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In classical controller design, closed-loop performance specifications arise naturally as constraints on restricted frequency bands. This leads to a difficult design problem, which is currently circumvented by heuristic techniques. In this paper, we develop a nonsmooth progress function algorithm which enjoys features similar to exact penalization strategies to solve the problem. This allows us to compute locally optimal solutions to the frequency shaping control design problem. The new technique is highly efficient, as we demonstrate by way of two case studies, a large dimension power system, and a flexible telescope.

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We present a method to efficiently compute locally optimal feedback controllers for synthesis problems formulated in the time-domain. We minimize a time-domain performance objective subject to state or input time-domain constraints. The possibility to include state or input constraints in the design is very appealing from a practical point of view, in particular for plants subject to operational limits as input saturations. Our method is based on a nonsmooth minimization technique, which can handle time-domain constraints as hard constraints.For model-based designs, a stability constraint can also be handled as a hard constraint. The validity and efficiency of the approach are demonstrated through a variety of numerical tests with comparisons with a state-of-the-art technique in constrained optimization.