This paper discusses a model based friction compensation for a frictional system and shows its simulation results of the adaptive parameter estimation and the dynamic pole assignment. The friction model with friction observer is one of the newly introduced dynamic velocity-friction model proposed by Canudas et. [1]. The model depicts various frictional phenomena, such as Stribeck effect, frictional memory, Stick-slip motion. We applied adaptive parameter estimation to the steady state velocity-friction model at first, and then to the dynamic velocity-friction model. Parameter identification algorithm are followed conventional RLSM adaptive rule. The modeling error and the filtered variable error are discounted. The simulation results are compared with the case only the conventional PD controller implemented. The result say that our parameterization for the adaptive parameter estimation and the proposed control strategy works well at the frictional system. The stability for the closed system was proved by the Lapunove criteria. Also the stability condition was proposed by the strictly positive real constraint. If a real system have dynamic friction property, the friction compensation with the dynamic friction model will improve the performance. The static friction model based compensation may lead to the system unstable. We derived a direct state feed-back term, for the dynamic pole assignment method, under the known parameters. Its simulation result shows a good transient performance compared to the case with static pole assignment on the regulation for the frictional system.
