Assessment and Future Directions of Nonlinear Model Predictive ...

Distributed Model Predictive Control of Large-Scale Systems 593many situations, the simple interconnection of these unit-based control configurationsachieves unacceptable closed-loop performance. To illustrate this point,consider the supercritical fluid extraction process (SFE) described in [14, 15].The SFE process consists of four main units–the extractor, stripper, reboiler andtrim cooler. The SFE process is characterized by significant coupling betweenthe different units and is known to represent a challenging plantwide controlproblem. A fixed decentralized control configuration, based on a physical decompositionof the plant, is assumed. A schematic of the SFE plant with thecontrol divisions is shown in Figure 1. In the decentralized control configurationtherearethreeMPCs,oneforeachcontrolsubsystem.ThefirstMPCmanipulatesthe solvent flowrate (S) to the extractor to control the raffinate composition(x ipaR) at the outlet of the extractor. The second MPC manipulates the reflux andboilup flow rates (L, V ) to control the top and bottom compositions in the stripper(x ipaD,xipa B). The third MPC manipulates the shell tube temperature (T sh) inthe trim cooler to control the temperature of the solvent entering the extractor(T S ). All inputs are constrained to lie between an upper and lower limit. In thecentralized MPC framework, a single MPC controls the whole plant.In the decentralized MPC framework, the interconnections between the unitsare ignored. Consequently, the setpoint tracking performance of outputs x ipaRand x ipa exhibits large tracking errors. Also, the upper bound constraint on theDsolvent flow rate S to the extractor is active at steady state (see Figure 3).Therefore, the setpoint is unreachable under decentralized MPC. CentralizedMPC, on the other hand, tracks the new setpoint with much smaller trackingerrors. None of the input constraints are active at steady state. Quantitatively,centralized MPC outperforms decentralized MPC by a factor of 350 (Table 1)basedonmeasuredclosed-loopperformance.In most cases, however, centralized control is not a viable plantwide controlframework. To the best of our knowledge, no large-scale centralized modelsare available today in any field. Operators of large, interconnected systems (anentire chemical plant, for instance) view centralized control as monolithic andinflexible. With many plants already functional with some form of decentralizedMPCs, practitioners do not wish to engage in complete control system re-designas would be necessary to implement centralized MPC. While a decentralizedphilosophy creates tractable modeling and control problems, choosing to ignorethe interconnections between subsystems may result in poor systemwide controlperformance.A recent article [5] points out that there has been a strong tendency in thecontrol community to look for centralized control solutions; however, the exponentialgrowth of the centralized control law with system size makes its implementationunrealistic for large, networked systems. The only recourse in suchsituations is to establish a “divide and conquer” strategy that allows one tobreak the large-scale control problem into several smaller subproblems. The underlyingchallenge in any “divide and conquer” control strategy is to establisha protocol for integrating different components of the interconnected system toachieve good overall performance.