A robust vibration suppression controller design for space flexible structures

Being an active vibration suppression method, the positive position feedback (PPF) control has attracted great attentions to damp out the flexible space structure vibrations which make adverse impacts for spacecraft attitude pointing precision. But the robustness with respect to the inaccurate structure modal frequencies is seldom considered in PPF controller designing. In this paper, robust asymptotically stability criterions are proposed to deal with the inaccurate structure modal frequencies. According to these criterions, a robust PPF controller design method is proposed. The robust PPF controller is derived from solving a group of LMIs with adjustable parameters. These parameters describe the robustness with respect to the structure modal frequency variations and convergence velocity of the vibration modes, respectively. Properly setting these parameters can achieve a tradeoff between the robustness for the modal frequency variations and the damping performances of the structure oscillations. Finally, a simulation is presented to illustrate the effectiveness of the proposed robust PPF controller design method.