Multivariable Virtual Reference Feedback Tuning for Non-Minimum Phase Plants

Data-Driven Control Design by Prediction Error Identification for Multivariable Systems

“…In the Model Reference approach to the design, the closedloop performance is specified through a rational transfer matrix T d (q, η), known as the reference model. While the poles of T d (q, η) are typically fixed according to the desired closed-loop behavior, the numerators of the elements of T d (q, η) can optionally be parametrized by a vector η ∈ D η ⊂ R nη and let free to vary in order to increase the flexibility of the method, as it will become clearer in Section IV (see also [10] and [11]). The controller parameters are then tuned as the solution of the problem:…”

“…Using the concept of the ideal controller, it is possible to turn the control design problem into an identification problem of the system, without using a model for the process. For that purpose we will adapt the OCI method [2], [4], [3] to the case where the reference model is parametrized, following the idea presented in [11] for the VRFT method. This formulation is specially suitable for NMP processes.…”

“…Identification and inclusion of these zeros in the reference model is now an established and safer solution whether in direct adaptive control [8], [9] or data-driven control designs [10], [7], [11]. In [11], a solution is proposed to the NMP issue in the multivariable case using the VRFT (Virtual Reference Feedback Tuning) data-driven method with a flexible criterion, where identification of the NMP transmission zeros is achieved along with the controller parameters in an iterative least-squares procedure. The solution, however, presents a drawback: the reference model has to be diagonal (with identical elements along the diagonal in a first step and possible retuning with different elements).…”

“…Both diagonal and block-triangular reference model structures are considered. Similar to the solution proposed in [10], [11] for the design with VRFT, we propose a flexible criterion for the OCI such that the NMP transmission zeros and the optimal controller can be simultaneously identified.…”

The effects of disturbances in non-iterative data-driven controller design

“…The VRFT method was first introduced in Campi et al (2000) and has been extended to solve important problems as the control of NMP systems (Bazanella et al, 2012) and MIMO systems (Campestrini et al, 2016;Goncalves da Silva et al, 2018) as well as to different control strategies (Lecchini et al, 2001;Eckhard et al, 2018). Besides, it has been widely applied to real systems (Campestrini et al, 2016;Rojas et al, 2010).…”