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The root locus of an open-loop transfer function H(s) is a plot of the locations (locus) of all possible closed loop poles with proportional gain k and unity feedback 2. Plotting the Root Locus of a Transfer Function. Consider an open loop system which has a transfer function of. A root locus plot shows the locus of the poles and zeros of in the complex plane as varies within an interval . Sometimes it is helpful to animate a root locus plot because this shows the orientations of the pole and zero trajectories better than a static plot. ROOT LOCUS TECHNIQUES In this lecture you will learn the following : The definition of a root locus How to sketch root locus How to use the root The root locus also gives a graphic presentation of a system s stability. Before presenting root locus, let us review two consepts that we need for the Root-locus diagrams are s-plane plots of the loci of closed-loop poles with open-loop gain K as a parameter. As K increases from zero, the closed-loop poles begin at open-loop poles and proceed toward open-loop zeros (some of which may be at infinity). When these poles leave the left half-plane G ( s ) = ks s + 3 determine when the root locus begins and ends Solution O.L.T.F pole s + 3 = 0 s = - 3 O.L.T.F zero ks = 0 s = 0 Hence the root locus begins at s = - 3 for k = 0 and ends at s = 0 for k = ? 88. Root Locus Lecture Notes by Ms Kiio 7.2 Angle and Magnitude Criterion The closed loop transfer Section 5: root?locus analysis. MAE 4421 - Control of Aerospace. & Mechanical Systems. ? Trajectory of closed?loop poles vs. gain (or some other parameter): root locus. ? Graphical tool to help determine the controller gain that will put poles where we want them. Root locus provides the better way to indicate the parameters. Now there are various terms related to root locus technique that we will use frequently in this Characteristic Equation Related to Root Locus Technique : 1 + G(s)H(s) = 0 is known as characteristic equation. Now on differentiating the A root locus branch exists on the real axis between the origin and -oo.There are three asymptotes for the root 1oci.The angles of asymptotes are &18O0(2k+ 1) Angles of asymptotes = = 60°, -60°, 180" 3 Referring to Equation (6-13), the intersection of the asymptotes and the real axis is obtained as Next. Consider a system like a radio. The radio has a "volume" knob, that controls the amount of gain of the system. High volume means more power going to the speakers, low volume means less power to the speakers. Sketch the root loci for the system shown in Figure 6-39(a). (The gain K is assumed to be positive.) Observe that for small or large values of K the system is overdamped and Chapter 6 / Root-Locus Analysis. 3. Determine the breakaway and break-in points.The characteristic equation for the system IS. Z-Domain Root Locus. In general the CE: 1 + GcGp H(z) = 0. will be a polynomial in z 2.14 Fall 2004. 23. Root Locus. ROOTS OF 1+KCG-P(z) = 0. Same rules as before: Starts at open loop pole = +p Real axis part to left of odd number of poles Ends at zero at infinity. Root Locus is a simple graphical method for determining the roots of the characteristic equation. It can be drawn by varying the parameter (generally gain of the system but there are also other parameters that can be varied) from zero to infinity. Root Locus Method with step by step solution. Root Locus is a simple graphical method for determining the roots of the characteristic equation. It can be drawn by varying the

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