μ综合中的D-K迭代算法  

D-K iteration algorithm for μ-synthesis

作　　者：何朕[1] 姜晓明[1] 孟范伟[1] 周荻[1] 

机构地区：[1]哈尔滨工业大学控制科学与工程系,黑龙江哈尔滨150001

出　　处：《电机与控制学报》2010年第9期31-35,共5页Electric Machines and Control

基　　金：国家自然科学基金(60674102)

摘　　要：针对μ综合的D-K迭代过程中出现不同的γ值和μ值的问题,分析指出在控制器K的优化求解中Hamilton阵H∞或J∞的一些特征值在γ迭代的进程中可能会相当接近,即出现病态特征值。此时γ迭代就会停在一个较高的γ数值上。实际上,当将控制器闭环后,系统的H∞范数会比这个γ值要低很多。在求解标定阵D(ω)的过程中也会有类似的问题,逐点最小化所得的μ值和用拟合的D(ω)来求得的μ值可能是不一致的,甚至不收敛。给出了正确进行D-K迭代的方法,所附的算例中也给出了各种中间结果来帮助说明D-K迭代中的问题。为了能方便地使用Matlabμ工具箱中的D-K迭代命令,还给出了带有参数不确定性系统的状态空间表达方式。For the resulting values of γ and μ in D-K iterations of the μ-synthesis are quite different from each iteration,in solving the optimal problem of the controller K,some eigenvalues of the Hamiltonian matrices,H∞ and/or J∞,will be very close to each other during the γ-iteration process,i.e.their eigenvalues will be ill-conditioned,and the γ-iteration will stop at a higher value of γ.In the closed-loop system,the real H∞-norm obtained by using the resulting K is much lower than that by the γ-iterations.During finding the scaling matrix D（ω）,the μ-value obtained by point-wise minimization is also different from that by using the fitted D（ω）,and the iterations may not be convergent.The proper steps for D-K iterations are proposed in this paper.A design example is also given by all the intermediate results to illustrate the above mentioned problems of the D-K iteration.The state-space form of the system with parametric uncertainties is also presented for easy use with the D-K iteration commands of the Matlab μ-Tools.

关 键 词：结构奇异值 结构不确定性 Μ综合 D-K迭代 H∞优化 

分 类 号：TP1[自动化与计算机技术—控制理论与控制工程]