Continuous bioreactors are critical unit operations in many biological systems, but the unique modeling is very complicated due to the underlying biochemical reactions and the distributed properties of cell population. The scope of this paper considers a popular modeling method for microbial cell cultures by population balance equation models, and the control objective aims to attenuate undesired oscillations appeared in the nonlinear distributed parameter system. In view of pursuing the popular/practical control configuration and the lack of on-line sensors, an approximate technique by exploiting the "pseudo-steady-state" approach constructs a simple nonlinear control model. Through an off-line estimation mechanism for the system having self-oscillating behavior, two kinds of nonlinear PI configurations are developed. Closed-loop simulation results have confirmed that the regulatory and tracking performances of the control system proposed are good.

The output regulation design of two bioreactor systems in the presence of self-oscillating behavior and inlet disturbances is addressed. By virtue of linearization, transformation, tuning parametrization, and some geometric control techniques, explicit formulations of nonlinear proportional−integral (PI) and proportional−integral−derivative (PID) controllers are obtained. For the prescribed second-order nonlinear system, the model-based PI controller connected to a linear transformation-based observer is developed. For the general class of third-order nonlinear systems, a PID-type feed-forward/feed-back controller that is connected to parametrized tracking modes is constructed. Using the numerical approximation for the reconstruction of equilibrium manifold, the simplified model-based PID control can be easily implemented. Finally, closed-loop simulations show the satisfactory output regulation performances.