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.