Global approximation of self-optimizing controlled variables with average loss minimization

Self-optimizing control (SOC) constitutes an important class of control strategies for real-time optimization (RTO) of chemical plants, by means of selecting appropriate controlled variables (CVs). Within the scope of SOC, this paper develops a CV selection methodology for a global solution which aims to minimise the average economic loss across the entire operation space. A major characteristic making the new scheme different from existing ones is that each uncertain scenario is independently considered in the new solution without relying on a linearised model, which was necessary in existing local SOC methods. Although global CV selection has been formulated as a nonlinear programming (NLP) problem, a tractable numerical algorithm for a rigorous solution is not available. In this work, a number of measures are introduced to ease the challenge. Firstly, we suggest to represent the economic loss as a quadratic function against the controlled variables through Taylor expansion, such that the average loss becomes an explicit function of the CV combination matrix, a direct optimizing algorithm is proposed to approximately minimize the global average loss. Furthermore, an analytic solution is derived for a suboptimal but much more simplified problem by treating the Hessian of the cost function over the entire operating space as a constant. This approach is found very similar to one of existing local methods, except that a matrix involved in the new solution is constructed from global operating data instead of using a local linear model. The proposed methodologies are applied to three simulated examples, where the effectiveness of proposed algorithms are demonstrated.