Control of sequential subsystem processes interconnected with transport delays

A lumped-model representation for large distributed-process systems is considered, using simplified subsystem structures interconnected with delayed-output variables and controlled with delayed inputs. The formulation and control of such an overall multivariable system are studied using a state-variable representation, and techniques are developed for obtaining an optimal-control solution related to quadratic performance functionals. Simplified solutions based on a multilevel-type formulation of the extended-state system, and a multistage iterative process for incorporating the predicted optimal trajectory, are investigated. The methods are illustrated with the control of an interconnected sequence of second-order linear systems, containing output and control variable transport delays.