Recursive Estimation of Modifiers for Real-Time Optimization with Gradient Adaptation

Abstract

Because of the uncertainties during the design phase of processes, the drift of process parameters during the plant lifetime and exogenous factors affecting the supply or demand of materials, the operation of continuous processes needs to be updated to track the economically optimal conditions that maximize the profit. For this reason, the practice of RealTime Optimization (RTO) has been established in the process industry to assist in selecting the setpoints to be used in the process. Real Time Optimization works by updating the setpoints of a plant using a model. To cope with the inevitable inaccuracy of the available models, various techniques have been developed, most notably parameter adaptation and Modifier Adaptation (MA). MA corrects the process model by bias and gradient correction terms for the variables of interest (typically the cost function and constraints), such that the RTO algorithm is guaranteed to reach a true (local) plant optimum upon convergence. The most crucial part in RTO-MA schemes is the estimation of the gradients, which requires the evaluation of the plant response at several points and determines the overall complexity of the RTO-MA problem. The goal of this contribution is to show how a recursive estimator that shares some similarities with the Kalman filter can be used to estimate the modifiers.