多变量特征轨迹方法及其计算

本文总结了以特征轨迹为基础的线性多变量反馈系统的分析和设计方法,并把这些分析和设计方法在PDP—11/24机上实现.其中线性多变量反馈系统在黎曼曲面上的特征轨迹的绘制采用MacFarlane等提出的网格法,在该方法的基本思想指导下,对判别黎曼曲面上的离散点的函数之间的连续性,提出了实际可用的判别公式,给出了一个判别黎曼曲面上的根轨迹点的详尽过程.设计方法的程序实现是采用ALIGN算法和最小二乘ALIGN算法.本文用奇异值分解方法解决了ALIGN问题最后导致的广义特征值、特征向量问题.在最小二乘算法的基本思想指导下,提出了一个求解最佳实结构的合理迭代过程,这个迭代过程同时考虑了结构因子调整与近似特征结构和近似逆特征结构之间的对偶性.

Multivariable Characteristic Loci Method and Its Algorithms

This paper gives the analysis and design methods of linear multivariable feedback systems on the basis of characteristic loci. All the algorithms for these purposes are programmed and realized on a PDP 11/24 computer. The main points of this paper are as follows: 1. The characteristic loci on the Riemann surface are developed step by step through grid-method calculation. 2. A detailed procedure is proposed for checking the continuation of two neighbouring points on the Riemann surface during curve plotting. 3. ALIGN and least squares (LS) methods are chosen for designing the compensator. Besides, a singular value decomposition algorithm is included for solving generalized eigenvalue and generalized eigenvector problems in the ALIGN method. 4. An iterative method which considers the duality of eigenframe and approximate reverse eigenframe is proposed to solve the optimal real structure of the compensator.