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Heavy disturbances caused mainly by wind and friction in the mount drive system greatly impair the pointing accuracy of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). To overcome this negative effect, a third order Higher Order Sliding Mode (HOSM) controller is proposed. The key part of this ap-proach is to design an appropriate observer which obtains the acceleration state. A nonlinear adaptive observer is proposed in which a novel polynomial model is applied to estimate the internal disturbances of the mount drive system. Theoretical analy-sis demonstrates the stability of the proposed observer. Simulation results show that this nonlinear adaptive observer can obtain a high precision acceleration signal which completes the HOSM controller. Furthermore, the HOSM approach can easily satisfy the position tracking requirements of the LAMOST mount drive system.