The points that are part of the root locus satisfy the angle condition. 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. Nptel video lecture topic list created by linuxpert systems. We know that, the characteristic equation of the closed loop control system is. 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 root locus is symmetrical with respect to the real axis. The number of branches of root locus equal to the number of closed loop poles. Root locus technique in control system electrical4u. The equation z e st maps continuous s plane poles not zeros into the z domain, where t is the sampling period. Design of sampled data control systems, lecture16, root locus based controller design using matlab, 70 kb. 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.
Design via root locus elec304alper erdogan 1 1 lecture 1 design via root locus motivation. Pid and root locus pid control design yvery common and classical control technique ygood tools for choosing gains root locus yshow closed loop poles as function of a free parameter. Therefore, lets explore the properties of root locus. The poles on the root locus plot are denoted by x and the zeros are denoted by o. Root locus is a plot of the loci of the poles of the closedloop transfer function when one of the systems parameters k is varied. Madan gopal, department of electrical engineering, iit delhi.
Example the root loci start at the poles and at the zeros. Lecture 6 the roots of a parameterized polynomial i. March 12, 2008 1 the root locus method the root locus method, as the name suggests looks at the locii of the roots as some parameter of interest within the system is varied. The branches of the locus begin at the openloop poles and terminate at the openloop zeros. Root locus plot consider a general feedback control system with a variable gain k. 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. Each branch of root locus originates at an open loop pole and terminates at. Jun 17, 2019 we can usually read the phase margin directly from the bode plot as shown in the diagram above. Root locus allows us to visualize the changes in the closedloop poles as the parameter k is increase from 0 to infinity. Determine the open loop poles, zeros and a number of branches from given gshs.
The goal is to find the compensator, kz, which gives a good response. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. You can also find a page that includes the rules for the complementary root locus k. Also, determine the number of breakaway points this will be. Rootlocus is a plot of the loci of the poles of the closedloop transfer function when one of the systems parameters k is varied. Lecture abstract ee c128 me c4 feedback control systems. Mar 25, 2017 root locus method with step by step solution. 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 table below summarizes how to sketch a root locus plot k. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Draw the polezero plot and determine the region of real axis for which the root locus exists. In the discretetime case, the constraint is a curved line. Root locus examples erik cheever swarthmore college. Manually plotting a root locus recall step response.
Tuesday, april 06, 1999 root locus design examples here we give a few design examples of the root locus technique. Nyquist stability criterion, bode plots and stability margins in frequency domain. Nptel video lecture topic list created by linuxpert. Matlab and flywheel introduction to the class project, team arrangements. Root locus elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus. Design via root locus elec304alper erdogan 1 1 lecture 1. Root locus design slide 6 specifications in the splane recall that the transient system specifications can be formulated in the splane t r. The breakaway point is midway between the two openloop poles at z b 0. Department of mechanical engineering indian institute of science bangalore, india, 560012 this draft.
These real pole and zero locations are highlighted on diagram, along with the portion of the locus that exists on the real axis. It may further be pointed out here that root locus technique is applicable to single as well as multiple loop system. The root locus method can also be used for the analysis of sampled data systems by computing the root locus in the zplane, the discrete counterpart of the splane. Sketch the root locus diagram for the parameter k for the closed loop system shown in the diagram. The root locus angle criterion states that si1 22 will be on the cl root locus. Because our system models are rationalpolynomial with real coef. Using root locus rules gives the root locus plot in figure 6. Sd agashe, department of electrical engineering,iit bombay.
Inclass iuse the gain expression to find the point at which the locus intersects the real axis. Note 8 rootlocus techniques college of engineering. Design via root locus elec304alper erdogan 1 18 ideal derivative compensation pd observations and facts. The critical gain now occurs at the intersection of the root locus with the unit circle. Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear. Along the real axis, the root locus includes all segments that are to the left of an odd number of poles and zeros. Note 7 rootlocus techniques college of engineering. Root locus elec304alper erdogan 1 4 drawing the root locus how do we draw root locus for more complex systems, and without calculating poles. The root locus is symmetrical about real axis gshs 1 rule 2.
