A General Form of FO PI-PD Controllers for Some Stable Integer and Non-Integer Order Plants with Transport Delay

An increase in flexibility of the Fractional Order (FO) controllers introduced over the years attracting attention with adjustable tuning parameters having the potential of better control effort are made available in the literature. It is very troublesome as well as quite demanding to arrive at a control with its feedback loop closed of a high order oscillatory mass spring damper system with good performance. Now, in order to reach the desired control performance it has to be characterized by satisfying the pre-defined specifications in both the domain of frequency and time simultaneously not guaranteed with the FO- \(PI^\lambda D^\mu\) controllers. A systematic design procedure is thus identified for a distinct cascaded FO PI and PD controller in terms of the required stability margins of the system to be controlled. Equating with the integer order (IO) controllers this controller will serve obvious benefits with the extra degree of freedom contributed by its non-integer orders achieving better servo tracking performance and loop robustness. Simple numerical examples with MATLAB simulations results illustrate its advantages while ensuring closed loop control stability of the system considered. (179 Words)