Plantwide control design using latent variables: An integration between control allocation and a measurement combination approach

LUPPI, P.A.; RODRÍGUEZ DEL PORTAL, S.; BRACCIA, L.; ZUMOFFEN, D.

JOURNAL OF PROCESS CONTROL

ELSEVIER SCI LTD

Año: 2022 vol. 120 p. 159 - 176

0959-1524

This paper presents a plantwide control design methodology based on anovel structure which consists of a decentralized strategycomplemented by a control allocation (CA) module and a measurementcombination (MC) block. Taking into account a principal componentsanalysis (PCA) selection approach, the CA and MC modules perform adimensional reduction of the original input–output variable spacein order to obtain sets of latent variables (or principal components)as control actions and controlled variables. The use of principalcomponents in the controller design provides several interestingfeatures given that: (i) the conditioning of the subsystem to becontrolled can be improved, (ii) when performing combinations ofvariables, the CA and MC modules act as steady-state decouplers andthus an apparently diagonal process is obtained, which favors thereduction of the variables interaction and the pairing problem isautomatically solved, and (iii) they allow to naturally handlenonsquare systems. The proposed design procedure is implementedthrough a multiobjective bilevel mixed-integer nonlinear programming(BMINLP) optimization problem. The leader problem is based on theminimization of three functional costs: 1- the well-known sum ofsquared deviations (SSD) index, 2- the number of selected manipulatedvariables (actuators), and 3- the number of selected measurements(sensors). The inner optimization minimizes the relative gain arraynumber (RGAN). This provides a good trade-off between the degree ofconditioning/controllability and the complexity/cost of the resultingsystem. This problem is efficiently solved through genetic algorithmsand allows to perform: (i) the selection of the manipulated variables(actuators) and the measurements (sensors) to be used, (ii) thecomputation of the matrices that characterize the CA and MC modules,and (iii) the stability analysis of the multivariable controlstructure. The overall design procedure only requires steady-statemodels of the process. The Tennessee Eastman case study is consideredfor the simulation and performance evaluation of the proposedsolutions.p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }