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SUMMARY This work is devoted to the multiharmonic analysis of parabolic optimal control problems in a time-periodic setting. In contrast to previous approaches, we include the cases of different control and observation domains, the observation in certain energy spaces, and the presence of control constraints. In all these cases, we propose a new preconditioned MinRes solver for the frequency domain equations and show that this solver is robust with respect to the space and time discretization parameters as well as the involved ‘bad’ model parameters of the state equation. Copyright © 2012 John Wiley & Sons, Ltd.