空军工程大学学报（自然科学版）
空軍工程大學學報（自然科學版）
공군공정대학학보（자연과학판）
JOURNAL OF AIR FORCE ENGINEERING UNIVERSITY (NATURAL SCIENCE EDITION)
2014年
6期
1-5
,共5页
模型降阶%集结法%可控性矩阵%最小范数最小二乘解%广义逆
模型降階%集結法%可控性矩陣%最小範數最小二乘解%廣義逆
모형강계%집결법%가공성구진%최소범수최소이승해%엄의역
model reduction%aggregation method%controllability matrix%minimum norm least squares%generalized inverse
针对单输入单输出系统，利用部分可控性矩阵的M-P 广义逆作为集结矩阵，提出了一种新的近似集结法模型降阶方法。首先给出了当系统可控与不可控时的2种降阶模型，然后通过误差最小分析归结为一种降阶模型，并利用向量到子空间的距离给出了不同阶降阶模型误差的一个简单计算方法。以此误差作为标准，可以方便地选择满足需要的降阶阶数及降阶模型。最后以实例表明了该方法的有效性和应用性。
針對單輸入單輸齣繫統，利用部分可控性矩陣的M-P 廣義逆作為集結矩陣，提齣瞭一種新的近似集結法模型降階方法。首先給齣瞭噹繫統可控與不可控時的2種降階模型，然後通過誤差最小分析歸結為一種降階模型，併利用嚮量到子空間的距離給齣瞭不同階降階模型誤差的一箇簡單計算方法。以此誤差作為標準，可以方便地選擇滿足需要的降階階數及降階模型。最後以實例錶明瞭該方法的有效性和應用性。
침대단수입단수출계통，이용부분가공성구진적M-P 엄의역작위집결구진，제출료일충신적근사집결법모형강계방법。수선급출료당계통가공여불가공시적2충강계모형，연후통과오차최소분석귀결위일충강계모형，병이용향량도자공간적거리급출료불동계강계모형오차적일개간단계산방법。이차오차작위표준，가이방편지선택만족수요적강계계수급강계모형。최후이실례표명료해방법적유효성화응용성。
For the single input and single output linear system,a new method of approximately aggregated model reduction is presented by using the Moore-Penrose generalized inverse of a partial block controllabil-ity matrix as an aggregation matrix.Two aggregated order reduction models are presented firstly under the condition that the system is controllable and uncontrollable,and then a unique least error reduced model is integrated no matter whether the system is controllable or not.A simple method is deduced to compute the errors of all order reduced models,which are the distances from some known vectors to some certain sub-spaces.The errors of all order reduced models can be used as a model reduced order selection criterion and according to this the best order reduced model can be chosen easily.Some examples are shown to verify the validity and feasibility of this method.
