Design of LQR based PI controller with optimum selection of weights for Time Delay Process

In this paper, an optimal PI Controller has been designed using continuous Linear Quadratic Regulator (LQR) theory for the application of first order plus time delay (FOPTD) systems. In general, time delays can limit and deteriorate the achievable system performance and induce stability. To achieve the optimal performance the LQR PI controller is designed, the selection of weight matrices Q plays a key role in the design in order to minimize settling time, peak overshoot and Integral Absolute Error (IAE). So, selection of Q matrices is proposed using Lyapunov Function incorporated with the state feedback gain matrix. In this, Lyapunov function gives the stability of the system and the state feedback gain matrix gives optimal PI Controller gains. The proposed methodology is validated using MATLAB on various FOPTD systems and gives robustness, less IAE and less settling time.