Comparison of Fractional-Order and Integer-Order H-infinty Control of a Non-Collocated Two-Mass Oscillator

TL;DR

This paper compares fractional-order and integer-order H-infinity control methods for a two-mass oscillator with input delay, focusing on their design, implementation, and performance through simulations and experiments.

Contribution

It provides a detailed comparison of fractional-order and classical H-infinity control approaches, highlighting their differences in feed-forward design and practical performance.

Findings

Both controllers achieve similar open-loop crossover frequencies.

No significant difference in disturbance rejection performance.

Distinct tracking behaviors due to different feed-forward implementations.

Abstract

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.