Design of a fractional-order integrator for high-precision stages

To provide more tuning freedom in the trade-off between overshoot and settling times of PID controlled stages, a PID controller with a fractional order integrator is studied. The fractional order integrator has two parameters dependent on the order λ. Namely, the corner frequency ω_i(λ) and the gain k_p(λ). Both parameters are designed such that robust stability is maintained independent on the choice of λ. It will be shown that the fractional order integrator can be approximated by a low-order loop shaping filter. As such, insights from fractional order control can be used by the control engineer to aid his tuning tasks. The controller is tested on a wafer stage system.