Output Regulation of Self-Oscillating Biosystems:  Model-Based Proportional−Integral/Proportional−Integral−Derivative (PI/PID) Control Approaches

Abstract

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.