块对角可控规范型多输入线性系统及极点配置  

Linear multi-input system of the new block diagonal controllable canonical forms and its pole placement

作　　者：高遵海[1] 陈绵云[1] 同小军[2] 

机构地区：[1]华中科技大学控制系,湖北武汉430074 [2]武汉工业学院数理系,湖北武汉430023

出　　处：《系统工程与电子技术》2007年第1期130-133,共4页Systems Engineering and Electronics

基　　金：国家自然科学基金(799970025);湖北省教育厅科研计划项目(D200618009)资助课题

摘　　要：基于向量空间的模结构分解和矩阵的有理标准形给出了定常多输入线性系统一类新的块对角可控规范型,其中的系统矩阵相似与一个块对角矩阵,该块对角矩阵类似于矩阵的有理标准形,与现在有的可控规范型比较,更容易反映系统的结构特征,证明步骤给出了求解方法。作为一个应用,讨论了定常多输入线性系统的极点配置问题,得到了反馈增益矩阵的一般表达式,此表达式中含有任意参数,此方法将多输入线性系统极点配置问题转化为个数为系统矩阵循环指数的单输入系统的极点配置问题,进而推导出确定一个反馈增益矩阵的最少元素个数即为系统的阶数。Based on the decomposition theorem for vector space with module structure and rational canonical form of matrix, a kind of new block diagonal controllably canonical forms are inferred when the time-invariant linear multivariable system is completely controllable,which the system matrix is similar to a block diagonal and has an analogy with its rational canonical form. Compare with current controllability canonical forms, this kind is easier to analyse the system constructional characteristic. The process of proof gives an effective solution method. As an example, a new method of pole placement based on this kind of controllability canonical forms in multi-input system is proposed. The theory and approach are introduced, and the general expression containing arbitrary parameter is obtained for the feedback gain matrix. This method changes the problem of multi-input system to several problems of single-input. The number is the cycle index of system matrix. Compare with some known results, this method put forward that the least number of unknown entries of the feedback gain matrix is the order of the system matrix.

关 键 词：定常线性系统 可控规范型 极点配置 

分 类 号：TP271.61[自动化与计算机技术—检测技术与自动化装置] O231.1[自动化与计算机技术—控制科学与工程]