Aiming to the shortage of conventional friction compensation methods and nonlinear characteristic of friction disturbance, the accuracy of the friction description by the LuGre model is used to analyze the design process of Luenberger-like Observer and Time Delay Estimator (TDE). Then, the method of synthesis of Luenberger-like Observer and TDE is given out as a friction compensation scheme. The experimental results show that, as the friction state is observed by Luenberger-like Observer,the friction disturbance estimator with LuGre friction dynamic model can be effective to friction compensation, and the application limitation that the disturbance is asymptotic variety is solved. At the same time, the survival error of friction compensation and exoteric disturbance are eliminated by TDE.