Root locus introduction definitions angle criterion angle of departure break point characteristic equation closedloop. Introduction the purpose of compensator design generally is to satisfy both transient and steadystate speci. This is because complex roots occur in conjugate pairs. Sketch the root locus diagram for the parameter k for the closed loop system shown in the diagram. The root locus is always symmetric with respect to the real axis. First design the minor loop then design the major loop. Because the open loop poles and zeros exist in the sdomain having the values either as real or as complex conjugate pairs. Design via root locus elec304alper erdogan 1 35 two approaches for feedback compensation 1. This fact can make life particularly difficult, when we need to solve higherorder equations repeatedly, for each new gain value. After studying these materials, you should be able to create a root locus and use the locus to understand the closedloop system behavior given an openloop system and a feedback controller.
Using matlab for root locus analysis as an example of how to use matlab to perform a root locus analysis, consider design problem dp6. The root locus is the plot of the roots of system characteristic equation or. Weve seen how the stability and response of a system depends on its poles. The goal is to use matlab to draw a root locus diagram for the parameter k, given the parameter m 4. In the discretetime case, the constraint is a curved line. Control systemsroot locus wikibooks, open books for an. Determine the parts of the real axis that are the root locus the root locus lies at all points on the real axis to the left of an odd number of poles and zeros that lie on the real axis. Since the lefthandside of 1 is a polynomial with real coefficients, its roots are either real or occur in complex conjugate pairs. Well learn techniques so we dont need to test each splane point. Root locus procedure ece 411 october 26, 2015 overview of root loci.
The root locus is obviously a very powerful technique for design and analysis of control systems, but it must be used with some care, and results obtained with it should always be checked. We include a variable gain k in a unityfeedback con. Sometimes, proportional control with a carefully chosen value of k is. Recall that any system is stable if all the poles lie on the lhs of the s plane. Each branch of the root locus begins at an openloop pole k 0 and ends at an openloop zero or at a zero at infinity k. The root locus is a graphical representation in sdomain and it is symmetrical about the real axis. Section 5 root locus analysis college of engineering. Imaginary axis crossings transition to instability. Lecture notes of control systems i me 431analysis and synthesis of linear control system me862 department of mechanical engineering, university of saskatchewan, 57 campus drive, saskatoon, sk s7n 5a9, canada 3 2. Consider compensation as adding poles and zeros to feedback section for the equivalent system.
Root locus definition the rootlocusis the set of all points in the s. Root locus elec304alper erdogan 1 1 lecture 1 root locus what is rootlocus. Real axis breakin and breakaway points nise figure 8. Because our system models are rationalpolynomial with real coef. To know if the system is absolutely stable and the degree of stability. As we change gain, we notice that the system poles and zeros actually move around in the splane. The number of root locus branches is equal to the order of the characteristic equation. The poles on the root locus plot are denoted by x and the zeros are denoted by o. We have also seen that feedback can change pole locations in the system transfer function and therefore performance is changed.
Root locus sketching rules negative feedback rule 1. A plot of the closedloop poles can be similarly helpful. Each plot starts at a location equal to the location of a root of the plant transfer function. Lecture abstract ee c128 me c4 feedback control systems. In this tutorial, we will introduce the root locus, show how to create it using matlab, and demonstrate how to design feedback controllers that satisfy certain performance criteria through the use of the root locus. A revision of root locus method with applications sciencedirect. Note 8 rootlocus techniques college of engineering. This method is very powerful graphical technique for investigating the effects of the variation of a system parameter on the locations of the closed loop poles. Design via root locus elec304alper erdogan 1 1 lecture 1. Root locus graphically shows how poles of the closedloop system varies as k.
Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear. The points that are part of the root locus satisfy the angle condition. In this technique, we will use an open loop transfer function to know the stability of the closed loop control system. Sketch the root loci of the control system shown in figure 640a. Root locus technique in control system root locus plot. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Rlocus analysis design nyu tandon school of engineering. In the root locus diagram, we can observe the path of the closed loop poles. Consequently, the root locus plot will be symmetric about the real axis rule 2. A graphical representation of closed loop poles as a system parameter varied. May 16, 2015 a root locus plot is simply a plot of the s zero values and the s poles on a graph with real and imaginary coordinates. Hence, we can identify the nature of the control system. Manually plotting a root locus recall step response.
Ee302 introduction to root locus depiero a root locus plot depicts the poles for a closed loop transfer function, ts ysrs, for values of the gain, 0 feb 02, 20 the root locus method is a fantastic way of visualizing how the poles of a system move through the splane when a single system parameter is varied from 0 to infinity. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Jun 16, 2017 download version download 9465 file size 30. The root locus of a feedback system is the graphical representation in the complex splane of the possible locations of its closedloop poles for varying values of a certain system parameter. 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. The solution to this problem is a technique known as root locus graphs. A polezero plot is simply a plot of the openloop poles in the complex plane. Note 7 rootlocus techniques college of engineering. Recall that any system is stable if all the poles lie on the lhs of the splane. To show potential pitfalls of this method, consider the two systems g1s and g2s. Weve also seen how a polezero plot can help us visualize the system behavior. The block diagram of the closedloop system is shown below.
Now, in a closed loop system the possibility of instability is always there. In the design and analysis of control systems, it is often required to investigate the sensitivity due to the variations of the parameters in the systemcontroller. 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. When used with the magnitude criterion, the angle criterion can also be used to determine whether or not a point in the splane is on the root locus. You can also download these free gate notes in pdf to help you with your exam preparation for gate, ies, barc, drdo, bsnl, ecil etc. The minor loop is designed to change the open loop poles and open loop transientresponse. Consider a feedback system that has one parameter gain k0 to be designed. The root locus is the locus of the roots of the characteristic equation by varying system. To predict a systems performance by an analysis that does not require the actual solution of the differential equations. Based on rootlocus graph we can choose the parameter for stability and the desired transient response. Thus, the root locus is symmetric with respect to the real axis.
This is also known as root locus technique in control system and is used for determining the stability of the given system. It has since become a very popular tool for analysis and design of servomechanisms and control systems with rational transfer functions in general. Root locus construction procedure ece 411 october 20, 2016 overview of root loci. Cse complete pdf notesmaterial 2 download zone smartzworld. Introduction to root locus technique root locus analysis.
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