

[15]  I. Podlubny Fractional differential equations , 1998 .

[16]  P. Arena,et al.  Nonlinear Noninteger Order Circuits and Systems — An Introduction , 2000 .