Robust data driven control in frequency domain: A model-free approach

Data-driven control methods in the frequency domain commonly require the determination of controller structure. Relaxing such restriction in the proposed algorithm, the controller design is transformed into an optimization problem, based on the υ-gap Metric criterion. By defining a desired stability margin and the desired frequency response of the controller, a criterion is determined to characterize a family of controllers. Therefore, a model free procedure is proposed to determine a family of controllers, by taking the plant frequency response and the desired stability margin. On the other hand, by adopting a new index, presented in this paper, the designer can determine the optimal controller, based on the implementation conditions. Another advantage of the proposed method is its applicability to uncertain Multi-Input Multi-Output (MIMO) systems. The loop performance in the presented algorithm can be also enhanced by appropriate selection of weighting matrices in a loop shaping procedure. Two examples are also presented to demonstrate the effectiveness of the method for multi-variable non-square uncertain systems, including a practical example of a purely delayed system.