Research ArticleTracking control of concentration profiles in a fed-batch bioreactor using a linear algebra methodology

•A new control law for the tracking of concentration profiles is presented.•The control actions are obtained by analyzing a system of linear equations.•This methodology can be applied to many nonlinear systems.•A Monte Carlo Randomized Algorithm is applied to verify the robustness of the controller.•The present methodology has the advantage of using discrete equations.

Based on a linear algebra approach, this paper aims at developing a novel control law able to track reference profiles that were previously-determined in the literature. A main advantage of the proposed strategy is that the control actions are obtained by solving a system of linear equations. The optimal controller parameters are selected through Monte Carlo Randomized Algorithm in order to minimize a proposed cost index. The controller performance is evaluated through several tests, and compared with other controller reported in the literature. Finally, a Monte Carlo Randomized Algorithm is conducted to assess the performance of the proposed controller.