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In this paper, a systematic procedure to identify a comprehensive version of friction model via limit cycle experiments using dual-channel relay feedback apparatus is presented and demonstrated on a 3-D Cartesian robotic system. This friction model, which contains static, Coulomb and viscous friction with Sticbeck effect, can describe the friction behaviour when the servo system operates at both low and high velocity mode. The limit cycle properties of the dual-channel relay feedback system are used for careful tuning of relay gains to run the system on either high or low velocity modes. Sets of explicit formulas are applied for direct computation of model parameters. Only the boundary lubrication velocity is estimated via one-dimensional optimisation. The friction compensation experiment shows the accuracy of the identified model and the effectiveness of proposed method.