Vehicle having electric power steering with active damping

A vehicle with an electric power steering system has a steering shaft with a resonant frequency of free rotational oscillation and a control which derives a driver assist torque signal, a return to center torque signal and an active damping torque signal and sums these signals to provide a motor command signal to the electric motor. The active damping torque signal is derived by filtering a generated steering shaft position signal in a filter having amplitude and phase characteristics of a differentiator from zero Hertz only through the resonant frequency of free rotational oscillation of the steering shaft and multiplying the filtered steering shaft position signal by a vehicle velocity factor derived from sensed vehicle velocity. Preferably, the electric motor is provided with one or more rotor position sensors used in the control thereof and rotor position signals from the rotor position sensors are provided as the steering shaft position signal.