Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications

Proportional-integral-derivative (PID) control is widely used to control stable processes; however, its application to integrating and unstable processes is less common. In the paper, simple formulas are derived to tune the PID controller for integrating and unstable processes with time delay to meet gain and phase margin specifications. With the proposed PID tuning method, a loop transfer function with a good shape, such as phase margin 60degrees, gain margin over 3, and the real part close to -0.5 in low frequencies, can be obtained. This guarantees both robustness and performance. Simulation examples are given to show the performance of the method.