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Nonlinear Control Algorithm for Improving Settling Time in Systems With Friction

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4 Author(s)
Bucci, B.A. ; Univ. of Pittsburgh, Pittsburgh, PA, USA ; Cole, D.G. ; Ludwick, S.J. ; Vipperman, J.S.

A nonlinear control algorithm that greatly reduces settling time in precision instruments with rolling element bearings is proposed. Reductions of 80.5%-87.4% in settling time were achieved when settling to within 3-100 nm of the commanded position. Final settling of such systems is typically impacted by the nonlinearity in the pre-rolling friction regime, which manifests as a hysteretic stiffness. Consequently, the integral term in the controller can take a long time to respond. In this paper, a nonlinear integral action settling algorithm is presented. The nonlinear integral gain takes the form of a Dahl friction model. Since the integral gain mimics hysteretic stiffness, the output of the integral control term is instantaneously set to a large value after each direction change, greatly improving settling response. A nearly first-order error dynamic results, which has a user-definable time constant. Before the algorithm can be implemented, the Coulomb friction and initial contact stiffness in the Dahl model must be experimentally determined for the stage. A sensitivity study is performed on the initial contact stiffness, which was found in other works to dictate the stability of the algorithm.

Published in:

Control Systems Technology, IEEE Transactions on  (Volume:21 ,  Issue: 4 )

Date of Publication:

July 2013

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