Exact plant inversion of flexible motion systems with a time-varying state-to-output map

Many high-accuracy positioning systems have a target performance location that varies with time and position. A typical example is given by wafer stage positioning systems in the lithographic industry. The design of feedforward compensators for such a class of systems, i.e. flexible motion systems having Linear Time Invariant (LTI) state dynamics with Linear Time-Varying (LTV) state-to-output map, can be considerably enhanced if such time or position-varying characteristics of the systems are taken into account. In this work, a strategy to construct a feedforward controller that exactly matches the time-dependent inverse of such a system is investigated. Analysis and simulation on a simplified model show the potential performance improvement obtained with such a strategy.