Robust IMC-Based Integer and Fractional Filter PID Controller Design for Non-minimum Phase Systems

The existence of right half plane (RHP) zeros makes controlling of non-minimum phase (NMP) processes difficult. This work focuses on designing a controller for such kinds of processes. In this article, a fractional filter internal model control (IMC)-based Proportional Integral Derivative (PID) controller is proposed for better set-point tracking and disturbance rejection of second-order non-minimum phase processes with dead time. The effect of time delays and RHP zeros on system’s controllability can be easily identified through IMC. Higher-order estimation for dead time is also considered in the design, as it provides a better response for higher-order processes. Designing a controller based on maximum sensitivity (Ms) is the novelty. A comparison study has also been conducted to demonstrate the superiority of IMC-based fractional order controllers over integer order IMC controllers. The closed-loop system results are evaluated for the perfect model, perturbed model, and measurement noise using integral absolute error (IAE). Total variation (TV) is used to estimate the controller effort. The range of Ms is discovered at which system provides stable performance for controllers developed utilizing different Pade’s estimation of time delay. Robust stability analysis is performed for model uncertainties, and a fragility study is conducted for controller uncertainties.