Research ArticleAn optimal PID controller via LQR for standard second order plus time delay systems

- Improved design of PID controller for standard second order systems with time delay.
- Method is based on optimal approach of LQR and dominant pole placement technique.
- Location of non-dominant pole affects the stability and robustness of the controller.
- Time response differs with non-dominant pole for delay and delay free processes.
- Simulation shows improved closed loop time response over existing tuning methods.

An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed.