Selection of controlled variables (CVs) has recently gained wide attention, because of its paramount importance in real-time optimization (RTO) of plant operation. The so-called self-optimizing control (SOC) strategy aims to select appropriate CVs so that when they are maintained at constant setpoints, the overall plant operation is optimal or near optimal, despite various disturbances and uncertainties. Recent progresses of the SOC methodology have focused on finding linear combinations of measurements as CVs via linearization of the process around its nominal operating point, which results in the plant operation being only locally optimal. In this work, the concept of necessary conditions of optimality (NCO) is incorporated into CV selection to overcome the "local" shortcoming of existing SOC methods. Theoretically, the NCO should be selected as the optimal CV, although it may not be practical because of the measurability of the NCO. To address this issue, in this work, CVs are selected to approximate unmeasured NCO over the entire operation region with zero setpoints to achieve near-optimal operation globally. The NCO approximation CVs can be obtained through any existing regression approaches. Among them, two particular regression methodsnamely, least-squares and neural networksare adopted in this work as an illustration of the proposed methodology. The effectiveness and advantages of the new approach are demonstrated through two case studies. Results are compared with those obtained by using existing SOC methods and an NCO tracking technique.

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 minimize 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 linearized 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. First, we suggest representing 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, and 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 to be very similar to one of the 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 two simulated examples, where the effectiveness of the proposed algorithms is demonstrated.

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