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Internal model control (IMC) structure is derived from classical control by introducing the model of plant in the control loop and thereby having significant advantages over classical control such as dual stability, perfect control and zero-steady state offset. The basic one degree of freedom (ODF) IMC provides good compromise between set-point tracking and disturbance rejection and works well for non-minimum phase (NMP) systems. In this work, an IMC based fractional order (FO) controller is designed for NMP system which satisfy desired phase margin (ϕ_m) at a desired gain-crossover frequency (ω_g). The domain of desired ϕ_m and ω_g is provided from which they can be selected. Simulation studies are done for (i) DC-DC boost converter which is a NMP system with one zero in right half of s-plane and (ii) first order plus time delay (FOPTD) system which is also a NMP system because of the delay. Significance of …