Reduced order asymptotic observer of friction in motion control

An asymptotic observer of the motion state variables with nonlinear friction [1] benefits from a robust to the noise state-space representation of the dynamic friction force, including pre-sliding transitions, and implements the reduced order Luenberger observation law with only measurable output displacement. The uniform asymptotic stability and convergence analysis of the proposed observer are elaborated by using the Lyapunov function-based stability criteria by Ignatyev and imposing the parametric constraints on the time dependent eigenvalues to be always negative real. A design procedure for assigning a dominant (thus slowest) real pole of the observer system matrix is proposed. A thorough experimental evaluation is given for the proposed observer-based friction compensation, which is performed for positioning and tracking tasks and compared with an optimally tuned PID feedback control.