Interaction of Design and Control: Optimization with Dynamic Models

Process design is usually approached by considering the steady-state performance of the process based on an economic objective. Only after the process design is determined are the operability aspects of the process considered. This sequential treatment of the process design problem neglects the fact that the dynamic controllability of the process is an inherent property of its design. This work considers a systematic approach where the interaction between the steady-state design and the dynamic controllability is analyzed by simultaneously considering both economic and controllability criteria. This method follows a process synthesis approach where a process superstructure is used to represent the set of structural alternatives. This superstructure is modeled mathematically by a set of diierential and algebraic equations which contains both continuous and integer variables. Two objectives representing the steady-state design and dynamic controlla-bility of the process are considered. The problem formulation thus is a multiobjective Mixed Integer Optimal Control Problem (MIOCP). The multiobjective problem is solved using an-constraint method to determine the noninferior solution set which indicates the trade-oos 1 between the design and controllability of the process. The (MIOCP) is transformed to a Mixed Integer Nonlinear Program with Diieren-tial and Algebraic Constraints (MINLP/DAE) by applying a control parameterization technique. An algorithm which extends the concepts of MINLP algorithms to handle dynamic systems is presented for the solution of the MINLP/DAE problem. The MINLP/DAE solution algorithm decomposes the problem into a NLP/DAE primal and MILP master problems which provide upper and lower bounds on the solution of the problem. The MINLP/DAE algorithm is implemented in the framework MINOPT which is used as the computational tool for the analysis of the interaction of design and control. The solution of the MINLP/DAE problems is repeated with varying values of to generated the noninferior solution set. The proposed approach is applied to three design/control examples: a reactor network involving two CSTRs, an ideal binary distillation column, and a reac-tor/separator/recycle system. The results of these design examples quantitatively illustrate the trade-oos between the steady-state economic and dynamic controllability objectives.