Enhanced structural controllers for non-collocated systems

The present work investigates the adverse effects of non-collocated sensors and actuators on the phase characteristics of flexible structures and the ensuing implications on the performance of structural controllers. Two closed-loop systems are considered. The first one consists of a pinned-free flexible beam with the control torque applied at the pinned-end. The second one is a clamped-free deformable beam with the control moment generated by two piezoelectric actuators bonded at the top and bottom surfaces near the clamped-end. The phase angle contours for both systems were generated as functions of the normalized sensor location and the excitation frequency. They illustrate the loci of the imaginary open-loop zeros along with the resulting minimum and non-minimum phase regions of the systems as the sensors sweep the entire span of the beams. Two structural controllers are designed based on the sliding mode methodology and the active damping control strategy to attenuate the undesired in-plane transverse deformation of the pinned-free beam. The results have revealed three distinct regions for the sensor’s location whereby the performance of the sliding mode controller can be stable, unstable, or stable after incorporating a remedial action into the control algorithm based on the phase angle contour information of the open-loop system. On the other hand, the active damping controller eliminated the overall in-plane transverse deformation by both active damping and having the first two elastic modes being equal in magnitude and opposite in sign. The dissipative nature of this controller and the dependency of its gains on the mode shapes of the beam have yielded a robust and stable performance of the closed-loop system irrespective of the sensor location.