Perturbation Methods for Modifier Adaptation with Quadratic Approximation

Real-time optimization (RTO) is a model-based technique that drives plants to optimal operating conditions. Modifier Adaptation (MA) is a class of methods that adjusts the optimization problem using gradient information. This enables the plant to reach the optimum operating point or batch trajectory without the need of a precise model which reduces the necessary modeling efforts. However, computing the gradients of the cost function or of the plant outputs with respect to the inputs online is a challenging task. Modifier Adaptation with Quadratic Approximation (MAWQA) integrates MA with Quadratic Approximation (QA), which helps mitigate the challenges of estimating gradients from noisy measurements by utilizing historical operating data. However, the distribution of these past operating points significantly affects the effectiveness of the MAWQA strategy. To address this issue in this contribution, new methods to compute probing points which lead to fast convergence to the optimum are proposed. The effectiveness of these methods is validated using the Williams-Otto reactor benchmark.