Active damping based on decoupled collocated control

Robust stability of controlled mechanical systems is often obtained using collocated actuator-sensor-pairs. Collocation enables the implementation of a passive control law, which is robustly stable, irrespective of structural modeling errors. Within the context of vibration control, this knowledge is used to obtain robust active damping. However, collocated control is inherently in terms of "local" coordinates, whereas vibration analysis is usually in terms of "modal" coordinates. Therefore, modal decoupling of the collocated control loops is required. It is shown that, under mild conditions, transformation of the control problem from local into modal coordinates yields control loops that again enable the implementation of passive and thus robustly stable control laws. The presented theory is illustrated by means of experiments on the six-degrees-of-freedom (DOF) actively controlled lens suspension within a micro-lithography machine.