The paper presents a model for motion generation of differential-drive mobile robots. The parameters of the dynamic model allow adjusting the robot translational and rotational behaviours separately. The model takes into account the robot kinematic and dynamic constraints, making the velocities and accelerations bounded and compatible with those the robot can perform. The main contribution of the paper is to use the model itself as a motion controller: under soft hypothesis on the velocities and accelerations, this approach allows an easy tuning of the controller parameters. A system stability and parameters sensitivity analysis is developed, in order to get guidelines for controller tuning. The clear physical sense of the parameters make this tuning easy and intuitive. Experimental results involving a real mobile robot show the performance of this approach.