High precision adaptive control for friction compensation

The high precision positioning and tracking control of mechanical systems in the presence of stiction, viscous and Coulomb frictions is studied in this paper. To compensate for the frictions, adaptive controls are proposed to enhance the performances of linear PD or PID control. Using the Taylor series to approximate the nonlinear stiction friction, usually given as a decaying exponential function of velocity, the friction can be expressed as a linear function of the unknown parameters. Based on this model, the adaptive control laws are designed for friction compensation in position control as well as tracking. Lyapunov analysis shows global asymptotic convergence of the positioning errors and tracking errors.