The root locations are important in determining the nature of the system response. Nptel mechanical engineering modeling and control of dynamic electro mechanical system. This is because complex roots occur in conjugate pairs. Design via root locus elec304alper erdogan 1 1 lecture 1. Design of control systems cascade root locus design this is the first lecture devoted to the control system design. Also, calculate the change in pole location for a 10% change. Ppt root locus powerpoint presentation free to view. Root locus goals rationale howto examples the root locus is a graphical procedure for determining the poles of a closedloop system given the poles and zeros of a forwardloop system. Root locus technique topic wise gate questions on control. In lecture 5 we had a brief introduction to the classic. 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.
Generalized root locus department of mechanical engineering 3. Design via root locus elec304alper erdogan 1 1 lecture. For example, it is useful to sweep any system parameter for which the exact value is uncertain in order to determine its behavior. It is an inputoutput, frequency domain design technique. Design with root locus the root locus method is usually used to obtain a simple picture of the effect that the gain k has on the positions of the closedloop poles. At the end, root locus design will design of control systems cascade root locus design this is the first lecture devoted to the control. 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. 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. Click on the locus to choose the location of the poles of the closed loop control system.
Root locus starts k0 at poles of open loop transfer function, gshs. Again, as compared to the rootlocus sketch of 1, the rootlocus has bended more to the right. Design via root locus elec304alper erdogan 1 18 ideal derivative compensation pd observations and facts. Say our design criteria are 5% overshoot and 1 second rise time. Show that as long as p 2, p 1 0, the root locus is similar to one given above. The points that are part of the root locus satisfy the angle condition. 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. Since root locus is a graphical angle technique, root locus rules work the same in the z and s planes. Root locus is a frequency domain technique used in investigating the roots of characteristic equation when a certain parameter varies. Lecture 25, routhhurwitz stability criterion and root locus. 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.
Based on rootlocus graph we can choose the parameter for stability and the desired transient. 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. We have also seen that feedback can change pole locations in the system. Cs root locus 4 we have to learn to visualize how all the poles move simultaneously in the complex plane as k increases see the animation not available in the pdf. 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 root locus gain is varied from zero to infinity. Introduction to root locus technique root locus analysis. Root locus endpoints the locus starting point k0 are at the openloop poles and the locus ending points k. To know if the system is absolutely stable and the degree of stability.
Because our system models are rationalpolynomial with real coef. Through the combined lecture, the student learning process can be executed more smoothly and effectively. Root locus examples erik cheever swarthmore college. Indeed, the system becomes unstable for a large value of k. The solution to this problem is a technique known as root locus graphs. Root locus elec304alper erdogan 1 1 lecture 1 root locus. In the previous lectures we laid the groundwork for design techniques based on root locus analysis. Pdf introduction to root locus method researchgate. Must be a singleinput and singleoutput siso system. Compensated poles have more negative real and imaginary parts. Design via root locus elec304alper erdogan 1 1 lecture 1 design via root locus motivation.
I system analysis via root locus i how to plot root locus bayen eecs, ucb feedback control systems september 10, 20 2 39 lecture outline 1 8 root locus techniques 8. As we change gain, we notice that the system poles and zeros actually move around in the splane. Rlocus analysis design nyu tandon school of engineering. Department of mechanical engineering indian institute of science bangalore, india, 560012 this draft. If these definitions do not adequately answer your questions, please consult the prerequisites for this lecture. Introduction to root locus islamic university of gaza. Root locus endpoints the locus starting point k0 are at the openloop poles and. The leftmost diagram below shows a root locus plot. Root locus introduction definitions angle criterion angle of departure break point characteristic equation closedloop complexplane splane forward loop magnitude. Control systemsroot locus wikibooks, open books for an. The root locus is the plot of the roots of system characteristic equation or. The root locus must have n branc hes, each branch starts at a pole of gs and goes to a zero of gs.
