Relationship of lambda and overshoot of step response for a direct synthesis PI controller

The direct synthesis (DS) tuning method is a model-based method for a feedback controller. The main principle of this method is to obtain the controller settings based on a predetermined desired closed loop response. The main advantage is that there is only one parameter to be adjusted, which is lambda (λ), the speed of the desired closed loop response. There are several guidelines available for selecting λ in order to ensure that the closed loop step response matches the desired response. In this paper, a guideline that relates λ and overshoot is proposed and it worked well over a wide range of R varying from 0.05 to 2. For a fair comparison of DS-tuned controllers with different λ guidelines, both performance and robustness for a unit step change in the set point are considered. It was found that the DS-tuned controller with this proposed guideline performed better and the gain margin (GM) and phase margin (PM) lie between 2≤GM≤5 and 30º≤PM≤75º, respectively. Besides, its overshoot changed less with a ±25% process model mismatch, except for τ mismatch.