On Asymptotic Global Error Estimation and Control of Finite Difference Solutions for Semilinear Parabolic Equations

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential equations. The approach presented there is combined with an estimation of the PDE spatial truncation error by Richardson extrapolation to estimate the overall error in the computed solution. Approximations of the error transport equations for spatial and temporal global errors are derived by using asymptotic estimates that neglect higher order error terms for sufficiently small step sizes in space and time. Asymptotic control in a discrete $L_2$-norm is achieved through tolerance proportionality and uniform or adaptive mesh refinement. Numerical examples are used to illustrate the reliability of the estimation and control strategies

Design, analysis and validation of a simple dynamic model of a submerged membrane bioreactor

In this study, a simple dynamic model of a submerged Membrane BioReactor (sMBR) is proposed, which would be suitable for process control. The system dynamics is first analyzed showing the existence of three different time scales. The existence of slow-fast dynamics is central to the development of a dedicated parameter estimation procedure. The proposed model structure is validated using realistic simulation data from a detailed simulator built in a well-established environment, namely GPS-X. Finally, a nonlinear model predictive control is designed to illustrate the potential of the developed model within a model-based control structure. The problem of water treatment in a recirculating aquaculture system is considered as an application example

Stabilizing the cake evolution for a class of submerged membrane bioreactors using a Lyapunov controller

International audienc

Corrigendum to “Design, analysis and validation of a simple dynamic model of a submerged membrane bioreactor”

International audienceIn this study, a simple dynamic model of a submerged Membrane BioReactor (sMBR) is proposed, which would be suitable for process control. The system dynamics is first analyzed showing the existence of three different time scales. The existence of slow-fast dynamics is central to the development of a dedicated parameter estimation procedure. The proposed model structure is validated using realistic simulation data from a detailed simulator built in a well-established environment, namely GPS-X. Finally, a nonlinear model predictive control is designed to illustrate the potential of the developed model within a model-based control structure. The problem of water treatment in a recirculating aquaculture system is considered as an application example