Proportional-integral-derivative controller design for time-delay systems via stability region centroid

Design of proportional-integral-derivative (PID) controller with proportional, integral, and derivative gains given by ,  and  respectively, for time-delay systems is presented in this study. The centroid of the convex stability region (CCSR) method in the -  plane for fixed  is used. PID controller design for time-delay systems in the -  plane for a fixed  and -  plane for a fixed  have been extensively researched. Despite the amenability of CCSR method to design of PID controller in the -  plane for fixed , its application in this regard has not been given serious attention. The stability region in -  plane for fixed  was determined and the required controller gains in the region were determined using the CCSR method. Using the determined controller gains, the system closed loop unit step response for all the considered regions was plotted on same axes. Based on the obtained results, different combinations of controller gains can be implemented depending on the system time domain performance measures (TDPMs) requirements. However, selection of an appropriate controller gains combinations, requires compromise among any of the conflicting TDPMs.