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七十年代,以Rosenbrock为代表的英国学派用频率域方法研究多变量线性系统,创立了借助计算机辅助进行多变量控制系统设计的一整套方法。在这个方法中用前后补偿器将系统的传递阵(或逆阵)补偿成对角优势,是设计控制系统的关键,特别是能否用简单易实现的实常阵补偿器,将系统补偿成对角优势,更是人们所关切的问题。本文给出了用实常阵补偿器补偿系统传递阵为对角优势的充分性定理和必要性定理,及按一种较好的对角优势尺度,确定实常补偿器的数学表达式。
In the seventies, the British school, represented by Rosenbrock, studied a multivariable linear system using the frequency-domain method and created a set of computer-assisted multivariable control system designs. In this method, using the front and back compensators to compensate the transmission matrix (or inverse matrix) of the system to the diagonal advantage is the key to designing the control system. In particular, whether the system can be compensated by using the simple and easy real real array compensator Diagonal advantages, but also people’s concerns. In this paper, the sufficient and rational theorems and the necessary theorems for compensating the system transfer matrix with real matrix compensator are given, and the mathematical expression of real compensator is determined according to a better diagonal predominance scale.