Abstract
This paper presents an effective procedure for model order reduction of discrete time control system. The exact model derived from complex dynamic systems proves to be very complicated for analysis, control and design. This necessity brings about using a tool known as model order reduction technique or model simplification. A novel mixed method has been implemented in this paper for reducing the order of the large scale dynamic discrete system. Dominant pole based pole clustering method has been used to derive the coefficients of denominator polynomial while Padé approximation has been applied to obtain the coefficients of numerator polynomial of the reduced order model. The proposed method is quite simple and able to generate a stable reduced order model from high order stable discrete systems. The dominancy of poles has been decided by values of the ratio of residue to its pole. The pole is considered dominant which have larger ratio value. An illustrative example has been considered to show the various reduction steps. The result obtained confirms the effectiveness of the approach.
Highlights
By applying linear transformation the original discrete time system is changed to continuous time system and the reduced order model is derivative of the original system by using the above stated techniques which imitates the behaviour of the original one (Ramesh, et al, 2017)
A method based on Dominant Pole Based Clustering Approach (DPBCA) using Padé Approximation Technique and Time Moment Matching of parameters along with the dominance of z plane has been used to reduce the model of higher order discrete time system
In this work, modified pole clustering is used for determination of denominator polynomial and Padé approximation is used for obtaining numerator coefficients of the reduced order model
Summary
There is some real world problem and the analysis is often too tedious and costlier due to its complexity. In arriving at the stable reduced order models, various methods based on the retention of dominant poles have been proposed; roots lying near the unit circle in the Z-plane have more effects on the system response than the others. Those roots are named as dominant roots whereas insignificant roots are lying close the origin. Kumar and Chandra (2014) have proposed the Padé approximants for reduction of higher order system in continuous-time domain (Hutton and Friedland, 1975) and discrete-time system have been suggested later in this paper in order to achieve stable model. Model Order Reduction Methods Many methods have been established for minimising the large scale system analysing the behaviour of the reduced model with the original which can be classified in general in two steps
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