PID controller tuning by frequency loop-shaping

A frequency loop-shaping technique is presented for tuning proportional-integral-derivative controllers. In this approach, the controller parameters are tuned so as to minimize the difference between the actual and a target loop transfer function, in the sense of the ℋ_∞ norm. The simple structure of these controllers allows the formulation of the loop-shaping objective as a convex optimization problem that can be solved numerically in a reliable way. Several examples are presented to illustrate the application of the proposed tuning technique and compare it with existing ones