Evaluation of Set-Membership Approaches for Data-Driven Tuning of Two-Degree-of-Freedom Controllers

Set-Membership theory offers solutions to the data-driven controller tuning problem that do not rely on stochastic models of noises and disturbances. In this paper, two approaches are evaluated for the design of Two-Degree-of-Freedom (2DoF) controllers. They are based on Errors-in-Variables and Output-Error formulations, assuming unknown but bounded noise sequences. First, it is derived a setting to estimate from data controllers capable of approaching a given closed-loop reference model and a sensitivity transfer function. Then, the controller estimation problems are transformed in equivalent Set-Membership Errors-in-Variables and Output-Error identification setups. Finally, both approaches are evaluated on a numerical example and it is observed that a similar performance is obtained by the two methods, while the Output-Error setting is more than one hundred times faster.