Like in the example, the section of the root locus between the pole at 0 and 1 has a single pole at 0 at the right end. Note that since the root locus may have more than one branch, when you select a pole, you may want to find out where the other poles are. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Ppt root locus powerpoint presentation free to view. Chapter 6 root locus notes, control system, electrical. The root locus plot gives us a graphical way to observe how the roots move as the gain, k, is varied. This is also known as root locus technique in control system and is used for determining the stability of the given system. Root locus allows us to visualize the changes in the closedloop poles as the parameter k is increase from 0 to infinity.
Root locus overview erik cheever swarthmore college. Nptel provides elearning through online web and video courses various. Root locus method part 2 engineering mathematics notes edurev is made by best teachers of engineering mathematics. Nptel video lecture topics for electrical engineering new no. Root locus for control systems national instruments. Lecture abstract ee c128 me c4 feedback control systems. This document is highly rated by engineering mathematics students and has been viewed 290 times. Nptel video lectures, iit video lectures online, nptel youtube lectures, free video.
Lecture 30 rootlocus method lecture 31 rootlocus rules lecture 32 asymptotes of root locus lecture 33 routh array lecture 34. Note 7 rootlocus techniques college of engineering. Thus, the root locus is symmetric with respect to the real axis. In control theory and stability theory, root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. Consequently, most contourdetection algorithms will identify negative real axis as a contour line, although it does not belong to the root locus. Root locus plot of dynamic system matlab rlocus mathworks. From the plot above we see that all the poles selected are at reasonable positions. Since the pole at s1 is closer to the origin, we would expect it to dominate somewhat, giving the system behavior similar to a first order system with. Along the real axis, the root locus includes all segments that are to the left of an odd number of poles and zeros. Root locus endpoints the locus starting point k0 are at the openloop poles and the locus ending points k.
The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the openloop transfer. Nptel video lecture topic list created by linuxpert systems. Nptel provides elearning through online web and video courses various streams. Ifcomplexpolesdidntexistinconjugate pairs,theresultingpolynomialwouldcontain complexcoecients. On the realaxis the root locus exists only in the segment. Introduction to control problem basic feedback structure introduction to control problem dynamic systems and dynamic response models of industrial control devices and systems basic principles of feedback control concepts of stability and routh stability criterion the performance of feedback systems compensator design using root locus plots the. The root locus of an openloop transfer function is a plot of the locations locus of all possible closedloop poles with some parameter, often a proportional gain, varied between 0 and. Root locus technique in control system electrical4u. Because our system models are rationalpolynomial with real coef. The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the.
Since root locus is a graphical angle technique, root locus rules work the same in the z and s planes. Typically, the parameter is a control gain, although any parameter of interest can be used. Lecture 30 root locus method lecture 31 root locus rules lecture 32 asymptotes of root locus lecture 33 routh array lecture 34 singular cases lecture 35 closed loop poles lecture 36 controller in the forwarded path lecture 37 mapping of control in the complexplane lecture 38 encirclement by a curve lecture 39 nyquist criterion. The number of branches of root locus equal to the number of closed loop poles. Evans, is a technique for determining how the poles of a feedback control system move in the complex plane as a parameter is varied. Nptel video course electrical engineering nonlinear dynamical systems subject coordinator prof. The roots of the characteristic equations are at s1 and s2. Now in order to determine the stability of the system using the root locus technique we find the range of values of k for which the complete performance of the system will be satisfactory and the operation is stable. Educational video lectures, tutorials nptel videos. Introduction to control problem basic feedback structure introduction to control problem dynamic systems and dynamic response models of industrial control devices and systems basic principles of feedback control concepts of stability and routh stability criterion the performance of feedback systems compensator design using root locus plots the nyquist stability. This is a technique used as a stability criterion in the field of classical control theory developed by walter r. For example, it is useful to sweep any system parameter for which the exact value is uncertain in order to determine its behavior.
