| We introduce a modeling framework for studying dynamics, distributed control, and optimization of complex chemical process networks. Stability and optimality follow as a consequence of how the networks are put together and how they are connected with boundary conditions or other networks. Decentralized control systems mirror the physical systems they control. By considering only the topology of the system and basic conservation principles, a result analogous to Tellegen's Theorem of electrical circuit theory is produced. Using this result and passivity theory, a network is shown under certain conditions to converge to a unique solution. The concavity of the entropy function is used to define a storage function for passivity design. The proposed storage function is closely related to the Gibbs tangent plane condition. Also, under similar conditions, we show that the network is self-optimizing in that the entropy production is minimized. The sufficient conditions for stability and optimality can be interpreted as dissipation conditions for generation and flow. We also develop flow and inventory control schemes for process units and networks. Examples of networked applications are investigated to illustrate these theoretical results. These models include simple chemical processing units (e.g. reactors, flashes), a plant-wide process control system, supply chains, and a biological process known as angiogenesis. |
