Gain-scheduling control of machine tools with varying structural flexibility

The high accelerations occurring in present-day machine tools are likely to excite the vibration modes of the machine structure. These structural eigenfrequencies are not constant but depend on the position of the tool in its workspace. High performance motion controllers should take into account these varying resonances. This paper discusses the gain-scheduling control approach for an experimental set-up containing a flexible beam of which the stiffness depends on its length. H∞-controllers are designed for several constant beam lengths and are linearly scheduled. Next to this ad-hoc scheduling, analytically scheduled controllers are synthesised. It is shown that the inherent conservatism in the design method limits the performance of the analytical approaches.