A frequency domain-based loop shaping procedure for the parameter estimation of the fractional-order tilt integral derivative controller

This paper demonstrates a frequency domain-based loop shaping method for the parameter estimation of a fractional order tilt integral derivative (FOTID) controller for the interval integer and fractional order time-delay systems. Along with the five nonlinear constraints usually considered for the design of the fractional order proportional integral derivative (FOPID) controller, a more flat phase concept signifying an enhanced robustness of the system towards gain variations is adopted as the sixth constraint for the tuning of a six variable tunable FOTID controller. The optimization toolbox fmincon in MATLAB is utilized for the solution process of the above constraint minimization problem. A certain class of fractional order plus time delay process is considered for the implementation and validation of the above procedure. The robustness of the FOTID controller optimized by the proposed method is tested against variations of the system parameters. By considering different numerical examples, the technical superiority of the FOTID controller over the FOPID controller is demonstrated through suitable comparisons in this current work.