Extension of modifier adaptation for controlled plants using static open-loop models

Abstract

Model-based optimization methods suffer from the limited accuracy of the available process models. Because of plant-model mismatch, model-based optimal inputs may be suboptimal or, worse, unfeasible for the plant. Modifier adaptation (MA) overcomes this obstacle by incorporating measurements in the optimization framework. However, the standard MA formulation requires that (1) the model satisfies adequacy conditions and (2) the model and the plant share the same degrees of freedom. In this article, three extensions of MA to problems where (2) does not hold are proposed. In particular, we consider the case of controlled plants for which the only a model of the open-loop plant is available. These extensions are shown to preserve the ability of MA to converge to the plant optimum despite disturbances and plant-model mismatch. The proposed methods are illustrated in simulation for the optimization of a CSTR.

Modifier Adaptation for Real-Time Optimization—Methods and Applications

“…In this case, the plant inputs are the controller setpoints r, while the model inputs are the manipulated variables u. Three alternative MA extensions have recently been proposed to optimize a controlled plant using a model of the open-loop plant [50]. The three extensions use the cost and constraint gradients of the plant with respect to the setpoints r:…”

“…The second approach, labelled "Method UU", solves the optimization problem for u, and computes the modifiers in the space of u. As shown in [50], the three extensions preserve the MA property of reaching a KKT point of the plant upon convergence.…”

“…(a) The original dual ISOPE algorithm [7,63] estimates the gradients by FDA according to (50) and introduces a constraint that prevents ill-conditioning in the gradient estimation. At the kth RTO iteration, the matrix…”

“…(b) Gao and Engell [14] proposed a MA scheme that (i) estimates the gradients from the current and past operating points according to (50), and (ii) enforces the ill-conditioning duality constraint (72). However, instead of including the duality constraint in the optimization problem, it is used to decide whether an additional input perturbation is needed.…”

“…The approach was labeled Iterative Gradient-Modification Optimization (IGMO) [80]. (c) Marchetti et al [64] considered the dual MA scheme that estimates the gradients from the current and past operating points according to (50). The authors showed that the ill-conditioning bound (71) has no direct relationship with the accuracy of the gradient estimates, and proposed to upper bound the gradient-error norm of the Lagrangian function:…”