ELE 639 Lecture Notes - Lecture 10: Root Locus, Algebraic Equation, Imaginary Number
14 Oct 2018
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Document Summary
The root locus method is a graphical technique used to plot the location of the poles of a closed loop system as one of the system parameters is varied. This technique is used to provide a measure of the relative stability of a system, as well as to determine appropriate parameter values, which will yield suitable root locations. In the general case the open loop transfer function is g(s)h(s). However, typically an equivalent open loop system is analyzed, with h(s) = 1. Root locus equations below are derived for such a case, without a loss of generality (see the notes on the equivalent unit feedback loop). Consider a simple unity feedback system, such as in figure 10-1, with the variable proportional controller gain k. The closed loop system transfer function and its characteristic equation are as follows: sgcl sy sr skg skg. Figure 10-1 closed loop equivalent unit feedback system under proportional control.
