Development and application of an automatic tool for the selection of control variables based on the self-optimizing control methodology

Abstract

-Rules for control structure design for industrial processes have been extensively proposed in the literature. Some model-based methodologies have a sound mathematical basis, such as the self-optimizing control technology. The procedure can be applied with the aid of available commercial simulators, e.g., PRO/II TM and AspenPlus®, from which the converging results are obtained more suitably for industrial applications, lessening the effort needed to build an appropriate mathematical model of the plant. Motivated by this context, this work explores the development and application of a tool designed to automatically generate near-optimal controlled structures for process plants based on the self-optimizing control technology. The goal is to provide a means to facilitate the way possible arrangements of controlled variables are generated. Using the local minimum singular value rule supported by a modified version of a branch-and-bound algorithm, the best sets of candidate controlled variables can be identified that minimize the loss between real optimal operation and operation under constant set-point policy. A case study consisting of a deethanizer is considered to show the main features of the proposed tool. The conclusion indicates the feasibility of merging complex theoretical contents within the framework of a user-friendly interface simple enough to generate control structures suitable for real world implementation.

Metamodel-Based Numerical Techniques for Self-Optimizing Control

“…The criterion function for the branch-and-bound used was the minimum singular value, which fortunately has a monotonic property. For a detailed proof of it, refer to Silva et al and Cao et al…”

“…The gradients and Hessians with respect to the reduced space problem were obtained using the DACE toolbox and the expression derived in this work. It was necessary in this case study, to do a slight modification in the Hessian matrix J uu , to make it positively definite, performing a modified Cholesky factorization, as done in the past by Silva et al Further explanation on how this factorization is done can be found on the work of Silva et al . and Nocedal and Wright…”

“…As a result, all subsets on this direction including X m can be "pruned" immediately. In this work, similarly as in Silva et al, 47 was used the bidirectional branch-and-bound proposed by Cao and Kariwala. 45 The search for the best sets of controlled variables is carried out in both directions, which generates a higher efficiency if compared with unidirectional branch-and-bound algorithms.…”

“…For the Hessian approximation: Silva et al, 47 in order to avoid the problem stated before, used the Akima cubic spline and the bicubic spline to evaluate the gradients and Hessians, respectively. However, as stated in their work, one disadvantage of using cubic splines is when there is an outlier in the region studied, jeopardizing the evaluation in some cases.…”

Engenharia no Século XXI - Volume 2

“…Machado (2009) avaliou a influência das variáveis operacionais, como pressão de operação e razão de refluxo, na separação das misturas de óleos lubrificantes, enquanto Orlando (2007) obteve as condições operacionais ótimas em uma coluna contendo recheio estruturado. O mesmo software foi aplicado na modelagem de um trem de destilação para determinação de condições operacionais apropriadas (SILVA, 2016), e no estudo de caso de uma torre de destilação para implementação de controle automático (SILVA et al, 2017).…”