Improvement of Systems Response of a PID Controller in Underdamped Condition

In control system design it is difficult to ascertain the appropriate value of controller gain. Generally a high gain value causes an excessively oscillatory response with the possibility of instability, while a low gain value produces a slow system response. The desired optimal response is a value of gain that produces a quick system response with minimal steady state error and oscillation; this paper investigates various steps to get this system response. The main objective of this proceeding is to achieve unit step response curve of the designed system which exhibits a maximum overshoot of no more than 15%. To check the system response for reducing maximum overshoot, the system has been controlled via a PID Controller with Variable Plant Transfer Function. The proposed controller is mathematically designed and modeled with MATLAB, and the results are presented to confirm the PID controller effectiveness. Furthermore, the proposed approach is fairly simple for implementation in real time.