Compensation and control of dither-smoothed nonlinearities

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.