Nonlinearities in Industrial motion stages - detection and classification

Abstract

Abstract-Detection and classification of nonlinearities in motion systems becomes of increasing importance with high demands on (closed loop) performance. In this paper two methods are compared that aim to measure both the linearized dynamics and the influence of nonlinearities. First, a broadband signal is used to measure a linear approximation of the systems dynamics. This method uses multisine signals with identical amplitude spectrum, but randomly distributed phases. Averaging over multiple periodic responses to the same signal and over multiple realizations of the random phase multisine allows the computation of the level of nonlinearities and external disturbances separately. This yields both a linear approximation of the systems dynamics and the amount of nonlinear 'disturbance' as a function of frequency. Second, single sine based measurements are used to measure the Higher Order Sinusoidal Input Describing Functions (HOSIDF) of the system under test. HOSIDFs describe the response of the system by describing not only the 'direct' response (gain and phase shift) of the system at the input frequency, but by describing the response at higher harmonics of the input frequency as well. This yields a quantitative measure of the power generated by nonlinearities at harmonics of the input frequency as a function of this frequency and the signal amplitude. In the paper these methods are utilized to acquire a non-parametric model for an industrial high precision stage. The effects of and sources for nonlinear influences are discussed for this particular case as well.

Frequency domain based friction compensation - Industrial application to transmission electron microscopes -

“…The results presented in the sequel rely on the quantification of nonlinear effects by measuring energy in the output spectrum at harmonics of the input frequency, when the system is subject to a sinusoidal input signal. This representation of nonlinear effects in the frequency domain is captured by the higher order sinusoidal input describing functions [2], [3], [4], [8], [10], which describe the systems response (gain and phase) at harmonics of the base frequency of a sinusoidal input signal. In [7], [9] recent results concerning frequency domain tuning of Coulomb friction feed forward are presented.…”