Model Order Reduction of Commensurate Fractional-Order Systems Using Big Bang – Big Crunch Algorithm

2019 ◽  
Vol 37 (5) ◽  
pp. 453-464
Author(s):  
Shivam Jain ◽  
Yogesh V. Hote ◽  
Sahaj Saxena
Keyword(s):  
Fractional Order ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Big Bang ◽  
Fractional Order Systems ◽  
Model Order ◽  
Big Crunch

scholarly journals Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 258
Author(s):  
Marek Rydel ◽  
Rafał Stanisławski ◽  
Krzysztof Latawiec
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Linear Time ◽  
Order Reduction ◽  
Balanced Truncation ◽  
Fractional Order Systems ◽  
Model Order ◽  
Reduction Techniques ◽  
Mathematical Formulas

In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems for restricted time and frequency ranges only, a special attention is given to time- and frequency-limited balanced truncation and frequency-weighted methods. Mathematical formulas for calculation of the time- and frequency-limited, as well as frequency-weighted controllability and observability Gramians, are extended to fractional-order systems. An instructive simulation experiment corroborates the potential of the introduced methodology.

scholarly journals Model order reduction of commensurate linear discrete-time fractional-order systems

2018 ◽  
Vol 51 (1) ◽  
pp. 536-541 ◽  
Author(s):  
Marek Rydel ◽  
Rafał Stanisławski ◽  
Krzysztof J. Latawiec ◽  
Marcin Gałek
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Fractional Order Systems ◽  
Model Order

scholarly journals Model Order Reduction: A Comparison between Integer and Non-Integer Order Systems Approaches

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 876 ◽  
Author(s):  
Riccardo Caponetto ◽  
José Tenreiro Machado ◽  
Emanuele Murgano ◽  
Maria Gabriella Xibilia
Keyword(s):  
Model Order Reduction ◽  
Control Strategies ◽  
Order Reduction ◽  
Open Loop ◽  
Long Term Memory ◽  
Fractional Order Systems ◽  
Model Order ◽  
Integer Order ◽  
Classical Control

In this paper, classical and non-integer model order reduction methodologies are compared. Non integer order calculus has been used to generalize many classical control strategies. The property of compressing information in modelling systems, distributed in time and space, and the capability of describing long-term memory effects in dynamical systems are two features suggesting also the application of fractional calculus in model order reduction. In the paper, an open loop balanced realization is compared with three approaches based on a non-integer representation of the reduced system. Several case studies are considered and compared. The results confirm the capability of fractional order systems to capture and compress the dynamics of high order systems.

scholarly journals Design of Low Frequency Suitable Fractional Order Differintegrators

2019 ◽  
Vol 8 (2) ◽  
pp. 3251-3255
Keyword(s):  
Fractional Order ◽  
Model Order Reduction ◽  
Continued Fraction ◽  
Low Frequency ◽  
Order Reduction ◽  
The Novel ◽  
Continued Fraction Expansion ◽  
Reduction Procedure ◽  
Model Order ◽  
First Order

Design of low frequency applicable fractional order digital differentiators and integrators using direct discretization is the main objective of this paper. Model order reduction procedure is used to obtain the novel first order s-to-z transform. Continued fraction expansion (CFE) technique is used to discretize that transform. The design of one-half digital differintegrators based on proposed transforms will be compared with the well known existing first order transforms namely, Bilinear and Al-Alaoui transforms. The efficacy of the designed methods presented interms of normalized magnitude error (NME). The designed fractional order digital filter coefficients are tabulated and all simulation results are carried out by using MATLAB software.

Sign in / Sign up

Export Citation Format

Share Document