Tuning of optimal and robust PID controller for open-loop unstable first-order plus time delay systems

This paper proposes a novel alternative method to tune an optimal and robust PID controller for open-loop unstable first-order plus time delay systems with gain margin (GM) and phase margin (PM) specifications. By exploiting the gain-phase margin tester method and the stability equation method, a gain and phase margin specifications-oriented region (GPMSOR), constituting all the feasible specifications-oriented robust PID controllers, is successfully located in the parameter plane. In addition, the integral of the absolute error (IAE) and the integral of the squared error (ISE) performance criterion of every representative point in the GPMSOR are computed. Accordingly, an optimal and robust PID controller set can be found inside the GPMSOR. Finally, an illustrative example cited from the literature is provided to show the effectiveness of the proposed method.