To solve the non-differentiable problem of original frictionmodel, an exponential function containing speed variables is introduced to design the continuous differentiable LuGre steady-state friction model for dual-motor driving servo systems. The proposed model captures the main characteristics of friction including Stribeck effect, coulomb and viscous friction.Based on the continuous differentiable model, a nonlinear variable coefficient characterizing the synchronization rate is used for fast terminal sliding mode, such that the system is proved to achieve synchronization and tracking control for the reference signal with prescribed performance by Lyapunov function.The simulations are included to verify fast convergence speed and high tracking precision of the proposed algorithm.