On the robustness of AVS controller to sensor-actuator noncollocation

This paper considers the problem of controlling flexible systems, such as rotating shafts, whose dynamics is described by the wave equation. In previous works, infinite dimension transfer functions were introduced. Their special structure lead to the absolute vibration suppression (AVS) linear collocated controller that results in a low order plus delay closed loop transfer function, hence eliminates the infinite number of poles. In this paper, the robustness problem of small, unintentional noncollocation between the control and the measurement is investigated for both conservative and non-conservative (damped) systems. It is shown that the loop can be robustly stabilized only if the load end of the structure contains damping. The use of robust AVS controller (RAVS) to overcome the problem of noncollocation is discussed and a tuning algorithm for it is suggested. Its improved performance is shown by means of an example.