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基于Hamilton变分原理,采用Mindlin厚板理论,研究了旋转状态中心刚体—悬臂厚板振动及其变结构控制问题。采用Hamilton状态空间法,应用弹性波与振动模态理论,确定了Mindlin厚板中的振动模态。针对该模型系统设计了控制器,采用滑模变结构控制理论,实现了对系统实施渐近稳定控制的设计。采用的变结构控制能使系统达到所期望的振动状态,有效地抑制了平板振动。最后,给出了数值模拟结果,讨论了中心刚体—悬臂厚板位移的动力学控制规律。该方法和计算结果可望能在带有柔性附件航天器的动力学控制中得到应用。
Based on the principle of Hamilton variational principle, the Mindlin plate theory is used to study the vibration of rigid-cantilever thick plate center and its variable structure control. Using the Hamilton state-space method, the vibration modes in the Mindlin slab are determined using the theory of elastic wave and vibration mode. A controller is designed for the model system. The sliding mode variable structure control theory is adopted to realize the design of asymptotic stability control for the system. The variable structure control adopted can make the system achieve the desired vibration state and effectively restrain the vibration of the slab. Finally, the numerical simulation results are given, and the dynamics governing the displacement of center rigid body-cantilever thick plate is discussed. The method and calculation results are expected to be applied in the dynamics control of spacecraft with flexible attachment.