A formulation for globally optimal controlled variable selection

Self-optimizing control (SOC) is a powerful tool to select controlled variables (CVs) so that when these variables are maintained at constant set-points, the entire process operation is automatically optimal or near optimal (self-optimizing) in spite of the presence of various uncertainties. Over a decade development, many SOC theories and methods have been developed to select optimal CVs. However, all these methods are based on local linearization of the process model at a nominally optimal operating point, hence referred to as local methods. Due to the nature of locality, existing SOC methods may cause a large performance loss when the feasible operation region is large and the process is highly nonlinear. In this paper, we propose a global approach to select optimal CVs for nonlinear processes so that the average loss over the entire feasible operation region is minimized. Firstly, the globally average loss minimization problem is formulated and a toy example is solved analytically to explain the difference between the global approach and other local methods. For more complex processes where an analytical solution is not tractable, a numerical approach is proposed to minimize the average loss globally. In the new approach, optimal CV selection is found by solving a regression problem to approximate the necessary conditions of optimality of the objective function. A case study on an exothermic reactor demonstrates the effectiveness of the new approach.