Optimal Robust Position Control with Input Shaping for Flexible Solar Array Drive System: A Fuzzy-Set Theoretic Approach

The position control and vibration suppression problems of the flexible solar array drive system containing uncertainty are considered in this paper. The uncertainty in system may be due to unknown parameters and external disturbance. The uncertainty bound can be described via a fuzzy set. In addition, there exists the flexible vibration in the system. A new optimal robust control approach with input shaping is proposed for the flexible solar array drive system. By designing the position command trajectory, the input shaper is proposed to suppress the flexible vibration. To enhance the position control performance, the optimal robust control is proposed by fuzzy description of the uncertainty bound. Neither the system nor the control is fuzzy if-then rule based. The global solution to this optimal design problem is demonstrated to be always existent and unique. The resulting control is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while minimizing a fuzzy-based performance index associated with both the fuzzy performance and the control cost. In addition, the flexible vibration can be effectively suppressed. The novelty of this research is a systematic control approach by blending input shaping technology, control theory, fuzzy set theory, and optimization theory into an integrated framework, for solving the position control and vibration suppression problems of flexible solar array drive system with mismatched conditions.