Guaranteed Model Adequacy for Modifier Adaptation With Quadratic Approximation

Iterative real-time optimization methods like modifier adaptation based techniques are used to identify the real process optimum in the presence of structural and/or parametric plant-model mismatch. For modifier adaptation based techniques, as a prerequisite, the a priori process model has to satisfy the model adequacy conditions, i.e. positive definiteness of the Hessian as only the gradients are corrected based on the available measurement information. Modifier adaptation with quadratic approximation (MAWQA) is a powerful real-time optimization tool in which either the surrogate quadratic approximation model or the a priori known process model with gradient correction is chosen for optimization based on how well they represent the process measurements. This can lead to the selection of a quadratic model which does not satisfy the model adequacy conditions and can cause undesired oscillations. It is therefore necessary to make sure that the chosen model is adequate. In this paper, we propose to use convex quadratic approximation and thereby to ensure satisfaction of the model adequacy conditions and the convergence to the real process optimum. We demonstrate the performance of the proposed MAWQA with guaranteed model adequacy (GMA) scheme using a chemical engineering case study.