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Observability singularity of batch bioreactors: A solution based on high order sliding mode differentiator approach

This paper deals with the observability singularity problem of batch bioreactors on the positive Orthant. This singularity is overcame by the dedicated approach based on the well-known high order sliding mode differentiator proposed by Arie Levant and the resolution of simple second order equation. Nevertheless, it is difficult to distinguish between both solutions, but the second differentiation of the output gives an appropriate test procedure for choice between both solutions. Some simulation results highlight the well-founded of the proposed method.