A robust adaptive controller for an anaerobic digester with saturated input: Guarantees for the boundedness and convergence properties

In this work an adaptive controller for an anaerobic digester is developed taking into account the input constraints. The following assumptions are considered: (i) the biomass and chemical oxygen demand concentrations are unknown, (ii) the model parameters are unknown and vary but they are bounded, and (iii) the upper or lower bounds of model parameters are unknown. The Lyapunov-like function method is used to derive the controller. A state observer is employed to handle the saturation of the control input, and updated parameters are used to handle the unknown bounds of the plant parameters. Some features of the control design are: (i) discontinuous signals are avoided, (ii) the boundedness of the updated parameters is ensured despite input saturation, in order to avoid parameter drifting, and (iii) the convergence of the observer error to a residual set of user-defined size is ensured despite input saturation.

► A robust adaptive controller for an anaerobic digester is developed.
► The control design includes unknown time varying but bounded behavior of the model parameters.
► The convergence of the observer error to a residual set defined by the user is ensured.
► The boundedness of updated parameters is ensured, so that parameter drifting is avoided.
► Lyapunov functions are used to prove the stability of the closed-loop system.