Nonlinear control of stick-slip oscillations by normal force modulation

The present paper investigates the efficacy of controlling friction induced vibration by normal load modulation. Friction-induced self-excited vibration, attributed to the low-velocity drooping characteristics of friction (Stribeck effect), is modelled by a mass-on-belt model where the normal force of the mass is being modulated based on the acceleration feedback followed by a second order filtering. Polynomial model is employed to study the friction phenomenon between the mass and the belt. The pole crossover design (to ensure faster transient and greater relative stability) is implemented to optimize the filter parameters with an independent choice of the belt velocity and control gain. These sets of optimized parameter values are then used to construct local stability boundaries in the plane of control parameters. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO (while using belt velocity as the bifurcation parameter) indicate that a significantly small-amplitude limit cycle resulting from a supercritical Hopf bifurcation stabilizes the extreme low velocity region at higher values of the control gain. With the increase of the control gain the subcritical nature of Hopf bifurcation changes to a supercritical one. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.