Simultaneous control of a precision linear stage in multiple lubrication modes with the complex lag

Precision linear stages can exhibit two markedly different dynamic behaviors during a single move as the lubrication condition of the bearings changes from elastohydrodynamic lubrication to boundary lubrication. For robustness purposes it is desirable to design a single compensator which provides stable behavior for both dynamic modes and transitions between them. One approach is to design a compensator for the elastohydrodynamic lubrication dynamics and then to cascade a lag compensator with that controller to accommodate the boundary lubrication dynamics. The lag compensator trades off phase margin of the loop in the elastohydrodynamic mode for increased performance when operating in the boundary lubrication mode. This paper demonstrates the superior performance of the complex lag compensator compared with a real lag compensator for simultaneous control of the two operating modes.