  We consider the robust control of a two-mass oscillator with a dominant input
delay. Our aim is to compare a fractional-order tuning approach including the
partial compensation of non-minimum phase zeros with a classical H-infinity
loop-shaping design, since both these designs lead to a relatively high
controller order. First of all a detailed physical model is derived and
validated using measurement data. Based on the linearized model both
controllers are designed to be comparable, i.e. they show a similar crossover
frequency in the open loop and the final controller order is reduced to the
same range for both designs. The major differences between both are the
different methods how the feed-forward action is included. The loop-shaping
approach with fractional-order elements relies on the plant inverse using a
flat output, whereas the H-infinty design incorporates a two-degree of freedom
control, i.e. the reference signal is included into the known inputs of the
generalized plant. Each controller is tested in simulation and experiment. As
both open-loops are nearly identical in the frequency range of interest, the
results from an input disturbance experiment show no major difference. The
different design approaches of the feed-forward path are clearly visible in the
tracking experiment.
