Agashe, department of electrical engineering,iit bombay. Effect of different parameters on root locus nptel. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Also, determine the number of breakaway points this will be.
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. Angle of departure from complex pole angle of departure from pole, p j is. The intersection of root locus plot with imaginary axis is given by the value of k obtained by. Root locus method part 2 engineering mathematics notes edurev is made by best teachers of engineering mathematics. The root locus is a graphical representation in sdomain and it is symmetrical about the real axis. The potential root loci for the stated parts are shown below.
In each case gain k is chosen such that percent overshoot is same. 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. Along the real axis, the root locus includes all segments that are to the left of an odd number of poles and zeros. Before digital computers, sketching of the root locus was performed by taking advantage of the angle and magnitude criteria. The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the. Both points lie on the root locus in between two openloop poles breakaway. As we change gain, we notice that the system poles and zeros actually move around in the splane. This fact can make life particularly difficult, when we need to solve higherorder equations repeatedly, for each new gain value. This is also known as root locus technique in control system and is used for determining the stability of the given system. Note 8 rootlocus techniques college of engineering. 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. Design via root locus elec304alper erdogan 1 1 lecture 1 design via root locus motivation.
Root locus sketching rules negative feedback rule 1. Rochester institute of technology a thesis submitted in partial fulfillment of the requirements for the degree of master of science in the school of electrical engineering and computer science in the college of engineering and computer science. Design via root locus elec304alper erdogan 1 18 ideal derivative compensation pd observations and facts. Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear.
The book pretends, above all, be a didactic text to teach and receive classes. 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. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Control system engineering root locus technique exam study. The root locus gives the information about the nature of the roots of the characteristic equation. Draw the polezero plot and determine the region of real axis for which the root locus exists. The root locus is symmetrical with respect to the real axis. 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. Matlab and flywheel introduction to the class project, team arrangements. 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. Nptel mechanical engineering modeling and control of dynamic electro mechanical system.
Pole zero plots for the system transfer function in eq. Therefore, lets explore the properties of root locus. This function can be applied to any of the following negative feedback loops by setting sys appropriately. Compensated poles have more negative real and imaginary parts.
Control systemsroot locus wikibooks, open books for an. If we remember the controller design in continuous domain using root locus, we see that the design is based on the approximation that the closed loop system. Oct 22, 2010 lecture series on control engineering by prof. Inclass iuse the gain expression to find the point at which the locus intersects the real axis. Note 7 rootlocus techniques college of engineering. Rlocus analysis design nyu tandon school of engineering. 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 of the system having the loop transfer function. Mar 25, 2017 root locus method with step by step solution. Root locus diagram technique is used for finding the roots of characteristic equation. Whether root locus gives the idea about the steady state error. If q0 there are asymptotes of the root locus that intersect the real axis at m ii i 1 i 1 pz n q, and radiate out with angles 180 r q, where r1, 3, 5 breakawayin points on real axis breakaway or in points of the locus exist where nsdsnsds0. We have also seen that feedback can change pole locations in the system transfer function and therefore performance is changed. The root locus of g c1 sg p s is plotted, and it is seen that the root locus of the compensated system does pass through s 1.
Each plot starts at a location equal to the location of a root of the plant transfer function. Rootlocus is a plot of the loci of the poles of the closedloop transfer function when one of the systems parameters k is varied. Sketch the root locus diagram for the parameter k for the closed loop system shown in the diagram. 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.
Because the open loop poles and zeros exist in the sdomain having the values either as real or as complex conjugate pairs. When working in industry, you are strongly advised to use design tools such as matlab. Root locus design slide 6 specifications in the splane recall that the transient system specifications can be formulated in the splane t r. The number of branches of root locus equal to the number of closed loop poles. This is because complex roots occur in conjugate pairs. Design via root locus elec304alper erdogan 1 1 lecture. In the discretetime case, the constraint is a curved line. General steps for drawing the root locus of the given system. Since the gain has been chosen to satisfy the magnitude criterion at s 1, then s 1 is an actual closedloop pole for the compensated system.
Rules for making root locus plots swarthmore college. We have also seen that feedback can change pole locations in the system. Lec30 compensator design using root locus plots youtube. The objective of this book is to present the methodologies and techniques of modeling and control of dynamic systems. To show potential pitfalls of this method, consider the two systems g1s and g2s. Ramkrishna pasumarthy, department of electrical engineering, iit madras. Design via root locus elec304alper erdogan 1 1 lecture 1.
The root locus can be easily sketched as given below. But it cannot give idea about the steady state errors. A comparison and evaluation of common pid tuning methods. This document is highly rated by engineering mathematics students and has been viewed 292 times. Real axis branch is to the left of four poleszeros even number. We exploit the properties of rootlocus to do a rough sketch. In this chapter, let us discuss how to construct draw the root locus. Root locus plot consider a general feedback control system with a variable gain k. We know that, the characteristic equation of the closed loop control system is.
The gain, k, at any point on the root locus is given by equation 1. Manually plotting a root locus recall step response. There will be one branch for each closed loop pole. Root locus endpoints the locus starting point k0 are at the openloop poles and. Root locus slide 17 basic root locus rules rule 4 starting and ending points as we saw, the root locus will start at the open loop poles the root locus will approach the open loop zeros as k approaches. 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 technique in control system electrical4u. Gate preparation, nptel video lecture dvd, electronicsandcommunicationengineering, controlsystemengineering, rootlocustechnique, control system basics.
The following five rules allow us to sketch the root locus using minimal calculations. Gs given, hs given, select the gain k and vary until you receive the desired response. 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. Kalyana veluvolu 18 information obtainable from the rootlocus. The equation z e st maps continuous s plane poles not zeros into the z domain, where t is the sampling period. Introduction design via root locus activecircuit realization in. Root locus endpoints the locus starting point k0 are at the openloop poles and the locus ending points k. The following rules facilitate the sketching of the root locus.
The root locus method for continuous time systems can be extended to discrete time systems without much modifications since the characteristic equation of a. 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. Lecture abstract ee c128 me c4 feedback control systems. The root locus is the locus of the roots of the characteristic equation by varying system gain k from zero to infinity. Madan gopal, department of electrical engineering, iit delhi. The solution to this problem is a technique known as root locus graphs. 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. Determine the open loop poles, zeros and a number of branches from given gshs. The book gives only 5 rules for root locus plotting.