Assessment and Future Directions of Nonlinear Model Predictive ...

592 A.N. Venkat, J.B. Rawlings, and S.J. Wrightprocedure was described. The opportunity presented for cross-integration withinthe MPC framework and potential requirements and benefits of such technologyhas been discussed in [4, 7, 9].2 MotivationConsider the distillation column described in [12, p. 813]. Tray temperatures actas inferential variables for composition control. The outputs y 21 ,y 7 are the temperaturesof trays 21 and 7 respectively and the inputs L, V denote the refluxflowrate and the vapor boilup flowrate to the distillation column. Two SISO PIDcontrollers with anti-reset windup are used to control the temperatures of thetwo trays. The implications of the relative gain array (RGA) elements on controllerdesign has been studied in [18]. While the RGA for this system suggestspairing L with y 21 and V with y 7 , we intentionally choose a bad control variable–manipulated variable pairing. PID-1 manipulates V to control y 21 .PID-2controlsy 7 by manipulating L. It will be shown later that unlike cooperation-basedformulations, decentralized or communication-based strategies cannot repair thiskind of bad design choice. The PID controllers are tuned employing the rulesdescribed in [12, p. 531]. The system exhibits unstable closed-loop behavior dueto the poor manipulated variable–control variable pairing. Expectedly, decentralizedMPC does not fare any better. For such a small control problem, the fixis well known and obvious; switching the manipulated variable–control variablepairing gives much improved performance (though suboptimal) with the twodecentralized PID and MPC controllers.Make up CO2FxFSubsystem 1FlashExtractorxFsLx ipaDStrippingColumnSubsystem 2SySRx ipaRTSReboilerTshFwTrim CoolerSubsystem 3Bx ipaBFig. 1. Supercritical fluid extraction (SFE) process. Supercritical CO 2 is used to extractiso-propyl alcohol (ipa) from a dilute aqueous solution.In a chemical plant with a network of interconnected units, the choice of whichmanipulated variable(s) to pair with which control variable(s) is a complicatedone. Often, the allocation of the set of control variables and corresponding manipulatedvariables is dictated by physical and/or operational constraints. In