| 分数阶系统极点分布与时间响应 |
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| 引用本文： | 李文.分数阶系统极点分布与时间响应[J].大连铁道学院学报,2006,27(3):44-47,76. |
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| 作者姓名： | 李文 |
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| 作者单位： | 大连交通大学电气信息学院 辽宁大连116028 |
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| 摘 要： | 与传统线性定常控制系统相比,分数阶线性定常系统极点分布与时间响应关系有所不同.本文通过分析多值函数特性在黎曼平面中的表达以及s-平面与w-平面的映射关系,给出了分数阶线性定常系统极点分布与时域响应的定性关系.对位于第二黎曼平面的极点更加远离s-平面的右半平面给出了形象化解释,并称其对应的时间响应为“超阻尼”响应.最后介绍了一种分数阶线性定常系统的稳定性判据.
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| 关 键 词： | 分数微积分 分数阶系统 黎曼平面 极点分布 时域响应 |
| 文章编号： | 1000-1670（2006）03-0044-05 |
| 收稿时间： | 2006-04-17 |
| 修稿时间： | 2006-04-17 |
Pole Distribution of Fractional-Order Systems and Time Response |
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| LI Wen.Pole Distribution of Fractional-Order Systems and Time Response[J].Journal of Dalian Railway Institute,2006,27(3):44-47,76. |
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| Authors: | LI Wen |
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| Institution: | School of Electrical Engineering, Dalian Jiaotong University, Dalian 116028, China |
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| Abstract: | The relations between pole distribution and time response of fractional-order systems are not the same as that of troditional systems.The characteristic expression of multi-value function by using Riemann surfaces is discussed,and the mapping from s-plane into w-plane is also analyzed.Then the relations between pole distribution of fractional-order systems and time-domain response are provided.It is explained visually that a pole located on a 2nd Riemann sheet is farther away from the right half s-plane,consequently its time-reponse is called the 'hyperdamped'.Finally a stability criterion is introduced for linear non time-varying fractional-order systems. |
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| Keywords: | fractional derivative and integral fractional-order systems Riemann surfaces pole distribution time response |
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