This paper presents the model identification and the velocity control of an autonomous car. The control system was designed so that the car is controlled at low speeds, where the main applications for the vehicle's autonomous operations include parking and urban adaptive cruise control. A longitudinal model of the car was used in the control loop to compensate the nonlinear behavior of its dynamics. Since the determination of the vehicle's model is a difficult step in the design of model-based controllers, the main contribution of this paper is the use of an empirically determined model to this end. In this paper, the structure of the model was conceived from the car's physics equations, but its parameters were estimated using data-based identification techniques. An important contribution of this paper is the fact that, although the model is strictly linear, we can change its parameters as a function of the operation point of the vehicle to represent the engine's and the transmission's nonlinear behaviors. Moreover, in this paper, we propose a way to include changes in the longitudinal dynamics caused by the automatic gear shifting. The validation of the proposed controller was conducted by computer simulations and real-world experiments.