Where can i get a dvd or hard disk containing all the. How do we design a feedback controller for the system by using the root locus method. Note 8 rootlocus techniques college of engineering. We exploit the properties of rootlocus to do a rough sketch. This document is highly rated by engineering mathematics students and has been viewed 292 times. Ece4510ece5510, rootlocus controller design 72 adding a lefthalfplane pole or zero what types of 1 compensation should we use, and 2 how do we. The roots of the characteristic equations are at s1 and s2. Do the zeros of a system change with a change in gain. Nptel video lectures, iit video lectures online, nptel youtube lectures, free video lectures, nptel online courses, youtube iit videos nptel courses. The rootlocus design method problems and solutions for section 5. Goals introduction goals rationale howto examples this lecture will help you understand what a root locus is and how to create and use one. 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.
The root locus is symmetrical with respect to the real axis of splane. Hence, only the portion between s 0 and s 1 is on the root locus. Electrical engineering digital control system nptel. Evans root locus method evans 1948 developed a method for plotting the variation of the roots of a polynomial equation as the value of a coefficient changes. Root locus plot of dynamic system matlab rlocus mathworks. Thus, the root locus is symmetric with respect to the real axis. Root locus design slide 26 lead compensation example first find a point in the splane that we. Apr 04, 2019 hence, all the negative real line is on the root locus.
To know if the system is absolutely stable and the degree of stability. We need to get a feel for how the root locus changes when poles. Rootlocus is a plot of the loci of the poles of the closedloop transfer function when one of the systems parameters k is varied. We know that, the characteristic equation of the closed loop control system is. Lecture notes feedback control systems aeronautics and. Root locus elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus.
Root locus stepsand procedure4 the stability of a given closed loop system depends upon the location of the roots of the characteristics equation, which is the location of the closed loop poles. Lec30 rootlocus method lecture series on control engineering by prof. This is due to the fact that the complex roots of an equation always occur in pairs. If we change some parameter of a system, then the location of closed loop pole changes in s plane. A plot of the possible closedloop pole locations as some parameter varies from 0 to 1. Therefore, lets explore the properties of root locus. Root locus elec304alper erdogan 1 4 drawing the root locus how do we draw root locus for more complex systems, and without calculating poles.
Root locus design slide 6 specifications in the splane recall that the transient system specifications can be formulated in the splane t r. The root locus can be used to examine the location of the roots of the characteristic polynomial as one parameter is varied. Root locus elec304alper erdogan 1 1 lecture 1 root 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. Root locus on matlab root locus stepsand procedure3 1. Set up the following characteristic equations in the form suited to evanss rootlocus method. This lecture covers the location of closedloop poles, rules that speed construction of the rootlocus diagram, and examples of these things. 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. In this chapter, let us discuss how to construct draw the root locus.
If the location of an openloop pole or zero is a system variable, then the root locus method suggests the way to choose the location of an openloop pole or zero. They are the roots of the numerator of the closedloop transfer. The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the. Where are the zeros of the closedloop transfer function. The root locus is a graphical representation in sdomain and it is symmetrical about the real axis. Sep 30, 2017 root locus plot determination of the stability of a system root locus stepsand procedure2 3. Application of numerical analysis to root locus design of. 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 2 1. Step 3 re im breakaway point 14 matlab command rlocus. How to download all the videos of a course by nptel, instead. Nptelhighquality free video tutorials by profs of iits. 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. The goal is to find the compensator, kz, which gives a good response.
The root locus originates at the poles of gshs and terminates at the zeros of gshs, including those zeros at infinity. Labview graphical approach we can create a vi to plot the root locus, using the cd root locus vi from the model construction section of the control design palette. Lecture abstract ee c128 me c4 feedback control systems. Each plot starts at a location equal to the location of a root of the plant transfer function. Nptel is an acronym for national programme on technology enhanced learning which is an initiative by all seven indian institutes of technology iits and indian institute of science iisc for creating course contents in engineering and science. In this paper we show that a similar analysis can be. Sd agashe, department of electrical engineering,iit bombay. Vast literature on these subjects can be found, for example in refs. It provides definitions of terms, a stepbystep guide to constructing a root locus, and details about how to design and evaluate controllers using the root locus method. Nptel provides elearning through online web and video courses various streams. Nov 29, 2008 home about 29 november 2008 nptel highquality free video tutorials by profs of iits. With the advent of the personal computer and the availability of faster processors, a suitable technique to be used in a personal computer is the root locus plotting. Relative to the microcontroller, a feedback system looks like its a discretetime system.
