Calculation of Feedback Control Systems by Log-Root-Locus : 3rd Report, Log-Root-Locus of Systems with Distributed Constants

Abstract

Log-root-locus method is applicable to the distributed system whose transfer function is transcendental equation. The dead time and the distributed lag which are frequently encountered in the process control can be treated as the distributed line of Fig. 25 or Fig. 28 and Fig. 29 which lead to the known transfer functions e^-Ts and e^-√(Ts). Their phase loci and gain loci are depicted in Figs. 30 and 31 which are used to trace log-root-loci of systems comprising those terms. Figs. 32 and 33 are depicted as to the representative process with the dead time. Generally speaking, the dead time is apt to make higher order terms unstable. Figs. 35 and 36 are log-root-loci of systems comprising the distributed lag. Comparing them with Figs. 32 and 33, it is seen that the distributed lag effects rather conservatively to the system dynamics compared with aggravating effects of the dead time. The equivalent dead time system for the distributed lag e^-√(s) was chosen to have the same fundamental root at the same gain corstant. Fig. 37 contrasts each indicial responses of both systems which confirms conventional way of choosing the equivalent system.