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In this paper, the mathematical modelling of a front-wheel steer-by-wire (SBW) system is studied and a terminal sliding mode control scheme for the SBW system with uncertain dynamics is developed. It is shown that a front-wheel SBW system, from the hand-wheel to the steered front wheels, is equivalent to a second-order system. A terminal sliding mode controller can then be designed based on the information of the bounds of uncertain system dynamics, in the sense that not only a strong robustness with respect to system uncertainties and nonlinearities can be obtained, but also the front wheel steering angle can converge to the hand-wheel reference angle in a finite time. A simulation example is presented to verify the proposed control scheme.