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Analysis of observability and detectability for CSTR model of biochemical processes under uncertain system dynamics and various sets of measured outputs

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Łangowski R. , Czyżniewski M.

tom Vol. 34, No. 4

667--696

An analysis of observability and detectability for continuous stirred tank reactor model of selected biochemical processes has been addressed in this paper. In particular, properties of observability or detectability of the considered system model have been proved under uncertain system dynamics in view of various sets of system measured outputs. It is related to considering system dynamics depending on initial conditions and the impact of inputs taking into account a given measured output. The method of indistinguishable state trajectories (indistinguishable dynamics) and tools based on the Lyapunov second method were used to investigate the observability and detectability properties. The analysis was performed for eight cases of different sets of measured outputs with association to the realistic features of measuring devices. The obtained research results are essential for system state estimation that involves the synthesis of state observers. The proposed approach may be successfully applied to the complex biochemical non-linear uncertain systems modelled as continuous stirred tank reactors.

A hierarchical observer for a non-linear uncertain CSTR model of biochemical processes

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Czyżniewski M. , Łangowski R.

tom Vol. 34, no. 1

45--64

The problem of estimation of unmeasured state variables and unknown reaction kinetic functions for selected biochemical processes modelled as a continuous stirred tank reactor is addressed in this paper. In particular, a new hierarchical (sequential) state observer is derived to generate stable and robust estimates of the state variables and kinetic functions. The developed hierarchical observer uses an adjusted asymptotic observer and an adopted super-twisting sliding mode observer. The stability of the proposed hierarchical observer is investigated under uncertainty in the system dynamics. The stability analysis of the estimation error dynamics is carried out based on the methodology associated with linear parameter-varying systems and sliding mode regimes. The developed hierarchical observer is implemented in the Matlab/Simulink environment and its performance is validated via simulation. The obtained satisfactory estimation results demonstrate high effectiveness of the devised hierarchical observer.