A systematic control strategy is proposed for optimal operation of plants containing integrated process units in the event of unit shutdowns or failures. This entails manipulating the degrees-of-freedom available during and after a shutdown in such a way that production is restored in a cost-optimal fashion while meeting all safety and operational constraints. In this work, we investigate the problem of coordinating various buffer tanks and recycle streams during the period of transition to minimize production losses. The problem is cast in a dynamic optimization framework. The case studies in our work are based on a simulation of a Kraft pulp mill where a process unit is shut down and taken off-line for a period of time, and is subsequently restored. Based on an estimate of the downtime, our proposed control system then computes and implements a set of optimal control trajectories that accommodates the shutdown. This work extends prior studies ([8], [24]) by considering in addition two key issues -inclusion of feedback mechanisms to counter uncertainty, and the development of a software-based modeling tool. The downtime estimate is a crucial parameter for performing the control calculations. This estimate will usually be based on past operational experience or on direct information about the prognosis of the shutdown. In practice, this estimate will not correspond exactly to the actual downtime; thus we consider re-optimization based on revised downtime estimates. The remainder of the trajectory is re-optimized from the current state of the system, and the controller performs what is essentially a mid-course correction. This feedback approach has considerable advantages over a multi-scenario optimization approach for dealing with uncertainty in the estimated downtime, in that the resulting control trajectories are less conservative. The performance of this re-optimization scheme is studied in this work under various failure scenarios. Uncertainty also exists due to model imperfections and unmeasured disturbances. We therefore account for this uncertainty by considering the trajectory optimization problem within an integrated nonlinear predictive control framework. The type of operation under consideration (response to partial shutdown conditions) is inherently unsteady in nature, and the control horizon as measured from the onset of the failure is fixed. Among the distinctive features of the controller are: a shrinking prediction horizon, an economics-driven objective function and the use of a nonlinear differential-algebraic equation-based model. The controller is also "event-cognizant" in the sense that explicitly known future events such as shutdowns and startups can be specified and accommodated within the prediction algorithm. Case studies demonstrating the performance of the overall feedback strategy are presented. In the course of this work, we developed a specialized software-based modeling tool that simplifies the tasks of representing, discretizing, and solving dynamic optimization problems. The main component of this tool is a domain-specific language named MLDO (Modeling Language for Dynamic Optimization). This tool is tailored to the representation of constructs specific to the dynamic optimization problem domain. Models written in MLDO are used as a precursors for generating intermediate AMPL-based models (discretized using an implicit Runge-Kutta method), which are subsequently solved using a large-scale nonlinear optimizer, IPOPT. / Thesis / Master of Applied Science (MASc)

This thesis presents new results on a few problems involving maximum flows. The first topic we explore is maximum flow network interdiction. The second topic we explore is reoptimization heuristics for rapidly solving an entire sequence of Maximum Flow Problems. In the Cardinality Maximum Flow Network Interdiction Problem (CMFNIP), an interdictor chooses R arcs to delete from an s-t flow network so as to minimize the maximum flow on the network induced on the undeleted arcs. This is an intensively studied problem that has nontrivial applications in military strategy, intercepting contraband and flood control. CMFNIP is a strongly NP-hard special case of the Maximum Flow Network Interdiction Problem (MFNIP), where each arc has an interdiction cost and the interdictor is constrained by an interdiction budget. Although there are several papers on MFNIP, very few theoretical results have been documented. In this talk, we introduce two exponentially large classes of valid inequalities for CMFNIP and prove that they can be separated in polynomial time. Second, we prove that the integrality gap of the commonly used integer linear programming formulation for CMFNIP is contained in the set Omega(|V| ^(1 e)) where |V| is the number of nodes in the network and e is in the interval (0,1). We prove that this result holds even when the linear programming relaxation is strengthened with our two classes of valid inequalities and we note that this result immediately extends to MFNIP. In the second part of this defense, we explore incremental algorithms for solving an online sequence of Maximum Flow Problems (MFPs). Sequences of MFPs arise in a diverse collection of settings including computational biology, finger biometry, constraint programming and real-time scheduling. To initiate this study, we develop an algorithm for solving a sequence of MFPs when the ith MFP differs from the (i-1)st MFP, for each possible i, in that the underlying networks differ by exactly one arc. Second, we develop maximum flow reoptimization heuristics to rapidly compute a robust minimum capacity s-t cut in light of uncertain arc capacities. Third, we develop heuristics to efficiently compute a maximum expected maximum flow in the context of two-stage stochastic programming. We present computational results illustrating the practical performance of our algorithms.