A physically parameterized continuous-time velocity-scheduled LPV state-space model of a heavy-truck is identified from measurement data. The aim is to develop a model for controller which steers the vehicle by braking either the one or the other front wheel. It can be applied in many vehicles, where the sole possibility to automate the steering in emergency situations, like e.g. unintended lane departure, is the application of the electronic brake system. Such steering controllers usually require the prediction of the yaw rate and the steering angle on every possible velocity. This problem deffnes the requirements for the model. Four different order model structures are derived from a certain physical description. Assuming state and output noise, all of them are identified in parameter-varying observer form using prediction error method. The quadratic criterion function is composed from measurement data of several different experiments. Each experiments are carried out on constant velocities but the cost is constituted from different velocity experiments. That structure is selected for controller design which has the best cost on test data out of those the poles of which are in the control bandwidth. The poles are defined on constant velocity. The resulted nominal model consists of the feedback connection of the yaw dynamics with one state-variable and the steering system dynamics with two states and of a first order actuator dynamics with time-delay. The predicted outputs show a good fit to the measurements.