On the actuation nonlinearity of normal-stressed electromagnetic nanopositioning stages

Normal-stressed electromagnetic actuator (NSEA) has been demonstrated promising for nanopositioning stages running in hundreds of micrometers. However, system nonlinearities and their influences on the actuation behavior in NSEA have not been well revealed, blocking the in-depth understanding and high -performance application of the NSEAs. This paper developed an intrinsic electromagnetic actuation model by systematically including the nonlinear position-varying flux leakages, nonlinear flux density related to the field strength (B -H curve), and magnetic saturation. Based on the model, the influences of those nonlinear factors on the actuation were characterized theoretically. Experiments well verified the theoretical model and further characterized the dynamic hysteresis in the actuation. Finally, a phenomenological Wiener model cascading linear system dynamics with a least-squares support-vector machine (LS-SVM) model was developed for the feedforward compensation for system nonlinearities. The maximum modeling error was less than +/- 4% for the excitation with frequency ranging from 25 Hz to 200 Hz. Tracking of a complex trajectory combining multiple harmonics with various frequencies and randomly chosen amplitudes exhibited a maximum tracking error of +/- 0.7 mu m, which was only 28% of that without compensations. The results demonstrated the effectiveness of the proposed nonlinear compensation strategy for NSEAs.