Graph Representation And Distributed Control Of Lumped And Distributed Parameter System Networks

Abstract

Chemical plants are complex, integrated networks of individual process systems. The process system dynamics along with the interconnections among them make the task of controlling chemical plants challenging. Distributed control is a promising approach towards achieving plant-wide control of tightly integrated networks. The identification of sparsely interacting sub-networks in a given chemical network is key towards achieving superior performance from the distributed control structure. To this end, community detection algorithms have been adopted to determine the optimal decompositions for chemical networks by maximization of modularity. These algorithms are based on equation graph representations of the network. For lumped parameter system (LPS) networks, such representations are standard. Since chemical networks usually comprise lumped as well as distributed parameter systems (DPSs), this thesis aims at incorporating within the framework described above, the variables and topology of DPSs, to develop a unified framework to obtain optimal network decompositions (control structures) for distributed control. To this end, an equation graph representation for a generic DPS and a parameter which captures the strength of structural interactions among its variables analogous to relative degree in LPSs are proposed. A relationship is established between the length of the input-output path in the equation graph and the structural interaction parameter, which enables the incorporation of DPSs variables in the graph based community detection algorithms. Also, since in chemical networks, often the measurement of the entire state is not available and estimation of the unmeasured variables is a computationally expensive task, this thesis also addresses the problem of combined distributed state estimation and distributed control, using community detection for determining network decompositions for estimation as well as control.