Lecture 31 compensator design using root locus plots continued. Root locus examples erik cheever swarthmore college. Rootlocus is a plot of the loci of the poles of the closedloop transfer function when one of the systems parameters k is varied. Root locus plots are a very useful way to predict the behavior of a closed loop system as some parameter of the system typically a gain is changed. Root locus design is a common control system design technique in which you edit the compensator gain, poles, and zeros in the root locus diagram. This document is highly rated by electrical engineering ee students and has been viewed 1117 times. Control engineering i online course video lectures by iit delhi. Find materials for this course in the pages linked along the left. We know that, the characteristic equation of the closed loop control system is. The next page click on the right arrow at the top left of this page gives a description of techniques for sketching the location of the closed loop poles of a system for systems that are much more complicated than the one displayed here. Control engineering online course video lectures by iit bombay. Nptel video lecture topic list created by linuxpert.
Root locus 2 root locus observations because we have a 3rdorder system, there are 3 separate plots on the root locus, one for each root. Lecture notes principles of automatic control aeronautics. Consequently, the root locus plot will be symmetric about the real axis rule 2. Realaxis root locus if the total number of poles and zeros of the openloop system to the right of the spoint on the real axis is odd, then this point lies on the locus. As the openloop gain, k, of a control system varies over a continuous range of values, the root locus diagram shows the trajectories of the closedloop poles of the feedback system. Aka put in the transfer functions numerator coefficients and denominator coefficients in descending order, and will output a root locus plot. Illustration of the steps of the numerical procedure for drawing root locus of w n s 1 s e. Control systems videos, control engineering video lectures, iit control systems video lectures, control. The idea of a root locus can be applied to many systems where a single parameter k is varied. There will be one branch for each closed loop pole. Oct 22, 2010 lecture series on control engineering by prof. Each plot starts at a location equal to the location of a root of the plant transfer function.
We include a variable gain k in a unityfeedback con. The root locus is symmetrical with respect to the real axis. Control engineering i online course video lectures by iit. Nptel, iit, lectures, courses, video, engineering, online.
The root locus method, also known as evans rules in honor of w. Root locus elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. This lecture covers the location of closedloop poles, rules that speed construction of the rootlocus diagram, and examples of. This lecture covers the location of closedloop poles, rules that speed construction of the root locus diagram, and examples of these things. In the discretetime case, the constraint is a curved line. The best way to download any youtube playlist is via youtubedl command prompt utility. The root locus is the locus of the roots of the characteristic equation by varying system gain k from zero to infinity. The various parts are moreorless stand alone, so if you want to skip one or more, that should not be a problem.
Lec31 compensator design using root locus plots contd. In mathematical terms, given a forwardloop transfer function, kgs where k is the root locus gain, and the corresponding closedloop transfer function the root locus is the set of paths traced by the roots of as k varies from zero to infinity. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. An alternate graphic representation of the evans root locus plot, called gain plots, which exposes the relationship between the gain and the pole locations in polar coordinates, is presented. A very basic executable file compiled via matlab and visual studio 2010 that will prompt you to give the numerator and denominator in an array format. Your browser does not currently recognize any of the video formats available. Ramkrishna pasumarthy, department of electrical engineering, iit madras. The poles on the root locus plot are denoted by x and the zeros are denoted by o. The design of leadlag compensators using root locus. Root locus plot consider a general feedback control system with a variable gain k. Agashe, department of electrical engineering,iit bombay.
Sometimes, proportional control with a carefully chosen value of k is. Madan gopal, department of electrical engineering, iit delhi. If you specify a settling time in the continuoustime root locus, a vertical line appears on the root locus plot at the pole locations associated with the value provided using a firstorder approximation. Note 8 rootlocus techniques college of engineering. Apr 21, 2020 chapter 6 root locus notes, control system, electrical engineering electrical engineering ee notes edurev is made by best teachers of electrical engineering ee. This is because complex roots occur in conjugate pairs. Nptel video lectures, iit video lectures online, nptel youtube.
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