振动控制设计中的等价鲁棒性极点配置问题

THE EQUIVALENT ROBUST POLE ASSIGNMENT IN VIBRATION CONTROL DESIGN

摘要: 本文首先用Householder变换将状态反馈鲁棒极点配置问题做一等价转换，然后基于以鲁棒度量尽可能小为准则确定相应的非线性规划问题，应用一种优化方法得到所求非线性规划问题的总体优化解．由于经过转换后的等价状态反馈鲁棒极点配置问题中的状态矩阵为上Hessenberg矩阵形式，这有利于迭代过程中的减少计算量，为工程应用开辟了一条新途径．

Abstract: In this paper, we consider the vibration controllable system where A ∈ R2n×2n,B ∈ R2n×m and X ∈ R2n×1, U ∈ Rm×1,, are the state and input of the above system. If we usestate feedback, that is, if we set U = FX, in which F ∈E Rp×2n, then we haveX = (A + BF)XFrom the control theory we know that if the system is controllable, then for any given numbersλ1，λ2，……λ2n. there exists a matrix F, such that matrix (A + BF) has eigenvalues λ1,λ2,… λ2n.Robust control is necessary for structures due to the inherent modeli...