ACTIVE CONTROL OF CHAOTIC VIBRATION IN A CONSTRAINED FLEXIBLE PIPE CONVEYING FLUID

An active vibration control system is designed, and is numerically ver ified, to suppress the undesirable chaotic vibration in a constrained flexible pipe conveying fluid, which exhibits regions of flutter and c haotic motions at sufficiently high flow velocity. The four-dimensiona l analytical model obtained from the continuous system by Galerkin's m ethod, that has been previously verified to represent adequately the d ynamics, is utilized for designing the control law. Various control de sign methodologies are investigated for different situations. Firstly, optimal regulator theory is applied to obtain feedback gains to stabi lize the system with full state information. The effects of the locati on and length of the piezoelectric actuators on the efficiency as a vi bration damper are theoretically examined in this case. Secondly, a st ate observer is added to estimate the required state signals. To cover the situation when the states are not directly measurable, dynamic co mpensators are obtained to control the system with only the output fee dback. Finally, a robust controller for such a system with large flow velocity variations, without sensing the flow velocity or gain-schedul ing, is developed. The robust control method is based on a newly devel oped sensitivity-based Quantitative Feedback Theory (QFT) scheme, whic h allows the controller;to make the closed loop system response meet q uantitatively specified performance requirements even though the syste m has large parameter variations. Numerical simulations are carried ou t for the different controllers and they validate the effectiveness of the proposed control scheme. The QFT scheme yields a remarkable resul t in stability robustness with respect to flow velocity variations.