Vibration Control on a Pulse and Ramp Driven System with Friction

Abstract

This paper investigates the sufficient stability condition of a three-phase proportional gain, pulse, and ramp (PPR) controller for pointing systems under the influence of friction. With the ramp and pulse schemes integrated, the PPR controller has been demonstrated to be an effective control strategy for fast and precise pointing applications. In this paper the LuGre model is used to derive the upper bounds of the ramp slope S_r for the sufficient stability condition to suppress vibrations around the [—0.5, +0.5] μm target region. Our study reveals that the frictional stiffness σ ₀ and the micro viscous damping coefficient σ ₁ in the LuGre model are required for the bounds of S_r . With the derived bounds of S_r , the Lyapunov direct method is applied to prove the stability of the PPR controller.