Bucci, BA and Cole, DG and Ludwick, SJ and Vipperman, JS
(2013)
Nonlinear control algorithm for improving settling time in systems with friction.
IEEE Transactions on Control Systems Technology, 21 (4).
1365 - 1373.
ISSN 1063-6536
Abstract
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. © 1993-2012 IEEE.
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