Cascaded Fractional Order (FO) Compensation of Linear Time-Invariant (LTI) Plants

Fractional order (FO) calculus extended from classical integer order, has emerged with notable significance in present day modeling and control applications. It empowers one to study the dynamics of the practical systems more accurately with valuable profound apprehension of the properties inherited naturally. Thus, the fractional order (FO) controllers based on added flexibility with the non-integer orders are competent of better performance collated to their integer order (IO) counterparts. However, there still persists some deficiency in defining the different possible forms of these FO compensators and their distinct design methods for any linear time invariant (LTI) plants. Therefore, this work considers compensators in cascaded FO structure and proposes the meticulous design steps for them, in order to dispense the requisite magnitude and phase at the given frequency. Accurate and distinct solution of the compensator numerical quantities with the non-integer orders obtained. Numerical examples are furnished in support of the proposed approach.