MINIMUM FORCE OUTPUT CONTROL METHOD FOR COUNTER-MASS WITH CABLE

Embodiments of the invention relate to a cable force feedforward approach that takes into account the cable force in the counter-mass trajectory computation to reduce or eliminate vibration of the lens body caused by the cable force disturbance and corrective force exerted by the trim motors. In one embodiment, a method provides cable force feedforward control for a counter-mass of a stage with a cable connected to the counter-mass and using the cable force feedforward control to control one or more trim motors to produce a trim motor output force to be applied to the counter-mass, the counter-mass moving in response to a reaction force from movement of the stage. The method comprises measuring a counter-mass position y of the counter-mass in response to forces applied to the counter-mass; measuring a cable force ƒ exerted on the counter-mass by the cable which is connected to the counter-mass; generating a cable force function {circumflex over (ƒ)}(y, {dot over (y)}) of the measured cable force ƒ versus the counter-mass position y; and computing the trim motor output force u aswhere w is a weighting function having a value from 0 to 1 and is selected for optimization.