(748h) Thin Falling Film Layer Monitoring and State Estimation Via Discrete Kuramoto-Sivashinsky Observer and Kalman Filter

Kuramoto-Sivashinsky equation (KSE) as a fourth order nonlinear partial differential equation (PDE) has been widely used as model for description of various complex phenomena, such as falling film fronts, unstable flame fronts, phase turbulence in Belousov-Zhabotinsky reaction diffusion and interfacial instabilities between multiple viscous phases [1-2]. Considering the four-order spatial derivative term and nonlinear multiplication term of the state and its first-order spatial derivative, solving this distributed fourth-order parabolic KSE is not a trivial task, which poses a challenge for its associated observer and state estimation design [3-5]. With the understanding that it is not feasible and practical to install distributed sensors to monitor the film layer propagation evolution due to given physical constraints and equipment costs, it is of significant interest to propose boundary applied discrete observer for state monitoring and estimation that can be easily realized in the state-of-the-art digital computing devices.

This work develops a discrete close-form solution for linearized infinite-dimensional Kuramoto-Sivashinsky partial differential equation (PDE) by solving for the four-by-four-matrix-form resolvent operator in this distributed parameter system setting. Furthermore, since the Euler discretization framework cannot avoid spatial and temporal approximation and/or induce numerical instability, energy preserving symmetric in time Crank-Nicolson integration method is utilized without any spatial approximation nor model reduction of the underlying KS linear PDE model [6-7]. Based on this, a four-by-four-matrix-form resolvent operator is derived [8], from which a discrete Luenberger [9] is designed for thin falling film layer monitoring. In order to consider the noise appearing in the state and output measurements, discrete Kalman filter is designed for linear Kuramoto-Sivashinsky PDE. Finally, different simulation studies which include different noise levels and/or input signals will be presented to verify performances of the proposed method.

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