Global Asymptotic Stabilization of a Spinning Top With Torque Actuators Using Stereographic Projection
Global Asymptotic Stabilization of a Spinning Top With Torque Actuators Using Stereographic Projection
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使用球极投影的扭矩执行器的旋转陀螺的全局渐近稳定
DOI：
10.1109/acc.1994.751795
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Dennis S. Bernstein
中科院分区：
文献类型：
--
作者：
C. Wan;Panagiotis Tsiotras;Vincent T. Coppola;Dennis S. Bernstein
利用泊松方程的赤平投影法，导出了旋转陀螺的动力学方程，其中的取向用复变量表示。用能量-Casimir方法导出了纺纱毛条失控运动Lyapunov稳定的充要条件。利用级联形式系统理论中的技巧，综合了用两个力矩作动器使纺纱陀螺运动全局渐近稳定到睡眠运动的控制律，并利用零动力学的Hamilton-Jacobi-Bellman理论进行了推广。总之，本文提供了一个很好的例子，说明了动力学和控制之间的相互作用产生了优雅而有力的结果。
The dynamical equations for a spinning top are derived in which theorientation is specified by a complex variable using stereographic projectionof Poisson's equations. Necessary and sufficient conditions for Lyapunovstability of the uncontrolled motion of the spinning top are derived usingthe Energy-Casimir method. Control laws that globally asymptoticallystabilize the spinning top to the sleeping motion using two torque actuatorsare synthesized by employing techniques from the theory of systems in cascadeform and generalized using Hamilton-Jacobi-Bellman theory with zero dynamics.In short, this paper provides a nice example where the interplay betweendynamics and control leads to elegant and powerful results.