This paper addresses the control of biomass growth rate in fed-batch bioreactors. The main difficulty when designing controllers for these processes is the lack of accurate on-line knowledge of the controlled variable as well as the strong parameter and model uncertainties. A completely novel approach to the control design is introduced in this paper which allows us to overcome these problems. In fact, the proposed controller, which is applicable to a large class of fermentation processes, requires minimal knowledge of the process parameters and only uses on-line measurement of volume and biomass concentration. First, a reference model is proposed and a goal manifold in the state space is derived where the control objective is satisfied. A partial state feedback law is then proved to be an invariant control for the goal manifold. Then, the feedback gain is dynamically adjusted via a discontinuous action that enforces a sliding regime such that all state trajectories are steered towards the goal manifold. This sliding mode controller presents very attractive robustness properties. The performance of the controller is evaluated through numerical analysis and experimental results.