The Bouncing Ball Apparatus as an Experimental Tool
The Bouncing Ball Apparatus as an Experimental Tool
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弹球装置作为实验工具
DOI：
10.1115/1.2194069
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
B. Paden
中科院分区：
文献类型：
--
作者：
Ananth Kini;T. Vincent;B. Paden
正弦振动板上的弹跳球具有丰富的非线性动力学行为，是最容易产生混沌行为的力学系统之一。设计了一个计算机控制系统，用于输出校准、状态确定、系统辨识和与磁力矩合作设计的新型弹跳球装置的控制。这里描述的实验构成了第一个研究与设备进行。实验方法用于确定球的恢复系数，这是建模和控制所需的一个非常敏感的参数。恢复系数的估计使用数据从一个稳定的单周期轨道和不使用相应的数据从球地图。为了控制的目的，使用两种方法来构造线性映射。通过直接从设备收集数据来确定第一图。第二个映射是使用高反弹近似解析导出的。该地图是用来估计域的吸引力，以一个稳定的单周期轨道。这些吸引域用于构造一种混沌控制算法，用于将球从任何初始状态驱动到稳定的一个周期。基于混沌控制算法的实验结果进行了比较，发现直接从数据中得到的线性映射不仅能更准确地表示吸引域，而且能更鲁棒地将球控制到稳定的单圈。
The bouncing ball on a sinusoidally vibrating plate exhibits a rich variety of nonlinear dynamical behavior and is one of the simplest mechanical systems to produce chaotic behavior. A computer control system is designed for output calibration, state determination, system identification, and control of a new bouncing ball apparatus designed in collaboration with Magnetic Moments. The experiments described here constitute the first research performed with the apparatus. Experimental methods are used to determine the coefficient of restitution of the ball, an extremely sensitive parameter needed for modeling and control. The coefficient of restitution is estimated using data from a stable one-cycle orbit both with and without using corresponding data from a ball map. For control purposes, two methods are used to construct linear maps. The first map is determined by collecting data directly from the apparatus. The second map is derived analytically using a high bounce approximation. The maps are used to estimate the domains of attraction to a stable one-cycle orbit. These domains of attraction are used to construct a chaotic control algorithm for driving the ball to a stable one-cycle from any initial state. Experimental results based on the chaotic control algorithm are compared and it is found that the linear map obtained directly from the data not only gives a more accurate representation of the domain of attraction, but also results in more robust control of the ball to the stable one-cycle.