Differential Geometry-Based Adaptive Nonlinear Control Law: Application to an Industrial Refinery Process

Abstract

In this contribution, an extended generic model control (EGMC) law is proposed based on differential geometry theory. This multivariable nonlinear control system requires the knowledge of the internal state of the process. To cope with this, an adaptive control scheme is formulated here. This adaptive nonlinear control law combines the EGMC with the Luenberger-type nonlinear state estimator (LNSE). Deriving the control law and the state estimator, the stability properties of the EGMC, LNSE and the combined EGMC-LNSE structure are developed. The application and performance of the proposed adaptive EGMC-LNSE control law are finally illustrated by a simulated industrial refinery process (i.e., debutanizer). The representative column has 169 state variables, and it was operated in the province of Alberta, Canada. It is surprising to note that the LNSE scheme aims to estimate a few states that are solely required for the controller based on only two component balance equations. As a consequence, there exists a significant structural discrepancy and despite it, the proposed nonlinear controller shows its superiority over the multivariable dynamic matrix controller.