Enhanced PID Controller for Non-Minimum Phase Second Order Plus Time Delay System

A tuning method is developed for the stabilization of the non-minimum phase second order plus time delay systems. It is well known that the presence of positive zeros pose fundamental limitations on the achievable control performance. In the present method, the coefficients of corresponding powers of s, s(2) and s(3) in the numerator are equated to alpha, beta and gamma times those of the denominator of the closed-loop system. The method gives three simple linear equations to get the PID parameter. The optimal tuning parameters alpha, beta and gamma are estimated by minimizing the Integral Time weighted Absolute Error (ITAE) for servo problem using fminsearch MATLAB solver aimed at providing lower maximum sensitivity function and keeping in check with the stability. The performance under model uncertainty is also analysed considering perturbation in one model parameter at a time using Kharitonov's theorem. The closed loop performance of the proposed method is compared with the methods reported in the literature. It is observed that the proposed method successfully stabilizes and improves the performance of the uncertain system under consideration. The simulation results of three case studies show that the proposed method provides enhanced performance for the set-point tracking and disturbance rejection with improved time domain specifications.