Comparative analysis of order reduction techniques

The mathematical models used to represent physical processes are generally large and complex. Since simpler models are commonly employed in control, design and analysis, it is required to reduce the order of complex systems. This paper presents a comparative analysis of the performance of four order reduction methods. The computation of the lower order transfer functions is based on balance truncation algorithm, Hankel operator, moment matching and optimization algorithm. To demonstrate the performance of the reduction methods, second and third order transfer functions are computed for a plant model of fractional order. The integer transfer function of the plant model is obtained by applying Oustaloup filter approximation technique. For comparison of the reduction methods with ideal response, the analysis has been done both in frequency-domain and time-domain using MATLAB.