We design a simple model of the growth of polymer-decomposing bacteria in a continuous stirred tank reactor. The dilution rate is controled to optimize the output of monomers. This model is studied in order to find the optimum at the stationary state. However, the optimal stationary state is not robust against perturbations, leading to washout in the bioreactor. We design a control that makes the closed system globally stable around the optimal equilibrium. Then, a more complex model for polymers and oligomers of any lengths is studied. It is shown that the same technics also lead to a globally stable optimal point for the controlled system.