International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014) 496 Reducing Model Ordering using Routh Approximation Method Mukesh Chand Assistant Professor, ECE Department, Poornima College of Engineering, Jaipur (Rajasthan) Abstract— The Higher order systems are frequently too arduous to be used in real time applications. Model order reduction was developed in the areas of systems and control theory, which studied properties of dynamical systems in application for reducing their complexity, while preserving their input-output behavior as much as possible. Routh approximation method (RAM) is one of the most elegant methods of model reduction which preserves the stability of original system in reduced system. Keywords-- Model order reduction, routh approximation method, I. INTRODUCTION The reducing of a high order system into its lower order system is well thought-out important in analysis, synthesis and simulation of practical systems. The task of replacing a given dynamical higher order system by a smaller model (with reduced complexity) is called model order reduction. Generally model order reduction is done in time domain and frequency domain approaches. An extensive range of model order reduction methods have been anticipated by several authors for the time of last few decades. In this paper, first we study the routh approximation method; then modified routh approximation method. A Numerical Analysis is also discussed to understand both methods. There are no. of methods for model order reduction of system given in literature [1]-[13], but routh approximation method, [2] always takes attention because of it stability preserving property of system. II. ROUTH APPROXIMATION METHOD Maurice F. Hutton and Bernard Friedland [2] gave a new method of approximating the transfer function of a high- order linear system by one of lower order is called the ―routh approximation method‖ because it is based on an expansion that uses the routh table of the original transfer function, the method has a number of useful properties: if the original transfer function is stable, then all approximants are stable; the sequence of approximants converge monotonically to the original in terms of ―impulse response‖ energy. Let us consider a linear, time-invariant SISO system having the transfer function 1 1 1 0 1 .............................. () ................. n n n n n bS b Hs aS aS a         (1) A linear time invariant system by m inputs and I outputs can be symbolized by a matrix of transfer functions of the form (1) through the numerator coefficients bi being I x m matrices. As the denominator of a Routh approximant depends merely on the denominator of H(s), a Routh approximant to an I-output, m-input system is computed by computing the Routh approximant for every one term in the matrix of transfer functions [10]. The denominator of the Routh approximant merely has to be computed once. Alogorithm Of Routh Approximation Method [10]: A reduced or lower model order of is obtained by following steps for a given transfer function G(s). Step 1: Apply reciprocal transform of G(s). Step 2: Construct  and  table form [10]. Step 3: Find  and  coefficient from  and  table (shown in Table I and Table II). Step 4: For kth order model, determine () k R s using recursive equation (10, 11) from [10]. () () () k k k Ps R s Q s  Step 5: Again applying reciprocal transform of () () () k k k Ps R s Q s  and find () k R s . This is the required reduced order model.