Fractional Order Phase Shaper Design with Routh's Criterion for   Iso-damped Control System
  Phase curve of an open loop system is flat in nature if the derivative of phase with respect to frequency is zero. With a flat phase curve, the corresponding closed-loop system exhibits an iso-damped property i.e. maintains constant overshoot with the change of gain and with other parametric variations. In recent past application, fractional order (FO) phase shapers have been proposed by contemporary researchers to achieve enhanced parametric robustness. In this paper, a simple Routh tabulation based methodology is proposed to design an appropriate FO phase shaper to achieve phase flattening in a control loop, comprising a system, controlled by a classical PID controller. The method is demonstrated using MATLAB simulation of a second order DC motor plant and also a first order with time delay system. 
Suman Saha, Saptarshi Das, Ratna Ghosh, Bhaswati Goswami, Amitava   Gupta, R. Balasubramanian, A. K. Chandra, Shantanu Das
cs.SY