This research is aimed at the unification of design and control for high performance processes under uncertainty. It has two main objectives: . A decision-hierarchy for the integration of process design and control objectives under uncertainty . Mathematical programming formulations and solution procedures to make the integrated design and control optimization tractable. To achieve this goal, the PI proposes a decision hierarchy with three levels: dynamic modeling, design optimization and optimal quality standards. The research plan involves two main research activities: . Task-A: Mathematical Problem Decomposition for design under uncertainty . Task-B: Computational Advances for Integrated Design and Control
Intellectual Merit:
Tight risk and uncertainty metrics: The integrated design and control approach accurately quantifies the dynamic system resilience under realistic operation. Rigorous detection and resolution of worst-case uncertainty and disturbance scenarios are presented. Combinatorial Complexity: A novel problem decomposition segregates the integrated design and control into two levels of optimization. The planned stochastic design optimization with embedded control reduces massively problem size and complexity. Case studies demonstrate convergence of the method with existing mathematical programming. The methodology should significantly improve the tractability of integrated design and control problems. New Stochastic Optimization Algorithms: The PI also proposes novel optimization procedures specifically tailored for discontinuous and open-ended design optimizations. A stochastic genetic program with population learning acceleration combines the robustness of genetic algorithms with the speed of gradient-based mathematical programming.
Broader Impact:
Manufacturers in today's global networks must deliver products that consistently meet customer quality demands worldwide. Unavoidable variability in raw materials and operating conditions and tight product specifications make robust process operation a necessity for future economic viability. This work is expected to impact modern process operation in the following ways: Systematic decisions for robust processes: Our methodology will provide analytical guidelines for addressing different types of uncertainties with integrated design and control. Integration of design and control: The globalization of supply and demand networks will require novel design methods that enable manufacturers to develop and operate processes that consistently meet customer demands at unparalleled performance levels. High fidelity models to tightly quantify uncertainty and risk will empower U.S. industry to safely operate closer to performance limits. Taming the Combinatorial Complexity: Innovative ideas to overcome the open-ended design problems are expected to impact design activities for high performance processes like fuel cells, energy integration and optimal supply management in which tight satisfaction of operational constraints are critical.
The educational plan foresees the introduction of flexible design and control into the chemical engineering undergraduate curriculum, specialized undergraduate research projects (NSF REU-Site) specifically reaching out to underrepresented groups and providing synergistic opportunities for K-14 science and math teachers serving minorities in urban areas (NSF RET-Site). A dissemination plan foresees academic outlet via publications and professional channels.
In classical process design under uncertainty, it is customary to study steady state performance. However, a rigorous proof for a design to be flexible at steady state is of little value, when dynamic constraint violations may occur. Designing processes without considering feedback control could lead to arbitrary process overdesign or under performance. Therefore it is necessary to integrate design and control decisions simultaneously to maximize overall system performance in the presence of operational and model uncertainty (Figure 1). However, the simultaneous search for structural decisions and continuous design variables, optimization control structure, and controller tuning alongside process design exceeds the capability of most existing optimization algorithms. To overcome these challenges, we developed new problem formulations with embedded control optimization to reduce the combinatorial complexity of design and control integration. The effort for the embedded control optimization is computationally extremely efficient for two reasons: First, identification can be implemented sequentially with algorithms based on sequential least-squares fitting. Second, the computation of optimal control moves of linear state space systems admits an analytical solution. Hence, the embedded control drastically reduces the master problem size and complexity. The separation of model equations for design and uncertainties from control strategies is another advantage. Our method has been applied to more complex flowsheet problems, with large number of units, with more processing parameters. For the study of finding optimal reactor volume size and tray number of distillation columns in a plantwide isomerization process, we developed a mathematical model and applied our algorithm to find the best design specification which requires minimum capital and operating cost. An overview of the integrated design and control methodology is given in Figure 2. To calculate optimal control performance more efficiently, we adopted different identification methods based on moving horizon estimation. Using our methodology, we could calculate optimal trade-off between design specifications and control strategy with less expensive cost. The total CPU cost of the stochastic design optimization with embedded control was typically two to three orders of magnitude faster than the simultaneous optimization approach. The successful development of our methodology will have significant impact on modern process operation as follows 1. Systematic decisions for robust processes will provide analytical guidelines for addressing different types of uncertainties with integrated design and control. 2. The ability to tightly quantify uncertainty and risk to evolve the optimum design as proposed in this research will significantly alter the industrial practice of process design, control and operations. 3. High fidelity models to tightly quantify uncertainty and risk will empower industry to safely operate closer to performance limits.
