Abstract: The analysis of fractional system model is very complicated and tedious. From literature it has been clear that for study of fractional system one should have very deep knowledge about this system. To overcome this problem fractional system approximation techniques are developed. In this chapter Oustaloupís approximation method has been used for approximating the fractional system. The approximated model of fractional system will be of very large order and again new problem arises that the controller designed for approximated model will be of very higher order. Hence controller designed will be very costly and larger in size. Thus Model Order Reduction Technique has been used to overcome from this problem. Using MOR the order of approximated model should be reduced and then reduced order controller has been designed for fractional order system.

Keywords: Fractional Syatem, MOR; Oustaloupís technique; Hankelnorm approximation; Fractional PID Controller.