A set-membership approach to direct data-driven control design for SISO non-minimum phase plants

In the context of direct data-driven design, we propose a controller design procedure on the basis of a set of experimental input/output data, with no identification of the plant model. The objective of the control problem is to make the closed-loop system to match the behavior of an assigned reference model as close as possible. As is well known, the presence of one of more non-minimum phase zeros in the plant transfer function makes the direct data-driven design procedure significantly harder since, no matter what is the considered approach among the ones proposed in the literature, the designed controller commonly leads to an unstable closed-loop system due to unstable pole-zero cancellations. In this paper we propose a new approach for performing the design of direct data-driven controller when the unknown plant may or may not have non-minimum phase zeros. The problem is formulated in the context of the set-membership estimation theory, and previous results from some ot the authors on errors-in-variables identification are exploited to compute the controller parameters. The effectiveness of the presented technique is demonstrated by means of two simulation examples.