A Robust Internal Model-Based Fractional Order Controller for Fractional Order Plus Time Delay Processes

Abstract

This letter proposes a fractional order internal model controller (FO-IMC) for a fractional order plus time delay (FrOPTD) process model to satisfy desired gain margin ( $A_{m}$ ) and phase margin ( $\phi _{m}$ ) specifications. A method is proposed to solve four equations arising from the $A_{m}$ and $\phi _{m}$ specifications, which also generates solution of the system gain-cross-over frequency ( $\omega _{g}$ ) and phase-cross-over frequency ( $\omega _{p}$ ) as intermediate variables. The designed FO-IMC is implemented on laboratory DC servo-system and compared with other integer order controller and fractional order controller.