平衡截断法与时间尺度法的降阶效能分析

摘要

To analyze the advantage and limitation of using balanced truncation method during controller designing, the comparison between balanced truncation method and timescale method is made in the decision of reducing dimension, the selection of the truncated states and the frequency response of the reduced order system. To evaluate the degree of approximation, a method using reduced controller control performance index is proposed. Two reduced order controllers are designed using the truncated system and slow timescale system, and the performances are compared. Simulation results show that the balanced truncation method is more precise in selecting the system state. For the system which has not change its open loop characteristics after adding the control, the reduced order system obtained by the balanced truncation method has better approximation than the timescale method, however, for the system has changed its characteristics with feedback control, the balanced truncation method can not be sensitive to the changes, the approximation is worse than the other method.%为分析利用平衡截断法截断系统设计控制器的优势及局限,对比分析了在对系统降阶的过程中平衡截断法和时间尺度法在降阶维数的判断、截断状态的选择及截断后降阶系统频率响应方面的区别与联系.提出一种以降阶控制器控制原系统的效果来判断降阶系统对原系统的近似方法.利用平衡截断后系统与慢时间尺度系统分别设计降阶控制器.仿真结果表明,平衡截断法在截断系统状态过程中更为精细,对于加入控制后为改变其开环特性的系统,依据平衡截断法得到的降阶系统对原系统逼近效果比时间尺度法好;而对于反馈控制改变其开环特性的系统,平衡截断法不能敏感到系统特性的改变,近似效果比时间尺度法差.