基于二次型性能泛函内平衡变换的模型降阶研究

Model Reduction Based on Internal Balance Transform for Quadratic Characteristic Indexes Function

土木工程结构振动控制由于模型的自由度数目较大,结构控制中控制器阶次较高,导致主动控制和半主动控制实施过程中时滞效应十分突出。本文在采用均衡实现技术对结构模型的状态变量重新排序形成内部均衡系统的基础上,对系统二次型性能指标泛函进行内平衡变换,略去对内平衡系统能量影响较小的状态变量,进行结构模型的降阶。通过对20层钢框架结构振动控制Benchmark模型二次型性能指标泛函进行内平衡变换,得到降阶的振动控制模型,计算表明本文方法是可行和有效的。

The models of civil engineering structures usually possess comparatively large DOFs,thus the controller designed directly with original structure model is high order,time delay gets often predominant when the active/semi-active control technologies are applied to suppressing the structure dynamic response.The balanced realization truncation is adopted to deduce the internal balanced model,and then to obtain the reduced model based on internal balance transform for quadratic characteristic indexes function is obtained.The feasibility and validity of model reduction with internal balance transform for quadratic characteristic indexes function are demonstrated by simulation for 20-story benchmark model.