摘要
针对线性时不变高阶MIMO系统模型难以直接进行计算分析的问题,对高阶模型进行模型降阶。依据模型降阶理论,对线性时不变系统进行Lyapunov方程求解,得到线性系统的完全可控Gramians矩阵和完全可观Gramians矩阵,对Gramians矩阵进行Cholesky分解,得到Cholesky分解因子,分解因子通过SVD(singular value decomposition)法求得Hankel奇异值,从而确定系统的平衡变换阵。计算可控可观Gramians矩阵的左右特征空间基底矩阵,利用左右特征空间的基底矩阵求得原系统降阶的系统,通过Hankel SVD方法确定降阶之后的误差范围。利用Matlab对SLICOT测试库中的便携式CDPlayer 120阶的高阶模型进行降阶,获取到50、30、20阶的降阶模型,对研究算法进行验证,结果表明,降阶效果理想。
For linear time invariant high-order system calculation and analysis model is difficult to directly, so we need to study on model order reduction of the model According to the basic theory of model order reduction, Lyapunov equation solution to linear time invariant system, completely controllable Gramians matrix and considerable Gramians matrix completely are obtained for a linear system, the completely controllable and considerable Gramians matrix Cholesky decomposition, the Cholesky decomposition factor and the factor decomposition by SVD （ singular value decomposition） method for Hankel singular value are given to determine the balance of the system transformation matrix. The reduced order system is given by based matrix of left and fight feature space which is obtained by the controllable and considerable Gramians matrix. The error bound for several reduced-order models are computed by using the method of Hankel SVD. In order to obtain the several reduce-order models, using Mtalb to turn CDPlyer high-order model that stored in SLICOT test library to a low-order system. The results show that the above order reduction method is feasible.
出处
《哈尔滨理工大学学报》
CAS
北大核心
2017年第2期50-54,60,共6页
Journal of Harbin University of Science and Technology
基金
黑龙江省自然科学基金(F201307)
关键词
线性时不变系统
模型降阶
Hankel奇异值
linear time invariant system
model order reduction
balanced transformation
