Control Systems engineering Forum. CTM: Root Locus Tutorial. In this tutorial we will introduce the root locus, show how to create it using MATlAB, and demonstrate how to design feedback controllers using the root locus that satisfy certain performance criteria. Key MATLAB commands used in this tutorial are: feedback , rlocus , step , sisotool Contents Closed-Loop Poles The root locus of an (open-loop) transfer function is a plot of the locations (locus) of all possible closed-loop poles with proportional gain K and unity feedback. The closed-loop transfer function is: and thus the poles of the closed-loop poles of the closed-loop system are values of such that If we write , then this equation has the form: Let = order of and (the order of a polynomial is the highest power of that appears in it). We will consider all positive values of K. , the poles of the closed-loop system are or the poles of . Or the zeros of No matter what we pick K to be, the closed-loop system must always have poles, where is the number of poles of .
Branches, each branch starts at a pole of .
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