Optimal Measurement Selection and Principal Component Analysis-Based Combination as Controlled Variables

Abstract

This work presents a methodology for defining the controlled variables based on two interrelated procedures. On the one hand, a linear combination of the selected measurements is performed through a combination matrix developed from the principal component analysis theory. On the other hand, the optimal sensor selection is formulated as a multiobjective optimization problem, which is efficiently solved via genetic algorithms. Three functional costs are considered, which provide a trade-off between controllability, interaction, and complexity of the resulting structures. The overall design procedure is based on steady-state information of the process. Moreover, the proposed formulation allows easily analyzing the control reconfiguration problem, particularly when potential modifications of the nominal sensor set are taken into account. For each considered scenario, a screening of the reconfiguration alternatives can be done from the obtained Pareto set. Then, the solutions of interest could be computationally simulated in order to choose the most convenient option. In this work, all the designs are implemented as conventional decentralized control structures based on multiple PI feedback loops, supplemented with the combination matrix. The latter enables the use of a number of sensors equal to or greater than the number of available actuators. These additional sensors can provide notable benefits to the dynamic performance of the system as well as flexibility to the design process, offering many more alternatives for an eventual reconfiguration action than the conventional square solutions. In addition, the reconfiguration process features reduced complexity because the controlled and manipulated variable structure remains unchanged when modifications in the sensor set occur. A rigorous nonlinear model of a bio-ethanol processor system coupled with a proton exchange membrane fuel cell is proposed as a case study.