How to draw root locus of a system with pictures wikihow. Lec30 rootlocus method control systems engineering nptel. Root locus endpoints the locus starting point k0 are at the openloop poles and the locus ending points k. Ramkrishna pasumarthy, department of electrical engineering, iit madras.
Root locus method part 2 engineering mathematics notes edurev is made by best teachers of engineering mathematics. Along the real axis, the root locus includes all segments that are to the left of an odd number of poles and zeros. Aug, 2017 52 videos play all control engineering nptel control engineering intro to control 12. In ece45105510, the methods we discuss are scienceinspired art. Plotting all points on the s plane which satisfies the angle condition produces the rootlocus. Nptel provides elearning through online web and video courses various. 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 a. 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. Pls note there are other ways to access the nptel video lectures. A thesis submitted in partial fulfillment of the requirements for the degree of.
The equation z e st maps continuous s plane poles not zeros into the z domain, where t is the sampling period. To predict a systems performance by an analysis that does not require the actual solution of the differential equations. This is because complex roots occur in conjugate pairs. Example the root loci start at the poles and at the zeros. This ocw supplemental resource provides material from outside the official mit curriculum. Aug, 2017 52 videos play all control engineering nptel control engineering designing a pid controller using the root locus method duration. The root locus tells you how the system can behave. Rootlocusplotlsys, k, kmin, kmax generates a root locus plot of a linear timeinvariant system lsys as the parameter k ranges from kmin to kmax. How to download all the videos of a course by nptel. This is a technique used as a stability criterion in the field of classical control theory developed by walter r. Root locus analysis for randomly sampled systems d. The root locus of gs is the set of points in the splane where the phase of gs.
Control systems videos, control engineering video lectures, iit control systems video lectures, control engineering lecture series, nptel video lectures, nptel video courses, nptel video classes. The axes of symmetry of polezero configuration can be thought as a new complex plane. For instance, assume that the nominal plant model is given by and that the controller has a transfer function descried as, where is a known quotient of two monic polynomials in s, and where k is a positive, but unknown. This technique gives accurate results and provides the designer with an. Rlocus analysis design nyu tandon school of engineering. By using the rootlocus method, it is possible to determine the value of the loop gain k that will make the damping ratio of the dominant closedloop poles as prescribed. Heemels abstract nroot locus analysis is a graphical method to determine how the roots of the characteristic equation of a linear timeinvariant feedback loop change with the loop gain. 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 openloop transfer.
Your browser does not currently recognize any of the video formats available. The root loci are symmetrical with respect to axes of symmetry of polezero configuration of gshs. 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. Hence, all the negative real line is on the root locus. Root locus examples erik cheever swarthmore college. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. Say our design criteria are 5% overshoot and 1 second rise time. Root locus introduction and its properities ece tutorials. In the motor control system only those points of the real line between s 0 and s 1 have odd number of roots at the right side. Root locus allows us to visualize the changes in the closedloop poles as the parameter k is increase from 0 to infinity. By using the root locus method, it is possible to determine the value of the loop gain k that will make the damping ratio of the dominant closedloop poles as prescribed. With the advent of the personal computer and the availability of faster processors, a suitable technique to be used in a personal computer is the rootlocusplotting. Lecture 31 compensator design using root locus plots continued.
Because the open loop poles and zeros exist in the sdomain having the values either as real or as complex conjugate pairs. Home about 29 november 2008 nptelhighquality free video tutorials by profs of iits. If the location of an openloop pole or zero is a system variable, then the rootlocus method suggests the way to choose the location of an openloop pole or zero. The poles on the root locus plot are denoted by x and the zeros are denoted by o. 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. Matlab and flywheel introduction to the class project, team arrangements. The root locus is the locus of the roots of the characteristic equation by varying system gain k from zero to infinity. Give ls,as, and bs and the parameter, k, in terms of the original parameters in each case. Control engineering nptel online videos, courses iit. 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. Once you pick a point on the root locus, k is found using the first equation. The previous answer is correct, but i would like to add more choices to access the video.
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