PID tuning for unstable processes based on gain and phase-margin specifications

PID control is widely used to control stable processes, however. PID control for unstable processes is less common. In the paper, simple formulas are derived to tune the PID controller for unstable processes to meet gain and phase margin specifications. The stability of the closed-loop system is ensured by the Nyquist stability criterion. These formulas are derived for first- and second-order processes with time delay. Simulation results are given to show the accuracy of the formulas and the performance that can be achieved