Robust complex order controller design for DC motors

In this paper a robust design method for a DC motor is proposed. A complex order controller is designed to control the speed of the DC motor. Complex-order controllers are the extended version of fractional order controllers in which the order of the transfer function has imaginary and real parts. Introducing a complex order for the controller makes it possible to fulfil additional specifications of design ensuring a robust performance of the closed-loop system with respect to gain variations. This extra parameter enables designing a controller which makes the phase diagram flat at a known gain crossover frequency.