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Fuzzy Boundary Control of Nonlinear Distributed Parameter Systems Through an Equivalent Punctual Control Form

Relying on the idea of formulating the problem of boundary control by means of equivalent punctual control problem, we present in this paper a novel design methodology of a fuzzy partial differential equation model based boundary geometric controller for nonlinear distributed parameter systems (DPSs). With regard to the distributed dynamics of DPSs, this control problem is formulated as a set-point reference tracking problem with an infinite characteristic index defined for a punctual output variable at a yields spatial position. To deal with this control design, it is first suggested to transform the boundary control problem to an equivalent in domain punctual control form by using Laplace transform in the spatial domain. Then, considering a punctual output, a weighted value of the variable, along the spatial domain, is defined as a controlled output. Processing the controlled output by means of geometric control rules and control objectives leads to the determination of the proposed fuzzy boundary geometric controller. Temperature gradient control in a thin non-isothermal catalytic reactor is considered as an application example to show the stabilizing performance of the developed control strategy.