対数根軌跡による自動制御系の計算法 : 第1報対数根軌跡の求め方および特性根の計算

概要

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This is a proposal of studying feedback control systems by means of Log-Root-Locus. Log-Root-Locus method is to pursue characteristic roots of a loop-transfer function on log s-plane instead of s-plane to the root-locus method. Log-Root-Locus is understood not only as one of phase loci as shown in Fig. 2,but as a project of the steepest descent line of log |G(s)| surface erected on log s-plane (Fig. 1). In practice, Log-Root-Locus can be plotted calculating ∠G(s) by (3・2) of which each ∠(1+Ts) is read simultaneously on los (1+s) chart (Fig. 3) used as Fig. 4,where P_i and Z_j correspond respectively to poles and zeros of G(s). Rules for it correspond to those of root-locus, but there are seversal rules specific to the Log-Root- Locus concerning symmetry (Fig. 7) and invertibility etc., which are advantageous1y utilized in plotting and also inducing a Log-Root-Locus of a certain function from that of another function. In the synthesis, characteristic roots can be found on Log-Root-Locus (Fig. 8), and corresponding gain can be calculated by (4・2) using again log(1+s) chart. Knowing gain constant, characteristic roots which sufficiently differ from leading one can be approximately calculated by (5・2) and (5・3) and using Fig. 9,magnifiedcentral portion of log(1+s) chart.
社団法人日本機械学会の論文
1955-11-25