The paper presents an efficient procedure for synthesizing PID controllers so as to maximize Smith’s vector stability margin, i.e., to minimize the H∞ norm of the sensitivity function, while ensuring specified values of the phase margin and gain crossover frequency. In this way, a trade-off between dynamic performance and robustness is achieved. The considered problem would be hard to solve with existing techniques; the suggested method, instead, leads to the desired result with remarkable computational simplicity, as shown by meaningful examples.
