Cloud applications and cyber-physical systems are becoming increasingly complex, requiring frequent reconfiguration to adapt to changing needs and requirements. Existing approaches compute new valid configurations either at design time, at runtime, or both. However, these approaches can lead to significant computational or validation overheads for each reconfiguration step. We propose a component-based approach that avoids computational and validation overheads using a representation of the set of valid configurations as a variability model. More precisely, our approach leverages feature models to automatically generate, in a component-based formalism called JavaBIP, run-time variability models that respect the feature model constraints. Produced run-time variability models enable control over application reconfiguration by executing reconfiguration requests in such a manner as to ensure the (partial) validity of all reachable configurations. We evaluate our approach on a simple web application deployed on the Heroku cloud platform. Experimental results show that the overheads induced by generated run-time models on systems involving up to 300 features are negligible, demonstrating the practical interest of our approach.