As a conceptual thought model and as long as linear theory remains the paradigm of choice, the root locus does a really good job of. Control systems lab manual grietelectrical and electronics. Therefore, lets explore the properties of root locus. 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. Gives the evans root locus for a siso linear system in statespace or transfer form hs. To know if the system is absolutely stable and the degree of stability. Determine the value of the gain k at the point where the root locus branches cross the imaginary axis, and the frequency value at. Introduction to root locus semester 083 page 6 lab assignment. 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. Draw bode, nyquist and root locus plots for the given transfer function. Lead compensation techniques based on the root locus. Jun 24, 20 this feature is not available right now. The equation z e st maps continuous s plane poles not zeros into the z domain, where t is the sampling period. The root locus plot gives us a graphical way to observe how the roots move as the gain, k, is varied.
Recall that any system is stable if all the poles lie on the lhs of the splane. In the discretetime case, the constraint is a curved line. Effect of open loop and zeroes on root locus contour b to estimate the effect of open loop gain on the transient response of closed loop system by using root locus c comparative study of bode, nyquist and root locus with respect to. Effect of pi controller and integral controller on system response. Analyze and interpret stability of the system through root locus, bode plot and nyquist plot. To learn that feedback control can be used in order to make an unstable system stable. 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. Discuss how these plots relate to the root locus and step response plots you made in step 3. 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. Execute time response analysis of a second order control system using matlab 2. Save the root locus diagram for your lab notebook, and save the step response plot for a few different gain values. After the successful completion of the course, the student will be able to 1. 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.
Experiment 11 root locus controller design pre lab in this lab you will explore the use of the root locus controller design methodology. 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. Root locus elec304alper erdogan 1 1 lecture 1 root locus. The figure below shows a unityfeedback architecture, but the procedure is identical for any openloop transfer function, even if some elements of the. Apr 19, 2020 root locus is going out of favor as a practical tool because it gets really complicated by digital sampling models. Locuslabs has helped 426,402,231 people search, navigate and discover what they are looking for in venues all over the world. Electrical simulation lab manual eee lendi institute of engineering and technology page 24 of 55 transfer function. The roots of the characteristic equations are at s1 and s2. Analyze and interpret stability of the system through root locus, bode plot.
Effect of addition of poles and zeros on the root locus. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. Design via root locus elec304alper erdogan 1 1 lecture 1. To show potential pitfalls of this method, consider the two systems g1s and g2s. Consequently, the root locus plot will be symmetric about the real axis rule 2. For a selected sample of gains k may 07, 20 btl control system lab manual 10 eel68 1. What is the real world application of the root locus.
Root locus examples erik cheever swarthmore college. The given system is represented by a transfer function as follows theoritical calculations. This function can be applied to any of the following negative feedback loops by setting sys appropriately. This is a graphical method, in which the movement of poles in the splane is sketched when a particular parameter of the system is varied from zero to infinity. By using the same transfer function, draw manually the root locus plot for the system and determine. The poles on the root locus plot are denoted by x and the zeros are denoted by o. Ece 429 control systems lab manual the gmu ece department. Design lag, lead, leadlag compensators and verify experimental. For a selected sample of gains k lab vi sem 4 course outcomes. Root locus for control systems national instruments.
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. From the plot above we see that all the poles selected are at reasonable positions. Then by adding zeros andor poles via the controller, the root locus can be modified in order to achieve a desired closedloop response. Sketch the root locus diagram for the parameter k for the closed loop system shown in the diagram. Use the locuslabs platform to create amazing indoor location experiences, track assets, visualize iot and more. Design via root locus elec304alper erdogan 1 1 lecture 1 design via root locus motivation.
Rlocus analysis design nyu tandon school of engineering. 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. 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 root locus plot. Root locus analysis of control systems to explore the root locus analysis of a control system. Roots is an m x n array, where n is the number of poles in the closedloop transfer function. By using the same transfer function, draw manually the root locus. Root locus introduction definitions angle criterion angle of departure break point characteristic equation closedloop. The root locus is a graphical representation in sdomain and it is symmetrical about the real axis.
You can tune compensator parameters using automatic pid controller tuning, bode loop shaping, root locus method, lqrlqg design, and other interactive and. Recall that any system is stable if all the poles lie on the lhs of the s plane. Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear. Note that since the root locus may have more than one branch, when you select a pole, you may want to find out where the other poles are. Lag compensation techniques based on the root locus. Each plot starts at a location equal to the location of a root of the plant transfer function. Control systems lab maual bms institute of technology. K is a 1darray of m elements of all the gain values that this vi uses to create the root locus. Root locus sketching rules negative feedback rule 1. Range of gain for stable operation using root locus. The first two software packages are free alternatives to matlab, and their use is encouraged. 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.
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. Cd root locus vi labview 2018 control design and simulation. Frequency domain analysis of control systems to explore the frequency response of a control system. Stability analysis of linear systems using root locus. The next page click on the right arrow at the top left of this page gives a description of techniques for sketching the location of the closed loop poles of a system for systems that are much more complicated than the one displayed here. Pdf lab manual control system matlab aamir sohail nagra. In this chapter, let us discuss how to construct draw the root locus. This is because complex roots occur in conjugate pairs. To design a pid controller using the root locus method. Root locus design oklahoma state universitystillwater. Obtain root locus plot of a system having forward path transfer. To predict a systems performance by an analysis that does not require the actual solution of the differential equations. Because the open loop poles and zeros exist in the sdomain having the values either as real or as complex conjugate pairs. The root locus is a plot of the roots of the characteristic equation of the closedloop system as a function of gain.
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