Multirate minimum variance control design and control performance assessment: A data-driven subspace approach

This paper discusses minimum variance control (MVC) design and control performance assessment based on the MVC-benchmark for multirate systems. In particular, a dual-rate system with a fast control updating rate and a slow output sampling rate is considered, which is not uncommon in practice. A lifted model is used to analyze the multirate system in a state-space framework and the lifting technique is applied to derive a subspace equation for multirate systems. From the subspace equation, the multirate MVC law and the algorithm are developed to estimate the multirate MVC-benchmark variance or performance index. The multirate optimal controller is calculated from a set of input/output (I/O) open-loop experimental data and, thus, this approach is data-driven since it does not involve an explicit model. In parallel, the presented MVC-benchmark estimation algorithm requires a set of open-loop experimental data and close-loop routine operating data. No explicit models, namely, transfer function matrices, Markov parameters, or interactor matrices, are needed. This is in contrast to traditional control performance assessment algorithms. The proposed methods are illustrated through a simulation example.