Design of PID controller satisfied sensitivity constraint and phase margin

The sensitivity constraint is an index of H_infin norm, and it is shown by some researches that using sensitivity is better to characterize the robustness of a system then using the stability margin. Up to now, there have been a lot of design methods of PID controller using directly the sensitivity constraint as the design index to be proposed, but they are yet difficult to applied and extended in engineering owing to they deal with much more complex computation. The PID design method presented by this paper uses still directly the sensitivity constraint as the design index, but by which the complex computation in the existed results is simplified and as the same times, the phase margin can be satisfied using the surplus freedoms. The validity of the presented method is illustrated by a design example.