A new adaptive controller for bio-reactors with unknown kinetics and biomass concentration: Guarantees for the boundedness and convergence properties

• An adaptive controller for bioreactors is developed.
• A new method to handle the unknown time-varying control gain is proposed.
• The output tracks the desired reference with a user-defined tolerance.
• The exact values of the plant parameters are not required to be known.
• Upper or lower bounds related to the plant parameters are not required to be known.

In this work, an adaptive controller for bioreactors, using the measurement of output gas flow rate to handle the uncertainty on biomass concentration and kinetic rate is developed. A mass–balance model based on a unique reaction pathway to represent the input–output behavior is considered. Time-varying and unknown but bounded behavior of plant parameters, including the substrate concentration at the inflow and the yield coefficients is taken into account in the controller. The Lyapunov-like function method to develop the controller is used. A new method to handle the unknown time-varying behavior of the control gain is developed; with this method it is assured that the output tracks the desired reference with a user-defined tolerance and parameter drifting is avoided. The main contributions of the scheme with respect to closely related works are: (i) the exact values of the plant parameters are not required to be known; (ii) upper or lower bound related to the plant parameters is not required to be known; (iii) the time-varying behavior of plant parameters in the control design and in the convergence analysis is considered.