Control of Systems With Hysteresis Via Servocompensation and Its Application to Nanopositioning

Partly motivated by nanopositioning applications in scanning probe microscopy systems, we consider the problem of tracking periodic signals for a class of systems consisting of linear dynamics preceded by a hysteresis operator, where uncertainties exist in both the dynamics and the hysteresis. A robustified servocompensator is proposed, in combination with an approximate hysteresis inverse, to achieve high-precision tracking. The servocompensator accommodates the internal model of the reference signal and a finite number of harmonic terms. Using a Prandtl-Ishlinskii (PI) operator for modeling hysteresis, we show that the closed-loop system admits a unique and asymptotically stable periodic solution, which justifies treating the inversion error as an exogenous periodic disturbance. Consequently, the asymptotic tracking error can be made arbitrarily small as the servocompensator accommodates a sufficient number of harmonic terms. The analysis is further extended to the case where the hysteresis is modeled by a modified PI operator. Experiments on a commercial nanopositioner show that, with the proposed method, tracking can be achieved for a 200-Hz reference signal with 0.52% mean error and 1.5% peak error, for a travel range of 40 μm. The performance of the proposed method in tracking both sinusoidal and sawtooth signals does not fall off with increasing frequency as fast as the proportional-integral controller and the iterative learning controller, both adopted in this paper for comparison purposes. Further, the proposed controller shows excellent robustness to loading conditions.