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A novel approach to linearize nonlinearities commonly inherent in actuators is proposed in this paper. This approach solves the inverse of the nonlinearity without requiring its I/O relations as a one-on-one map, which is necessary for the current inverse-model method. By introducing the concept of the equivalent gain, the proposed method systematically finds the inverse model of the nonlinearity by solving a zero-finding problem. Discussions on the existence and uniqueness of the solution are given in this paper. A simulation example is presented to demonstrate how the task in finding the inverse of a complicated nonlinearity can be simplified by the proposed method. Experimental evaluations on a position servo system with conspicuous friction reveal that the dither-smoothed nonlinearities are still nonlinear, and compensating action like the proposed method is necessary for control systems using the dithering technology.

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.