Abstract
This work introduces a novel variant of controller having basic structure of Proportional Integral Derivative (PID) controller as PI x+iy D a+ib . The controller is termed as Complex Fractional-order Proportional Integral Derivative (CFOPID) controller, since it has orders of fractional and complex form. This controller has more parameters to tune than the other variants of PID controller known as Fractional-order PID (FOPID). The paper employs Genetic Algorithm based tuning method for determining the parameters of PID, FOPID and CFOPID controllers by minimizing the cost function in the form of weighted sum of error specifications (due to complexity of the structures of the latter two controllers, GA proves to be handy tool). The paper, further, simulates and compares the results of the three controllers based on servo, regulatory and stability performances on a standard second order plus time delay system. Henceforth, practical results of controllers are analyzed from a case study on DC servomotor. This research is based on tuning the three PID variants through the said technique and comparing them on their controlling performances.