Root-locus Plots Of Negative-feedback And Positive Feedback Systems

Root-Locus Plots of Negative-Feedback and Positive Feedback Systems

Fig: 1                                                                                                      Fig: 2

Figure 1 shows the root loci for the given positive-feedback system. The root loci are shown with dashed lines and curve.

Note that if

one real root enters the right-half s plane. Hence, for values of K greater than 3, the system becomes unstable. (For K > 3, the system must be stabilized with an outer loop.) Note that the closed-loop transfer function for the positive-feedback system is given by

To compare this root-locus plot with that of the corresponding negative-feedback system, we show in Figure 2 the root loci for the negative-feedback system whose closed-loop transfer function is

where GH is the open-loop transfer function. In Table 1, the root loci for negative feedback systems are drawn with heavy lines and curves and those for positive feedback systems are drawn with dashed lines and curves.