  This paper contributes to the design of a fractional order (FO) internal
model controller (IMC) for a first order plus time delay (FOPTD) process model
to satisfy a given set of desired robustness specifications in terms of gain
margin (Am) and phase margin (Pm). The highlight of the design is the choice of
a fractional order (FO) filter in the IMC structure which has two parameters
(lambda and beta) to tune as compared to only one tuning parameter (lambda) for
traditionally used integer order (IO) filter. These parameters are evaluated
for the controller, so that Am and Pm can be chosen independently. A new
methodology is proposed to find a complete solution for controller parameters,
the methodology also gives the system gain cross-over frequency (wg) and phase
cross-over frequency (wp). Moreover, the solution is found without any
approximation of the delay term appearing in the controller.
