The stabilization of front solutions in reaction-convection-diffusion systems is studied by presenting a hierarchical picture of one-dimensional models that admit such solutions and that may be approximately reduced to a two-variable system incorporating a fast and diffusing activator and a slow and localized inhibitor. The control procedures are studied using the reduced models with approximate (polynomial) kinetics, for which case some analytical results may be derived, as well as the full model of an exothermic reaction in a fixed bed, where only numerical results are available. In the former case, we reduce the partial differential equation model to a simple ODE that describes the front position, accounting for effects of convection, system size, and boundary conditions; linear stability analysis of the stationary-front solution without and with control was conducted as well. We consider the simplest control strategy based on a single sensor, placed at the front position, and a single space independent actuator that affects one of the parameters or the flow rate or the feed (boundary) conditions; mathematically, these three modes affect the source function, the convective term, or the boundary conditions. The front could be controlled at its stationary position, using either the first or second mode, but the third mode generally failed to stabilize the system. The reduced system was found to be a useful learning tool for the analysis of the full model.