A controller consisting of three schemes, one proportional gain, one pulse, and one ramp, is proposed to achieve precise and fast pointing control under the presence of stick-slip friction. Design of the controller is based on two distinctive features of friction, the varying sticking force and presliding displacement of contacts under static friction. The latter is the main idea behind the ramp scheme to accomplish the fast pointing task. Implementation of this multistage control strategy requires position measurement only. Experimental results demonstrate the effectiveness of the proposed controller for the desired performance.
This paper presents the studies of stick-slip friction, presliding displacement and its influence on hunting. Experimental studies reveal that presliding displacement could affect the stability of hunting. A modified Coulomb friction model integrating presliding displacement in the microsliding regime is proposed to demonstrate such effect. Finally, step responses obtained from experiments and from the modified model are compared. These comparisons yield the conclusion that the transition of friction between the sticking state and the sliding state is smooth and continuous, not abrupt. Such a smooth transition of friction is critical to the studies of systems performing high-speed cyclic motion.
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 Sr for the sufficient stability condition to suppress vibrations around the [—0.5, +0.5] μm target region. Our study reveals that the frictional stiffness σ0 and the micro viscous damping coefficient σ1 in the LuGre model are required for the bounds of Sr . With the derived bounds of Sr , the Lyapunov direct method is applied to prove the stability of the PPR controller.
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