Efficacy of order reduction techniques in the analysis of fractional order systems

Model order reduction plays an important role in the analysis of the fractional order systems. Fractional systems being more complex in nature are not easily processable. Hence for mathematical understanding of such systems it is fundamentally important to derive their proper integer order approximations. These integer order approximations are obtained using a well known technique, the Oustaloup method of approximation. Usually, the order of such approximations, which closely fit with the ideal characteristics of fractional order systems is high. The lower order models which still retain the necessary characteristics of the original fractional order systems are computed using model order reduction techniques. In this contribution, four model order reduction techniques are used, and models having order as low as 3 have been obtained. These model order reduction techniques are based on the concepts of calculating moments (Moment matching technique), energy of each state in the system (Schur balance order reduction technique & MatchDC technique) and optimization (Suboptimal reduction technique). Simulations have been performed in Matlab and it is ascertained that lower order models preserve the attributes of the original fractional order models. A comparative analysis of step and frequency responses of all the models is also performed. The motivation of this work lies in the fact that reduced order models can be easily realized in hardware.