  In this paper, a framework for the combination of robust fractional order
CRONE control with non-linear reset is given for both first and second
generation CRONE control. General design rules are derived and presented for
these CRONE reset controllers. Within this framework, fractional order control
allows for better tuning of the open-loop responses on the one hand. On the
other, reset control enables a reduction in phase lag and a corresponding
increase in phase margin compared to linear control for similar open loop gain
profile. Hence, the combination of the two control methods can provide
well-tuned open-loop responses that can overcome the fundamental linear control
limitation of Bode's gain-phase relationship. Moreover, as established
loop-shaping concepts are used in the controller design, CRONE reset can be
highly compatible with the industry. The designed CRONE reset controllers are
validated on a one degree-of-freedom Lorentz-actuated precision positioning
stage. On this setup, CRONE reset control is shown to provide better tracking
performance compared to linear CRONE control, which is in agreement with the
predicted performance improvement.
