Real-Time Optimization via Modifier Adaptation using Partial Plant Models

Abstract

Abstract Modifier adaptation is a real-time optimization method that has the ability to reach the plant optimum upon convergence despite the presence of uncertainty in the form of plant-model mismatch and disturbances. The approach is based on modifying the cost and constraint functions predicted by the model by means of appropriate first-order correction terms. The main difficulty lies in the fact that these correction terms require the plant cost and constraint gradients to be estimated from experimental data at each iteration. Although the model used can support a significant level of approximation, it must satisfy the following two requirements: (i) a model adequacy condition related to the second-order optimality conditions must be valid at the plant optimum, and (ii) the model must have the same input variables as the plant. In this paper, we consider the case where (ii) is not verified because only a partial or incomplete model is available. We propose to approximate the unmodeled part of the system by a linear model that is identified using the same excitation that is used in modifier adaptation for gradient estimation. The approach is illustrated through the simulated example of a reaction-separation system with recycle.