We propose an adaptive output feedback framework to address the output feedback control problem for transport-reaction processes with unknown parameters. The mathematical description of these processes by nonlinear parabolic partial differential equation (PPDE) systems from the basis for our effort. Such systems frequently appear in chemical and advanced materials production industries, e.g., packed and fluidized bed reactors in refinery and petrochemical processes, polymerization and crystallization processes, and chemical vapor deposition in microelectronic fabrication processes. The infinite-dimensional representation of PPDE systems in appropriate functional spaces can be decomposed to a finite-dimensional slow (and possibly unstable) and infinite-dimensional fast (and stable) subsystems . Due to the existence of a time-scale separation between slow and fast subsystems we can approximate the PPDEs by a finite number of ordinary differential equations (ODEs). This low-dimensional approximation (that can be employed as the basis for model-based adaptive output feedback control design) is constructed by discretizing the PPDEs using Galerkin’s method. The required basis functions for such discretization are obtained by applying adaptive proper orthogonal decomposition (APOD) to the spatial profiles of the system states during process evolution. Obtaining such highly informative profiles might not be feasible owing to limited availability of sensors which frequently sample the entire process domain. To overcome such limitation, we use a PDE-based Luenberger-type dynamics observer to reconstruct the spatial profiles by employing measurement outputs from a set of moving sensors . The effectiveness of the proposed adaptive control approach is illustrated on the thermal regulation problem of a tubular reactor where an irreversible reaction takes place in the presence of unknown diffusivity coefficient and reaction rate constant.
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