Continuous–discrete cell mass distribution observer design using impulsive ISS Lyapunov functions

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The problem of estimating the cell–mass distribution in a yeast cell fermentation process based on non–periodic discrete–time cell mass distribution measurements is addressed. Given that the underlying problem can be cast into a nonlinear error propagation subsystem coupled with an impulsive (i.e., at discrete moments in time) stabilization scheme for the observation error, the design problem is addressed within the framework of impulsive ISS Lyapunov theory. Using a finite–dimensional approximation of the cell population balance equations modeling the cell mass distribution evolution over time, the proposed approach yields conditions on the maximum time between measurements and the resulting ISS gain with respect to the measurement noise disturbance. In order to make the resulting global conditions more accessible and easier to verify in a real process application, the obtained conditions are cast into an additional application–oriented approximation that is amenable to tuning for a given process at hand. The approach is illustrated and tested using experimental data from a yeast batch fermentation.