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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.

PI controllers for first-order time-delayed processes can be designed on the basis of a normalized model according to open-loop frequency-domain specifications. To this purpose, it is convenient to refer to the charts representing the loci of constant stability margins and cross-over frequencies in the plane of normalized parameters. It is shown how the designer can avail himself of these charts to easily evaluate the effects of changes in the process parameters and, thus, control system robustness. In particular, the situation corresponding to the least stability margin is identified together with the related cross-over frequency. The procedure is illustrated with the aid of representative examples.

This paper is concerned with the problem of controlling the molten metal level in continuous casting processes with particular reference to high-speed slab casters with large-size mold. The main objectives to achieve in these cases are robust stability and good disturbance rejection: the first derives from the rather large plant perturbations caused by the metal flow, whereas the second refers to the sudden drops of clogged material in the mold. To this purpose, the parameters of a standard PID controller are tuned so as to meet the desired time response characteristics and to ensure a sufficient stability margin for all possible plant models. The results obtained show the validity of the proposed procedure.