DBFact applied to minimum variance performance assessment for nonminimum phase multivariate systems from closed-loop data

This paper introduces an approach for determining a minimum variance control (MVC) benchmark for nonminimum phase (NMP) multi-input multi-output (MIMO) systems using closed-loop operational data. The MVC benchmark is derived from the MVC law of DBFact factorization introduced by Lima, Trierweiler, and Farenzena. Unlike other factorization methods, DBFact offers advantages such as non-iterative computation and ensuring internal stability of the MVC law. This approach considers the inherent directionality of NMP MIMO systems, enhancing the reliability of the control performance index. However, the original method relies on prior knowledge of the process model. To overcome this limitation, this paper proposes a method for calculating the MVC benchmark when prior knowledge is absent. It introduces a MIMO system identification strategy employing minimally invasive signal tests. The methodology is evaluated across various control conditions using a quadruple-tank plant with additional time delays. The study emphasizes the importance of directionality in assessing MIMO system performance, particularly in evaluating individual loop performances. Results demonstrate the identification procedure's effectiveness in accurately calculating the proposed MVC benchmark, even with a mere 1% increase in output variance considered.