A finite dimensional nonlinear observer for an exothermic stirred-tank reactor

A finite dimensional nonlinear observer is constructed to provide an exponentially convergent estimate of reactant concentration from temperature measurements in an exothermic stirred-tank reactor with a single, first-order, irreversible reaction. The observer is suitable for batch or continuous reactor operation when the reactor is subject to measured time-varying feed an coolant temperature fluctuations. The construction of a nonlinear observer for this process is an unexpected result due to the very narrow class of nonlinear systems for which such observers are known to exist. The paper presents explicit formulae for the observer. The required nonlinear observer gains are obtained by straightforward numerical quadratures. Preliminary simulation results demonstrate the utility of the observer in implementing nonlinear state feedback control. Extension to other reaction systems or to the case of unmeasured time-varying feed concentration will require additional theoretical development.