Because friction is a phenomenon that is present in the vast majority of mechanical systems producing some unwanted effects such as tracking errors, limit cycles, and stick‐slip motion, friction model based compensation has been previously proposed. We present a simple adaptive friction compensator, developed from a simple friction model, that achieves the control objective (friction compensation). This simple model was effectively used to obtain a friction compensator with smooth terms avoiding the use of signum and absolute functions presented in previously reported works on friction compensation. Considering that the velocity is bound away from zero and using Lyapunov stability analysis, exponential stability of the closed loop system is shown; i.e., the tracking errors and the parameter estimation error converge exponentially to zero. Because our friction compensator is based on a simple friction model, numerical experiments using a more representative friction model are given to support our theoretical findings.

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Development of velocity observers for mechanical systems with friction deserves a special emphasis, because as evidenced in numerical and experimental tests when a state-of-the-art observer is armed, friction can induce high-frequency oscillations in the estimated signal. In this short paper, two new velocity-observation algorithms are designed, based on this previously reported observer, that eliminate the high-frequency oscillations noted. Numerical and experimental performance comparisons are carried through making use of LuGre model and a mechanical PID control system that incorporates the estimated velocity into the feedback loop.