Design of an enhanced fractional order PID controller for a class of second-order system

Purpose: This paper aims to design a modified fractional order proportional integral derivative (PID) (FO[PI]^λD^µ) controller based on the principle of fractional calculus and investigate its performance for a class of a second-order plant model under different operating conditions. The effectiveness of the proposed controller is compared with the classical controllers. Design/methodology/approach: The fractional factor related to the integral term of the standard FO[PI]^λD^µ controller is applied as a common fractional factor term for the proportional plus integral coefficients in the proposed controller structure. The controller design is developed using the regular closed-loop system design specifications such as gain crossover frequency, phase margin, robustness to gain change and two more specifications, namely, noise reduction and disturbance elimination functions. Findings: The study results of the designed controller using matrix laboratory software are analyzed and compared with an integer order PID and a classical FOPI^λD^µ controller, the proposed FO[PI]^λD^µ controller exhibit a high degree of performance in terms of settling time, fast response and no overshoot. Originality/value: This paper proposes a methodology for the FO[PI]^λD^µ controller design for a second-order plant model using the closed-loop system design specifications. The effectiveness of the proposed control scheme is demonstrated under different operating conditions such as external load disturbances and input parameter change.