| 修正Hamilton方法及其在车载倒立摆稳定化问题上的应用 |
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| 引用本文： | 张振兴,刘岩,王红.修正Hamilton方法及其在车载倒立摆稳定化问题上的应用[J].工程数学学报,2012,29(2):267-277. |
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| 作者姓名： | 张振兴 刘岩 王红 |
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| 作者单位： | 1. 南开大学数学科学学院,天津,300071
2. 南开大学数学科学学院,天津300071;南开大学核心数学与组合数学教育部重点实验室,天津300071 |
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| 基金项目： | The Natural Science Foundation of Tianjin(05YFJMJC01200) |
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| 摘 要： | 本文基于反馈控制和带有控制的Hamilton系统的修正Hamilton函数,研究了车载倒立摆系统的稳定化问题.给出了利用修正Hamilton方法稳定化带有控制的Hamilton系统的一个准则.通过复杂的计算,证明了车载倒立摆系统的不稳定平衡态可以通过增加反馈控制的方式成为渐近稳定的平衡态.利用仿真验证了所给控制的有效性.
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| 关 键 词： | 车载倒立摆 修正Hamilton方法 稳定化 |
The Modified Hamiltonian Method and its Application in the Stabilization of the Inverted Pendulum on a Cart |
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| ZHANG Zhen-xing
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LIU Yan
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WANG Hong.The Modified Hamiltonian Method and its Application in the Stabilization of the Inverted Pendulum on a Cart[J].Chinese Journal of Engineering Mathematics,2012,29(2):267-277. |
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| Authors: | ZHANG Zhen-xing LIU Yan WANG Hong |
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| Affiliation: | 1,2(1-School of Mathematical Sciences,Nankai University,Tianjin 300071;2-The PMC Key Lab ME of China,Nankai University,Tianjin 300071) |
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| Abstract: | Based on the feedback control and modified Hamiltonian for the Hamiltonian system with control,the stabilization of the inverted pendulum on a cart system is explored in this paper.A criterion of stabilization of a Hamiltonian system with control is given by the modified Hamiltonian method.By a complicated calculation,the unstable equilibrium of the inverted pendulum on a cart system can be proved to achieve asymptotically stability by adding feedback control.A simulation is presented to show the efficiency of the designed feedback control law. |
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| Keywords: | inverted pendulum on a cart modified Hamiltonian method stabilization |
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