Root locus page 33 characteristic equation root locus is obtained by for a fixed k 0, finding roots of the characteristic equation, and sweeping k over real positive numbers. In each case gain k is chosen such that percent overshoot is same. Oct 22, 2010 lecture series on control engineering by prof. This point is known as the gain crossover frequency. Root locus design i root locus design selecting parameter value motivation on compensation reading. 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. Compensated poles have more negative real and imaginary parts. There will be one branch for each closed loop pole. This is also known as root locus technique in control system and is used for determining the stability of the given system. Relative to the microcontroller, a feedback system looks like its a discretetime system. Each plot starts at a location equal to the location of a root of the plant transfer function. The value of the parameter for a certain point of the root locus can be obtained using the magnitude condition. We include a variable gain k in a unityfeedback con. The root locus gives the information about the nature of the roots of the characteristic equation.
Sunday, march 28, 1999 root locus design feedback control design techniques include statevariable feedback, outputfeedback, root locus, bode design, nyquist design, polynomial design, and other techniques. Control systemsroot locus wikibooks, open books for an. Design via root locus elec304alper erdogan 1 1 lecture. Ramkrishna pasumarthy, department of electrical engineering, iit madras. Whether root locus gives the idea about the steady state error. Root locus endpoints the locus starting point k0 are at the openloop poles and the locus. General steps for drawing the root locus of the given system.
Root locus design imag axes real axis waterbed reduced sensitivity. This is because complex roots occur in conjugate pairs. 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. Section 5 root locus analysis college of engineering. Using root locus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Plot the openloop poles x and zeros 0 on the splane.
Sometimes, proportional control with a carefully chosen value of k is. 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. The book gives only 5 rules for root locus plotting. As we change gain, we notice that the system poles and zeros actually move around in the splane. But it cannot give idea about the steady state errors. This document is highly rated by engineering mathematics students and has been viewed 290 times. Thus, the root locus is symmetric with respect to the real axis. Controls design techniques can be basically divided into statespace techniques vs. If the characteristic polynomial is order n, there will be n closedloop poles and hence n branches of the root locus. The root locus exists on real axis to left of an odd number of poles and zeros of open loop transfer function, gshs, that are on the real axis. The solution to this problem is a technique known as root locus graphs. Locus segments now, determine if point 6is on the root locus again angles from complex poles cancel always true for real. This fact can make life particularly difficult, when we need to solve higherorder equations repeatedly, for each new gain value.
The roots of the characteristic equations are at s1 and s2. Design of sampled data control systems modelling of dynamic system, lecture1. 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 method part 2 engineering mathematics notes edurev is made by best teachers of engineering mathematics. Rlocus analysis design nyu tandon school of engineering. Root locus locus of roots as parameter value is changed ycan plot pole location versus any parameter. In a feedback control system, at least part of the information used to change the output variable is derived from measurements performed on the output variable itself.
Agashe, department of electrical engineering,iit bombay. Lec30 rootlocus method control systems engineering nptel. We exploit the properties of rootlocus to do a rough sketch. This function can be applied to any of the following negative feedback loops by setting sys appropriately. 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. Bode plot, gain margin and phase margin plus diagram. The root locus technique is introduced for determining the loop gain and the effect of pole location on performance is described in this context. The following rules facilitate the sketching of the root locus. Root locus endpoints the locus starting point k0 are at the openloop poles and the locus ending points k. This is done by calculating the vertical distance between the phase curve on the bode phase plot and the xaxis at the frequency where the bode magnitude plot 0 db. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity.
So from it, root locus gives the idea about the overall stability of the system and the nature of the transient response. Finally, some of the implications of right half plane zeros are discussed using the root locus plot. Both points lie on the root locus in between two openloop poles breakaway. The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the. Nptel video lecture topic list created by linuxpert systems, chennai.
Craig 4 the root locus plot is a plot of the roots of the characteristic equation of the closedloop system for all values of a system parameter, usually the gain. Basics of control design, the proportional, derivative and integral actions. The root locus is the locus of the roots of the characteristic equation by varying system gain k from zero to infinity. 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. Lec30 rootlocus method lecture series on control engineering by prof. 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. 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. Sketch the root loci of the control system shown in figure 640a.