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针对由飞轮控制的欠驱动航天器,研究了直接以飞轮转速为控制输入时航天器姿态的小时间局部可控性与可镇定性。首先,视飞轮转速为输入,将航天器与飞轮总角动量守恒的约束直接纳入系统动力学方程中。然后,利用非线性系统的可控性与可镇定性理论分析该系统方程在分别带有一个和两个飞轮时的控制特性。结果表明,仅在带有两个非共轴的飞轮时航天器的姿态才有可能满足局部可控;同时,系统已经不能被时不变光滑状态反馈渐近镇定,但至少可以被分段连续的状态反馈渐近镇定。据此,设计了基于四元数的非光滑控制器使得航天器的姿态迅速镇定,同时飞轮转速不超过最大转速,既验证了理论分析结果的正确性,又具有一定的实用意义。
Aiming at the underactuated spacecraft controlled by flywheel, the local controllability and the stablity of spacecraft attitude during direct control of flywheel speed are studied. First of all, depending on the rotational speed of the flywheel, the constraints of the total angular momentum of the spacecraft and the flywheel are directly incorporated into the system dynamics equations. Then, using the controllability and the calibratable theory of nonlinear system, the control characteristics of the system equation with one and two flywheels respectively are analyzed. The results show that the attitude of the spacecraft is only partially controllable when there are two non-coaxial flywheel. At the same time, the system can not be asymptotically stabilized by the time-invariant smooth state feedback, but it can at least be segmented continuously The state feedback asymptotic calm. Accordingly, a quaternion-based non-smooth controller is designed to make the attitude of the spacecraft quickly calm down while the flywheel speed does not exceed the maximum speed, which not only verifies the correctness of the theoretical analysis results, but also has certain practical significance.