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

Author(s):  
Riccardo Caponetto ◽  
Emanuele Murgano

It is very important task to study the behavior of the processes occurring in the industry. To attain this task, the knowledge of the transfer function of the system should be there. When working in robust environment, these transfer functions becomes so tedious that it becomes very difficult to obtain these transfer functions and hence affects the study of the behavior of these system. Due to this, the requirement for reduction of these transfer function becomes a necessity to analyze the behavior of foresaid systems and it becomes easy to do the desired modifications in the system i.e addition of any feature, desired changes in the behavior etc., furthermore the thing to be kept in consideration while doing the reduction in transfer function that the behavior viz. peak overshoot, settling time, steady state error of the two systems (reduced and the original system) should be approximately same, so it is prime importance that the applied model order reduction technique should provide a more accurate approximation of original higher order system. The paper presents here the different categories of model order reduction techniques that can be applied to achieve the motto of model order reduction of higher order systems. The techniques presented are categorized into the four different categories to understand them and their merits and demerits and these will help in proper selection of the model order reduction technique to obtain the most accurate reduced order approximation of large scale system.


Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 876 ◽  
Author(s):  
Riccardo Caponetto ◽  
José Tenreiro Machado ◽  
Emanuele Murgano ◽  
Maria Gabriella Xibilia

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.


Author(s):  
Vladimir Lantsov ◽  
A. Papulina

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.


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