| 一类不确定性鲁棒LQR的奇异值特性分析 |
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| 引用本文： | 顾生杰,田铭兴,王果. 一类不确定性鲁棒LQR的奇异值特性分析[J]. 控制工程, 2012, 19(4): 709-711 |
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| 作者姓名： | 顾生杰 田铭兴 王果 |
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| 作者单位： | 1. 兰州交通大学光电技术与智能控制教育部重点实验室,甘肃兰州730070;兰州交通大学自动化与电气工程学院,甘肃兰州730070
2. 兰州交通大学自动化与电气工程学院,甘肃兰州,730070 |
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| 基金项目： | 甘肃省自然科学基金项目，甘肃省高等学校基本科研业务费专项资金 |
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| 摘 要： | 针对系统矩阵存在的范数有界不确定性,基于一种鲁棒线性二次调节器(LinearQuadratic Regulators,LQR)的设计,利用其鲁棒回差方程,详细推导了这种鲁棒LQR灵敏度函数的奇异值最大值与规范LQR灵敏度函数的奇异值最大值之间的关系,证明这种鲁棒LQR相对于规范LQR具有较小的灵敏度函数的最大奇异值,灵敏度函数的奇异值特性分析说明这种鲁棒LQR设计相对规范LQR有较好的控制性能。表明灵敏度函数的奇异值特性分析,是一种有效的控制系统性能分析方法。
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| 关 键 词： | 线性二次调节器 不确定性 鲁棒回差方程 灵敏度函数 奇异值 |
Singular Value Properties of Robust LQR for a Class of Uncertainty |
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| GU Sheng-jie , TIAN Ming-xing , WANG Guo. Singular Value Properties of Robust LQR for a Class of Uncertainty[J]. Control Engineering of China, 2012, 19(4): 709-711 |
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| Authors: | GU Sheng-jie TIAN Ming-xing WANG Guo |
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| Affiliation: | 1.Ministry of Education Key Laboratory of Opto-Electronic Technology and Intelligent Control,Lanzhou Jiaotong University,Lanzhou 730070,China; 2.School of Lanzhou Automation & Electrical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China) |
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| Abstract: | A robust LQR is designedbased on the norm-bounded uncertainty model.By considering robust difference equality,the function expression of maximum singular value of sensitivity function between the robust LQR and LQR is derived in details.The results show that maximum singular value of sensitivity function of the robust LQR is less than that of the standard LQR.So the designed LQR has better robustness performance than common LQR according to the analysis of singular value of the sensitivity function.It is believed that our propose method is useful in analyzing a class of control systems. |
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| Keywords: | linear quadratic regulators uncertainty robust difference equality sensitivity function singular value |
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