Optimal Controller Identification for multivariable non-minimum phase systems

This work deals with data-driven control for non-minimum phase (NMP) systems, where the goal is to design a controller for a plant whose model is unknown by using a batch of input–output data collected from it. The approach is based on the Model Reference paradigm, where a transfer function matrix – the reference model – is used to specify the desired closed-loop performance. The NMP systems issue in Model Reference approaches is a well-known problem in control literature and it is no different in data-driven methods. This work explains how to adapt the formulation of the Optimal Controller Identification (OCI) method to cope with this class of systems. Considering a convenient parametrization of the reference model and a flexible performance criterion, it is possible to identify the NMP transmission zeros of the plant along with the optimal controller parameters, as it will be shown. Both diagonal and block-triangular reference model structures are treated in detail. Simulation examples show the effectiveness of the proposed approach.