| 引用本文: | 胡庭姝, 施颂椒 ,张钟俊.状态反馈系统的H∞低敏感性的设计*[J].控制理论与应用,1991,8(4):379~385.[点击复制] |
| Hu Tingshu, Shi Songjiao And Zhang Zhongjun.H∞-Control By State Feedback Under the Constraint of pole assignment[J].Control Theory and Technology,1991,8(4):379~385.[点击复制] |
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| 状态反馈系统的H∞低敏感性的设计* |
| H∞-Control By State Feedback Under the Constraint of pole assignment |
| 摘要点击 792 全文点击 379 投稿时间：1990-02-01 修订日期：1990-10-04 |
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| DOI编号 |
| 1991,8(4):379-385 |
| 中文关键词 H∞控制 H∞范数 状态反馈 极点配置 梯度法 |
| 英文关键词 H∞-control H∞-norm state feedback pole assignment gradient method |
| 基金项目 |
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| 中文摘要 |
| 本文用状态空间方法对状态反馈系统进行H∞低敏感设计。利用H∞范数与系统状态空间实现的关系，将极点固定条件下的状态反馈系统的H∞控制问题转化为时域上的鲁棒性问题，并由此提出了反映H∞范数的目标函数。该目标函数为反馈矩阵F与闭环系统矩阵A+BF的特征向量矩阵V的函数，在极点固定的限制条件下，F与V可通过一Rmxn→Rmxn的映射参数化为一U∈Rmxn的函数。这样，目标函数为U的泛函，并且?J/?u可以求出。因此，可用梯度法优化J，从而使H∞范数降低。在梯度法优化中，每项迭代只须求解2n个n阶代数方程，与传统的H∞方法求解Riccati方程相比，要简单许多。实例说明，梯度法收敛速度较快，优化效果良好。 |
| 英文摘要 |
| A simple relation between H∞-norm of a transfer matrix and its state space representation is developed. Through this relation, the H∞-control problem by state feedback under the constraint of pole assignment is reduced to a problem similar to robust design, and a performance index related to the H∞-norm is naturally derived. The set of feedback matrices that assign the poles of a system is determined through an Rmxn→Rmxn function. Using this function, the performance index related to -norm can be minimized by gradient method. Thus reduce the H∞-norm. In each step of the gradient method, only two special Sylvester equations, which are equivalent to n n-ordered linear algebraic equations, are included. Example show that the convergence speed of the gradient algorithm is fast. |
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