Generalized Global Self-Optimizing Control for Chemical Processes Part I. The Existence of Perfect Controlled Variables and Numerical Design Methods

Self-optimizing control (SOC) maintains the near-optimal operation of chemical processes by selecting appropriate controlled variables (CVs). However, most existing works still adopt linear combinations of measurements as the CVs, which inherit the invariant active-set assumption and leave the general achievable performance of the SOC unknown. In this series of works, we present the so-called generalized global SOC (g2SOC) approach. The g2SOC extends the concept of SOC to cover the entire operating space using general nonlinear CVs, without any restrictions on the active-set. In part I of this work, theoretical analysis of the g2SOC is introduced, where the existence of perfect global CVs is illustrated under proper technical conditions. Then, two numerical design methods for g2SOC are outlined: one is the regression-based approach, and the other is the optimization-based approach. These developments are illustrated through a numerical example and a CSTR case study, both of which demonstrate the superior performance of the g2SOC by using nonlinear CVs. In part II of this work, we deal with the algorithmic aspects of g2SOC, where efficient algorithms are developed for large-scale problems.