If gs has more p oles than zeros as is often the case, m lecture 9. Graphically, the locus is the set of paths in the complex plane traced by the closedloop poles as the root locus gain is varied from zero to infinity. Pdf the introduction to root locus method find, read and cite all the research you need on. Root locus elec304alper erdogan 1 1 lecture 1 root locus what is rootlocus. The system could be presented in state space form so we enter the system in state space form if we wont to draw the root locus for multi systems in the same graph write rlocussys1,sys2. Root locus introduction and its properities ece tutorials. The location of poles and zeros are crucial keeping view stability, relative stability. Any physical system is represented by a transfer function in the form of we can find poles and zeros from gs. Transient response and pole location settling time t. Inclass iuse the gain expression to find the point at which the locus intersects the real axis. Both points lie on the root locus in between two openloop poles breakaway. Each plot starts at a location equal to the location of a root of the plant transfer function.
In each case gain k is chosen such that percent overshoot is same. In this lecture we shall introduce the root locus technique, developed by evans during world war 2 while working at north american aviation. Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear. If gs has more p oles than zeros as is often the case, m 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 elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus. Root locus plot consider a general feedback control system with a variable gain k. Note 7 rootlocus techniques college of engineering.
Root locus design slide 26 lead compensation example first find a point in the splane that we. Rootlocus is a plot of the loci of the poles of the closedloop transfer. 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. 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. The open loop transfer function gs has one pole at zero and two poles at 1. Again root locus help you to put this poles en roots in the splane. Root locus sketching rules negative feedback rule 1. Ppt root locus powerpoint presentation free to view id. 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 method can also be effectively used in more general controller. A graphical representation of closed loop poles as a system parameter varied. Sketchingtherootlocus wecanseethattherootlocuscanbeplottedbylocatingthepointsinthesplanefor whichtheanglesadduptoanoddmultipleof 180o. This is also known as root locus technique in control system and is used for determining the stability of the given system. Thus, the root locus is symmetric with respect to the real axis.
Dec 31, 2010 lecture in control system analysis arabic, yanbu industrial college yic. The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the. 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. Recall that any system is stable if all the poles lie on the lhs of the s plane. Lecture 28, root locus, steps 4, 5, sisotool and matlab files for examples, lecture 29, root locus, step 6. The book gives only 5 rules for root locus plotting.
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. Lecture abstract ee c128 me c4 feedback control systems. In the discretetime case, the constraint is a curved line. This fact can make life particularly difficult, when we need to solve higherorder equations repeatedly, for each new gain value. Weclome to me451 control systems college of engineering. Lecture on root locus techniques free download as powerpoint presentation. 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 technique in control system electrical4u. 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 locus of roots as parameter value is changed. Sometimes, proportional control with a carefully chosen value of k is. To predict a systems performance by an analysis that does not require the actual solution of the differential equations. The distance from the origin to point a is given as 0. Manually plotting a root locus recall step response.
The root locus of the system for varying k is shown in the figure. Me 176 control systems engineering root locus technique department of mechanical engineering. Weclome to me451 control systems michigan state university. The root locus technique in control system was first introduced in the year 1948 by evans. Introduction to root locus in this experiment we will learn the following things how to plot root locus using matlab how to enter a system state space, transfer function in labview how to plot root locus using labview how to find the step response using labview types of system connections. 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. How do we design a feedback controller for the system by using the root locus method. Along the real axis, the root locus includes all segments that are to the left of an odd number of poles and zeros. The roots of the characteristic equations are at s1 and s2. The idea of a root locus can be applied to many systems where a single parameter k is varied. This section contains definitions of root locus terms and concepts. We include a variable gain k in a unityfeedback con. Example the root loci start at the poles and at the zeros. This is a highly intuitive pictorial technique for control system design working in the splane.
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. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Locus segments now, determine if point 6is on the root locus again angles from complex poles cancel always true for real. What is the physical significance of pole and zero in a transfer function. Lecture 27, root locus, step 3, an illustrative example for utilizing the auxiliary polynomial in routhhurwitz stabiltiy criterion test. Section 5 root locus analysis college of engineering. The lesson here is that while the poles of a system the roots of the denominator polynomial are very important in determining. How to enter a system transfer function or state space to labview.
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