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The frictional modelling literature is reviewed, and it is demonstrated that unrealistic drift results when the shape coefficient is 1.0 for the LuGre and the integral friction models. Drift will not occur but other dynamic friction characteristics can't be represented when the shape coefficient is 0. Based on the above, the LuGre friction model and the Integral friction model are improved. The velocity-friction characteristic, the stick-slip and the cycling caused by friction and the drift are compared in simulation. The results show that the improved friction model well reflects realistic friction dynamic characteristics and avoids drift. Finally, the improved friction model is used in a nonlinear mathematic model of a valve controlled hydraulic cylinder system. The cylinder's motion at low velocity is simulated and the related experimental results are presented. The results show that the improved friction model gives realistic low velocity motion of the cylinder.