Control of Linear Time Invariant Plants with the Cascaded Form of a Fractional Order Compensator

With the advent and emergence of calculus with fractional order (FO), the generalized form of the integer order (IO) has created significant advancement in the field of control. The real time systems represented by FO models are accurate enough developing improved performance in contrast to the classical IO one. In this context, the area is still deficient of methodical design algorithms with the different available structures of the FO compensator to control the various types of Linear Time Invariant (LTI) plants. The cascaded structure of the FO compensator is therefore employed here to exhibit the design method explicitly through a numerical study. These compensators help one to add the required exact magnitude and phase to the plant to be compensated at a particular frequency thus leading to the unique solution of the desired compensator parameters. This proposition has been further extended to compensate a highly non-linear unstable non-minimum phase (NMP) Cart-Inverted Pendulum System.