PID tuning with exact gain and phase margins

In this paper, a simple PID controller design method that achieves user-specified gain and phase margins is proposed. Unlike other existing methods in the same category where assumptions on the process dynamics are made to simplify the non-linear problem encountered in computation, our method can yield exact solution for a general linear process. Since the set of unknowns outnumbers the set of equations in the problem, an extra equation is introduced by relating the closed-loop bandwidth to the process bandwidth. This also leads to a simple solution to the gain and phase margin problem. Simulation examples are included to demonstrate the effectiveness of the method.