Active Vibration Control Of Flexible Structures With Mixed Uncertainty

Flexible structures exhibit low damping and large flexibility, so they are easy to present vibrations when suffer from the internal motivation and external disturbances. In order to meet performance requirements, the active vibration control is needed. However, during the modeling of the flexible structural system, there are always various parameter uncertainties, and it is easy to overlook the uncertainty in high order. Sensor noises and additional disturbances of actuators excitation may also affect system performance, when it is running. In this paper, the robust active vibration control of flexible structures with mixed uncertainty is considered.Based on the structured singular value theory, the weighting functions are selected according to vibration character of the flexible structure and the control index, and the various perturbations are separated, then the generalized control system of flexible structures is established. Taken the flexible cable-strut structure and tensegrity structure as examples, theμcontroller is designed by D-K iteration with performance adjustment, H∞controller is also designed for comparison. The simulations show thatμcontrollers can guarantee that the closed-loop system of flexible structures with mixed uncertainty is stable, and has good robust performance with disturbances rejection. The conservativeness of H∞controller in dealing with such type of problem is avoided. The validity and advantages ofμsynthesis approach in dealing with the active vibration control of the flexible structures with mixed uncertainties are embodied.Then, the order of theμcontroller of the flexible structure is reduced by balanced truncation method. The simulations show that the reduced orderμcontroller can also guarantee the original system is stable and meet the robust performance requirements. It decreases the implementation complexity ofμcontroller.Finally, based on the fundamental of distributed control, the simplified subsystem model of interconnect system in series model is proposed. The combination technology of H∞,μcontrol and distributed control is explored, and is applied to vibration control of tensegrity structure, and results in good performance. The work in this paper is helpful for the application of the active vibration control of flexible structures.