A modified PID controller (PIIσβD)

The purpose of this study is to modify the traditional PID controller in order to improve its performance (stability and tracking) by changing the length of integration interval. The performance of the traditional PID controller was improved by changing the length of integration interval to make the most of the returns of the PID and PIσD controllers. The asymptotic stability domain, in terms of the feedback gains, is derived for systems of second order using the modified controller which will be identified as PIIσβD. Comparing this controller with the traditional PID controller and PIσD controller proposed in [1], it proves that it is more accurate and more stable. For illustration and comparison, two examples have been simulated to evaluate the performance of the modified controller. All simulation results indicate that the modified controller is better than the traditional PID controller and the PIσD controller from the accuracy and stability point of view.