Linear System Order Reduction Model Using Stability Equation Method and Factor Division Algorithm for MIMO Systems

Abstract

A New mixed method is proposed which combines the advantages of Stability Equation method and factor division algorithm in deriving the reduced order models for higher-order linear dynamic systems. The denominator of the reduced order model is obtained by the stability equation method and the numerator values are calculated using factor division algorithm. The reduced order models retain the steady-state value and guarantees stability of the original system. The proposed algorithm has also been extended for the design of PID controller for MIMO systems. The numerical examples are solved in literature to show the flexibility and effectiveness over other existing methods

Introduction

I. INTRODUCTION

Since recent years design, Control and Analysis of large-scale systems is emerging as an essential area of research. Involvement of large number of variables in the high order system makes the analysis process computationally tedious. Majority of available analysis fail to give reasonable results when applied to large-scale systems. At this juncture the advantageous features of order reduction make the application of reduction procedures inevitable. The order reduction procedures are mainly classified into either time domain or frequency domain. Basing on the simplicity and amicability the frequency domain dependent methods have become more prominent. Further, the extension of single-input single-output (SISO) methods to reduce multi-input multi-output (MIMO) systems has also been carried out in [1]-[9].Each of these methods has both advantages and disadvantages when tried on a particular system.  In the field of engineering practical systems available are of higher order. The analysis, design and simulation of these higher order systems become computationally tedious. In order to overcome this problem an approximate reduced model of the original higher order model is used in spite of the original higher order model. There are several methods available in literature for the reduction of higher order SISO systems, but very few methods are available for the reduction of higher order MIMO systems.

The existing methods for the reduction of SISO systems like Pade Approximation, Continued Fraction expansion involve simple computations but have serious drawback of generating unstable reduced models sometimes.

In this paper, a new mixed method for the reduction of higher order MIMO systems has been introduced.Many of the methods available in the international literature can be easily extended for the reduced of linear MIMO (Multi input–Multi output systems).S. Mukherjee and R. N. Mishra [3] are proposed a method “Reduced order modeling of linear multivariable systems using an error minimization technique”. This method becomes complex when the input polynomial is of high order.GirishParmar and Manisha Bhandari [9] proposed “Reduced order modeling of linear dynamic systems using Eigen spectrum analysis and modified cauer continued fraction method”. A combined method using the advantages of the stability equation method and factor division algorithm is proposed for single as well as multivariable linear dynamic systems. In this method the reduced denominator is obtained by The Stability Equation and numerator of the reduced model is determined by the factor division algorithm. The proposed algorithm has also been extended for the design of PID controller for MIMO systems.

II. REDUCTION PROCEDURE FOR PROPOSED METHOD

References

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Copyright

Copyright © 2022 Mr. M. Sudheer Kumar, Mr. S. Harish. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.