Active multivariable optimal control of a planar magnetic levitator

We discuss multivariable optimal control of a six-degree-of-freedom magnetic levitator with large planar motion capability. A single moving part, namely the platen, generates all the motions required for focusing and alignment, and large planar motions (50×50 mm) for positioning for photolithography in semiconductor manufacturing. We derive a state-space dynamic model for the planar levitator, and implement a multivariable optimal controller for its lateral mode control. The magnetically levitated stage shows tens-of-nanometer positioning noise suitable for the next generation photolithography. We also demonstrate that it follows a 20-mm step motion command in only 120 ms. The position command is planned by adapting a time-optimal control result. Magnetic levitation is a promising technology for use in high-precision active motion control applications