Smooth extremum-seeking control for fed-batch processes

Many biotechnological processes have optimal substrate concentrations where a maximum growth rate is achieved. In this work an extremum seeking controller and a gradient estimator are proposed to maximize the growth rate in fed-batch bioprocesses even when the substrate to growth rate map is unknown. Both the controller and estimator are obtained with high order sliding mode algorithms. Stability proofs are given, and tools to tune the algorithms in terms of bounds of the hessian of the map are derived. Simulation results that illustrate the performance of the controller are shown.