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Estimation of the clogging time of linear filters based on experimentally determined particle-size distribution function

Baran B., Domański Z.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2006

Vol. 5, nr 1

5-8

Several mathematical models have been designed to described the clogging process in porous media. Most of models use the continuum scale. Because of inherent heterogeneity and interconnectivity existing in porous media several phenomena occurring at the pore-scale cannot be modeled effectively at the continuum scale. The aim of this work is to use experimentally observed distributions of pores and particles sizes to obtain qualitative and predictive results of clogging filter time τ. For bundle of linear pores we computed the clogging time distribution:P( τ ) ≈ (1/ τ)5 / 4 exp[-(1/ τ )1/ 4 ].

Numerically robust synthesis of discrete-time H[infinity] estimators based on dual J-lossless factorisations

Suchomski P.

Control and Cybernetics

2003

Vol. 32, no 4

761-802

An approach to the numerically reliable synthesis of the H[infinity] suboptimal state estimators for discretised continuous-time processes is presented. The approach is based on suitable dual J-lossless factorisations of chain-scattering representations of estimated processes. It is demonstrated that for a sufficiently small sampling period the standard forward shift operator techniques may become ill-conditioned and numerical robustness of the design procedures can be significantly improved by employing the so-called delta operator models of the process. State-space models of all H[infinity] sub-optimal estimators are obtained by considering the suitable delta-domain algebraic Riccati equation and the corresponding generalised eigenproblem formulation. A relative condition number of this equation is used as a measure of its numerical conditioning. Both regular problems concerning models having no zeros on the boundary of the delta-domain stability region and irregular (non-standard) problems of models with such zeros are examined. For the first case, an approach based on a dual J-lossless factorisation is proposed while in the second case an extended dual J-lossless factorisation based on a zero compensator technique s required. Two numerical examples are given to illustrate some properties of the considered delta-domain approach.