Culculation of Feedback Control Systems by Log-Root-Locus : 4th Report, Log-Root-Locus of Pulsed Systems

Abstract

Pulse transfer function 〓(z) which is a z-transform of G(s) is studied on log z-plane. 〓(z) is generally a rational function of z as expressed by (15·8), so that its log-root-locus is traced following the same procedure as in the ordinary transfer function. In the synthesis of the pulsed feedback control system, adequate stability is specified on log z-plane as shown in Fig. 41. Log-root-loci of simple pulsed servos each lacking and comprising the dead time are depicted respectively in Figs. 43. and 44. Pulsed compensating network is most profitably discussed on log z-plane by pole and zero configuration. Sequence of transient response can be calculated by difference equation or by characteristic roots in the form of (17·9) and (17·10). In connection with the frequency response of the pulsed feedback system of Fig. 40, W^*'(jw) of (18·1) is seen to be equal to w'(jw) of (18·4). Frequency response of pulse transfer function is calculated in the same way as in the ordinary transfer function, and expressed as gain and phase diagrams as Fig. 47.