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 lambda. Namely, the corner frequency omega(i)(lambda) and the gain k(p)(lambda). Both parameters are designed such that robust stability is maintained independent on the choice of lambda. 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.