Pole-placement vs. loop-shaping design for gain-scheduling control of machine tools with position dependent dynamics

The high accelerations together with the high controller band-widths required from present-day machine tools are likely to excite the vibration modes of the machine structure. In order to achieve a high control bandwidth and high contouring accuracy, these structural eigenfrequencies need to be incorporated in the controller design. An additional complication with machine tools is that the structural eigenfrequencies are not constant but depend on the position of the tool in the workspace of the machine tool, with as consequence that the machine model is position dependent and therefore cannot be modelled as a single linear time-invariant (LTI) model. To control such linear time-varying (LTV) systems, two approaches are possible: (i) the controller is such that the system behaviour is largely independent from system parameter variations (robust control), and (ii) adapt the controller structure or parameters to the system parameter variations, e.g. by gain-scheduling. In this paper an experimental set-up, consisting of one axis of an industrial pick-and-place machine, driven by a linear motor, is controlled based on the gain-scheduling approach. The set-up contains a flexible arm of which the stiffness depends on its length. Pole-placement and loop-shaping controllers are designed for several constant arm lengths and these controllers are linearly scheduled in a global gain-scheduling controller. Experiments show that scheduling is necessary if high-performance controllers are demanded.