Discussion: “Friction-Compensating Command Shaping for Vibration Reduction” (Lawrence, J., Singhose, W., and Hekman, K., 2005, ASME J. Vib. Acoust., 127, pp. 307–314)

Abstract

In their paper (1), the authors consider a nonlinear mechanical system represented by Display Formulamẍ+(Kd+b)ẋ+Kpx=Kdu̇+Kpu−sign(ẋ)μkN (1) In Eq. 1, m is the mass of the system, Kd is the derivative gain, Kp is the proportional gain, b is the viscous friction, μk is the kinetic coefficient of friction, N is the normal force, x is the system displacement, and u is the applied control input. The nonlinearity in the system is the Coulomb friction, which is represented by sign(ẋ)μkN.