Robust adaptive controller for continuous bioreactors

• A modified back-stepping was proposed to overcome operating at a singular point.
• The parameter of the designed control law can be intuitively understood.
• The proposed control shows the best performance when compared to existing methods.
• The proposed control drove the bioreactor to its optimal productivity point.

Bioreactor control has become very important in recent years due to the difficulty in controlling highly non-linear behavior, model mismatch and parameter variation. Adaptive back-stepping control is a recursive design method that employs the Lyapunov stability theory in its design procedures. Adaptive back-stepping control is applied to the problem, which drives a continuous bioreactor to its optimal productivity point. However the designed control law may not work at the optimal productivity point, since controlling the optimal productivity point frequently causes the control system to fall into a singular point. Thus in this study, we apply the back-stepping design to a bioreactor system by introducing a simple parameter into the design techniques to prevent the control system from operating at a singular point. The parameter introduced in the control law can be understood intuitively and the proposed control scheme is endowed with strong robustness properties. The resulting controllers are compared to the feedback linearization based proportional-integral controller and internal model control, as well as nonlinear model predictive control and observer-based linearizing control by theoretical simulations. It is shown that the proposed control strategy is versatile and effective in implementing robust control for regulating productivity in the presence of model mismatch, model uncertainty and parameter variation. The proposed control scheme successfully drives the productivity of the controlled continuous bioreactor to its optimal point.