Energy Technology & Ecological Concerns: A Contemporary Approach ISBN: 978-81-93024-71-3 103 Model Order Reduction by Pade Approximation and Improved Pole Clustering Technique Kaushal Ramawat 1 , Manisha Bhandari 2 , Anuj Kumar 3 1,2,3 Department of Electronics Engineering, University College of Engineering, Kota (Raj.) 1 kaushalramawat@yahoo.com Abstract: The authors offered a mixed technique for reducing the order of the high order dynamic systems. A pole-clustering based method to derive a reduced order approximation for a stable single-input single- output (SISO) continuous time system is presented. In this method, the denominator polynomial of the reduced order model is obtained by improved pole- clustering approach and the numerator polynomial is obtained through Padé approximation technique. The reduced order model so obtained by improved clustering algorithm guaranteed the stability in the reduced model and also preserves the characteristics of the original system in the approximated one. Keywords: Order reduction, Padé approximation, pole clustering, Dominant pole, Mean Square Error, Transfer function, IDM. 1. INTRODUCTION Model order reduction are often take interest in system modelling and design of high order systems. There are lots of methods proposed in the literature reflect the importance of producing a reduced order model for the system. It gives better considerate of the physical systems, reduced computational complexity, reduced hardware complexity, simplified controller design and cost effective solutions. The Padé approximation technique has been successfully applied to find the reduced system of higher order system, but sometimes this method has the drawback of resulting in unstable reduced order models of high order stable systems. For the stable reduced order models, various methods based on the preservation of dominant poles have been proposed [2]. The reduced-order model retains the basic physical features (such as time constants) of the original system and the stability of the simplified model is guaranteed. In classical approach, the modes with the largest time constants i.e. slow modes or the poles nearest to imaginary axis are usually considered dominant. This approach is good, still with some demerits. Firstly slow modes may not be dominant, another in some cases the system may have all the poles arise in a small region in s-plane or modes with similar time constants, and lastly the for complex poles is not straightforward. Various mixed methods based on the clustering of poles and Padé approximations are also proposed [4]. Methods describe the poles of the reduced system is use as the cluster centre of the pole clusters of the original system which obtained by Inverse distance measure (IDM) criteria. The choice of the clusters are either taken arbitrarily based on the order of reduction or it is the investigator. In this proposed method, the reduced order denominator polynomial has been obtained using an a dominant pole based pole-clustering approach for reduced order model. The method uses the improved clustering approach by deciding the value of the ratio of the residue to real parts of poles, taken in descending order and its corresponding reduced order model was obtained through a simple mathematical procedure. The model so obtained preserves the stability. The clustering method proposed in this paper differs from the existing pole clustering technique by considering the distance of system poles from the first pole in the group clustering process and it gives better approximation for order reduction. 2. PROBLEM STATEMENT Consider an linear SISO time invariant system of n th order . Higher order transfer function be in the form G(s)= ⋯ ⋯ (1) Where m n G(s) = () () = (2) Corresponding desired reduced order model of ! order should be given by " # (s) = $ $ ⋯ % % $ % % & & & ⋯& ’ & ’ & ’ ’ (3) Where l r " # (s) = ’ () ’ () = $ ( ( % ( & ( ( ’ ( (4)