Experimentally validated three-parameter dual-loop hybrid fractional-order-TID-PD controller for stable and...

In this study, a robust dual-loop hybrid Fractional Order Tilt Integral Derivative (FOTID)-Proportional Derivative (PD) controller is developed to track both step and ramp signals. Here, the inner loop is an integer-order PD controller that shifts the process pole away from the origin, and the outer loop uses an FOTID controller. The proposed control scheme consists of only three tunable parameters, determined through an analytical design procedure supplemented by a simple one-dimensional graphical/numerical selection (via M_s-K_p characteristics), thereby reducing the overall design intricacy. The controllers are tuned using maximum sensitivity (M_s) and stability margins to provide good robustness in the closed-loop response. Using these design criteria, analytical solutions of the controller parameters are also obtained in terms for plant parameters. Case studies on a heat exchanger, a higher-order integrating process, and a two-area time-delayed cyber-physical power system have been undertaken to validate the effectiveness and reliability of the proposed control mechanism. The robustness of the suggested controller is examined by introducing a 20% perturbation to the plant parameters. Moreover, the simulated results are evaluated with respect to different errors. It is worth noting that for stable first-order plants, the proposed FOTID-PD framework reduces to an FOTI controller, since the inner PD loop is not necessary for plant stabilization. This simplified structure is used for experimental validation. Lastly, the proposed methodology is experimentally validated on a two-tank level loop.