Root Loci of Retarded Control Systems

Abstract

This is an attempt to apply the root locus method to process control systems and to bring the method closer to optimum adjustments theories. Typical root loci graphically traced are shown with superposed constant setting lines to show the effects of controller adjustments, optimum points suggested thus far are also plotted in them. The controller actions treated are from proportional to three term modes as defined by eq. 3. The process was assumed to be single capacity plus dead time types, fig. 3 and eq. 5. Figs. 4 and 5 are principles of graphical solution for dimensionless form of loop transfer function of eq. 7. Figs. 7 to 9 are root loci for respective modes of control. The 25% damping condition is expressed by OE lines in the figures. This line in fig. 7, J and C in fig. 8, and C in fig. 9 are for Cohen-Coon's optimum. ZN and J in fig. 7, Z in fiig. 8 are Ziegler-Nichols's optimum, and T in the figures are Takahashi's optimum defined as the minimum control area of transient response.