CAJ | 학술논문

利用一种完全参数化的设计方法,直接在矩阵二阶系统的框架下研究不确定性矩阵二阶系统的H∞观测器设计问题,目标是使观测过程在保持鲁棒稳定并达到期望的动态特性的同时,还能使得外部干扰到误差状态的传递函数的H∞范数小于事先给定的上界数值.基于矩阵二阶系统的Sylvester方程的完全参数化解,通过一组设计参数建立了观测器的所有增益矩阵以及观测器系统矩阵的左特征向量的完全参数化形式.并在此基础上,将H∞范数的上界约束条件转化成一个等价的约束设计参数的条件.该方法能够提供所有的设计自由度,有很强的应用价值.最后通过一个弹簧质量系统表明此方法的有效性.
이용일충완전삼수화적설계방법,직접재구진이계계통적광가하연구불학정성구진이계계통적H∞관측기설계문제,목표시사관측과정재보지로봉은정병체도기망적동태특성적동시,환능사득외부간우도오차상태적전체함수적H∞범수소우사선급정적상계수치.기우구진이계계통적Sylvester방정적완전삼수화해,통과일조설계삼수건립료관측기적소유증익구진이급관측기계통구진적좌특정향량적완전삼수화형식.병재차기출상,장H∞범수적상계약속조건전화성일개등개적약속설계삼수적조건.해방법능구제공소유적설계자유도,유흔강적응용개치.최후통과일개탄황질량계통표명차방법적유효성.
The problem of H∞ observer design for uncertain matrix second-order linear systems is considered in the matrix second-order framework by using a complete parametric design approach. The goal is to design a matrix second-order linear state observer so that the observer process remains robustly stable and achieves the desired dynamical performance, and the transfer function from exogenous disturbances to error state output meets the prescribed H∞ norm upper bound constraint. Based on the complete parametric solution to the Syvester matrix equation of matrix second-order linear systems, complete parameterizations for all the observer gain matrices as wel as the left eigenvectors of the observer system matrix are established in terms of a set of design parameters. Also, based on these parametric gain matrices and left eigenvectors, the prescribed H∞ norm upper bound constraint is transformed into an equivalent constraint condition which restricts the design parameters. The proposed approach provdides all the degrees of freedom and has great potential in applications. A sprign-mass system is utilized to show the effect of the proposed approache.