Robust vibration control of flexible tensegrity structure via μ synthesis

SUMMARY μ synthesis is formed by combining the structured singular value concept and H∞ theory. The vibration control of the flexible tensegrity structure with mixed uncertainties via μ synthesis is presented. The uncertainties including parametric uncertainties of modal frequency and damping, the high‐frequency unmodeled dynamic uncertainty, and the uncertainties of sensors and actuators are analyzed. Based on the μ theory, the generalized control system of flexible structure is established. The robust stability and robust performance are analyzed in the standard framework of μ synthesis based on the μ controller which is designed by the D‐K iteration. Finally, the numerical simulation of a tensegrity structure is given. The simulation results show that μ controller can guarantee the closed‐loop system of the flexible tensegrity structure stable while exist the parametric perturbation and overflow problems simultaneously. μ controller takes greater control force to realize the rapider vibration attenuation compared with H∞ controller. The balanced realization of μ controller shows that the reduced order μ controller still meets the robust stability and performance requirements for the vibration control of the tensegrity structure. Copyright © 2011 John Wiley & Sons, Ltd.