(105c) Model Predictive Control and Observer Design for a Chemostat Reactor

The chemostat is a reactor that is generally used to cultivate organisms on a small scale [1]. Thus, this type of reactor is important in environmental research, ecology, evolutionary biology, and biotechnological industry. In the reactor’s operation, the volume is kept constant, such that the feed of fresh medium is continuously added at the same rate as the fluid containing metabolic products and some microorganisms are removed. Generally, the control in the reactor is carried out by changing the inlet and outlet flow rate, while the other conditions, such as temperature, pH, and mixing are kept constant. This alters the dilution rate (thus, the residence time) inside the reactor, which can be used to control the growth rate of the organism [3].

As the control of this process can result in higher production, in this contribution the Model Predictive Control (MPC) for the chemostat reactor is derived. This type of controller can be used to optimize the performance of a system subjected to constraints [3], while the model generally used to represent the dynamics inside the reactor is a nonlinear first-order hyperbolic partial integro-differential equation (PIDE) with integral boundary conditions [4]. Furthermore, as the MPC requires full state feedback and only the total amount of organisms in the reactor is available for measurement, the observer design is also addressed. Finally, the results from simulation studies show the controller’s performance.

[1] Smith, H. L., and Waltman, P., 1995. “The theory of the chemostat-dynamics of microbial competition”. Cam bridge University Press

[2] Toth, D., and Kot, M., 2006. “Limit cycles in a chemo stat model for a single species with age structure”. Mathematical Biosciences, 202, pp. 194–217

[3] K. R. Muske and J. B. Rawlings, “Model predictive control with linear models,” AIChE Journal, vol. 39, no. 2, pp. 262–287, 1993

[4] Gurtin, M., and MacCamy, R., 1974. “Non-linear age dependent population dynamics”. Arch. Ration. Mech. An., 54, pp. 281–300.