Abstract: A positioning system used, by way of example, for lithography, uses the position of the wafer stage as the trajectory command for the reticle fine stage control circuit. The reticle fine stage position is combined with the position of the wafer stage to generate a synchronous error. The reticle fine stage control circuit uses a Jacobian differential transformation to convert the synchronous error into an positional error for the center of gravity of the reticle fine stage. Thus, any inaccuracies due to measurement errors caused by rotation of reticle fine stage are avoided. A controller filter circuit uses the positional error for the center of gravity to calculate the force on the center of gravity that will minimize the synchronous error. The controller filter circuit includes saturation limited integration behavior that minimizes the settling time. A feedforward loop also generates a feedforward force, which reduces settling time, and is combined with the force signal from the controller filter.