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对一个 m 输入 m 输出的对象,设计动态补偿器 K(s)=K~(?)s~(?)+…+K~((-1))s~(-1)+K~((0))+K~((1))s+…+K~((β))s~β使补偿后的系统传函矩阵成为对角优势,是现代频域设计技术的关键环节。迄今为止,解决这一问题的实用方法是准对角化法及其各种推广,但最后都要归结为一个(α+β+1)m×(α+β+1)m 维矩阵的特征值特征向量问题的求解过程。本文从准对角化思想出发,提出准优势化算法,使这一求解过程减化为一个2×2维对称实阵的相应问题,使计算量大为缩减,相应提高了计算精度,也便于程序编制。文中对两个实例进行设计,与旧法比较,设计结果表明了新算法的满意效果。此外,本文对某些有关的理论问题的部分研究成果进行了概述。
In this paper, we design the dynamic compensator K (s) = K ~ (?) S ~ (?) + ... + K ~ (-1)) s ~ -1 + K ~ 0) + K ~ ((1)) s + ... + K ~ ((β)) s ~ β make the compensated system transfer matrix diagonal advantage, which is the key link of modern frequency domain design technology. So far, the practical method to solve this problem is quasi-diagonalization and its various promotion, but in the end it must be reduced to the feature of an (α + β + 1) m × (α + β + 1) Solution Process of Value Eigenvector Problem. Based on the idea of quasi-diagonalization, a quasi-dominant algorithm is proposed in this paper to reduce this solution to the corresponding problem of a 2 × 2-D symmetric real matrix, which greatly reduces the computational complexity and increases the computational accuracy accordingly Programming. In this paper, two examples are designed, compared with the old one, the design results show the satisfactory effect of the new algorithm. In addition, some of the relevant theoretical issues related to the research findings are summarized.