In designing laglead compensators, we consider two cases where and. This document is highly rated by students and has been viewed 261 times. The basic thought here is that if we add a controller or modify the gain to our process then we. Lecture notes of control systems i me 431analysis and synthesis of linear control system me862. Root locus lead compensator design example polezero. Note 8 rootlocus techniques college of engineering. Basuki rahmat jurusan teknik elektro sekolah tinggi teknologi telekomunikasi bandung2004 2. Using the root locus method a general stability criterion is defined for any order linear systems. Overshoot %os vsmaller compensator design achieving a desired transient with a given rl 2. Unesco eolss sample chapters control systems, robotics, and automation vol. You can use rlocus to plot the root locus diagram of any of the following.
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. Rules for making root locus plots swarthmore college. View notes additional root locus notes from enme 462 at university of maryland. Calculation of the roots, given a change in gain, can be readily accomplished by using design packages such as matlab. 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. In this section we introduce their structures and indicate their main properties. First of all, you should know that root locus method is used to find the values of k i. Lec32 compensator design using root locus plots contd. Design of lead compensator using bode plots duration. From given specifications determine the damping ratio and the natural frequency. With this proposed approach, students can concentrate on the larger control system design issues, such as compensator selection and closedloop performance.
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. In terms of rootlocus you obtain the same diagram because what matters is the product gshs. For an interactive approach to root locus plotting, see control system designer. A new approach to the calculation of the points at which the root locus crosses the imaginary axis is proposed and the corresponding parameters are given. Gain computation for marginal stability, by using gain computation for marginal stability, by using routhhurwitz criterion angle of departure angle of arrival can be obtained angle of departure angle of arrival can be obtained by a similar argument. Ii design methods for digital controllers, samplerate paraskevopoulos p. Root locus elec304alper erdogan 1 1 lecture 1 root locus.
Design via root locus elec304alper erdogan 1 1 lecture. Adding a zero to the system can pull the root locus farther to the lefthalf plane. A unified procedure for discretetime root locus and bode design. Computer aided design of lead compensator using root locus. Design via root locus elec304alper erdogan 1 18 ideal derivative compensation pd observations and facts. Determine the parts of the real axis that are on 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. Meeting design specs using root locus bison academy. If damping ratio alone is given then draw the root locus and draw line from origin at an angle to intersect the root locus, the point of intersection is the dominant pole. Tune electrohydraulic servomechanism using root locus. Root locus elec304alper erdogan 1 1 lecture 1 root locus what is rootlocus.
Rohan munasinghe bsc, msc, phd, mieee department of electronic and telecommunication engineering faculty of engineering university of moratuwa 10400 problem of root locus design root locus design can locate poles only on the root locus. Then design the lag compensator to meet the sse specifications. In this video, you will find the solution of the second question of the robt 303 midterm exam, which includes block diagram reduction, closedloop system analysis and root locus analysis. Design of controller using root locus method notes edurev. Root locus plot of dynamic system matlab rlocus mathworks. It is shown that this approach is simple and useful to determine the hurwitz stable polynomial. The gain margin difference between unity and the actual gain when and phase margins difference between and the actual phase when are used to measure how far the system is away from this undesirable instability in general, if some of the poles of are in the right half of. Sometimes, proportional control with a carefully chosen value of k is sufficient for the closedloop system to meet. It can offer for the students a better comprehension on this subject. How do i define settling time vertical line on root locus. Lec30 compensator design using root locus plots youtube.
A calculation method for series lagging correction based. 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. Jongeun choi department of mechanical engineering michigan state university lecture 20 root locus. Pdf the application of the root locus method for the. Meeting design specs using root locus so far, we have lead compensators which cancel a pole and move it left, speeding up the root locus. Root locus technique things to know the definition of root locus how to sketch the root locus how to use the root locus to find the poles of a closedloop system how to use the root locus to design a parameter value to meet a. You can use this plot to identify the gain value associated with a desired set of closedloop poles. We include a variable gain k in a unityfeedback con. This is recommended in case errors have been made in. They are known as pd, pi, pid, phaselag,phaselead,and phaselagleadcontrollers. This polezero pair in series with the plant makes the root locus pass through the point s1. Rule name description locus on real axis the locus exists on real axis to the right of an odd number of poles and zeros. Because the open loop poles and zeros exist in the sdomain having the values either as real or as complex conjugate pairs. The application of the root locus method for th e design of pitch controller of an f104a aircraft 5 branches, where each branch starts at a pole and ends at a zero of the lo op transfer function.
The purpose of compensator design generally is to satisfy both transient and steadystate speci. Root locus analysis for stability analysis, transient performance, etc. A lead compensator design example is worked based on improving transient time domain specifications. Compensator design using root locus plots contd yes friends, let us take up the last phase of our discussion on root locus design. Pid compensators which add a zero at s0 and add zero, one, or two zeros, pulling the root locus left. Block diagram reduction and root locus analysis youtube. In this chapter, let us discuss how to construct draw the root locus. Generic compensators en 2142 electronic control systems dr. If q0 there are asymptotes of the root locus that intersect the. Without precise drawing of root locus of the system and fussy trying, this method gives precise and satisfying correction results, providing a simple but effective route to the designing of linear control systems.
Combining analytic geometry with root locus method, this paper introduced a calculation method for series lagging correction. A method for plotting the complementary root locus using. Complementary root locus to sketch complementary root locus k. 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. These results present a procedure to avoid problems that appear in rootlocus plots for.
In this case, the design process is a combination of the design of the lead compensator and that of the lag compensator. According to the distribution of real roots in even and odd parts of characteristic equations, the relative damping character of high order systems can be predicted. Dr hassouneh dr chopra umd enme 462 lecture 17 18 root locus method part 1 week university of maryland, college park. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. Pdf root locus design using matlab matlabassignment.
With the leadcompensated transfer function in 4, the step response has an overshoot of 19. Rootloci analysing impact of lag compensators using. Pdf merge tool is a simple, fast and easy tool for merging pdf files. The root locus is a graphical representation in sdomain and it is symmetrical about the real axis. Root locus, physical meaning of the roots of the ch. Compensator design using the root locus mit opencourseware. More elaborate techniques of controller design using the root locus are available in most control textbooks. The steps to design the lead compensator are with root locus are. Feedback control systems are difficult to comprehend from a qualitative. I want to understand how in process of design of a controller i have to meet requirements using root locus method. Fall 2008 15 summary and exercises examples for root locus. High order system analysis and design using the root locus. To check whether a proportional controller isnt a possibility, well look at the root locus of with the desired closed loop pole locations indicated with orange xes the root loci do not move through the desired locations, but. Computer aided design of lead compensator using root locus method conference paper pdf available april 2015 with 2,026 reads how we measure reads.
Encyclopedia of life support systems eolss the rootlocus method is a direct method for determining gzc and is. I know that for the given damping ratio i need to estimate the arccos of it and. In this handout we introduce the idea the root locus which as a graphical. Control systems design by rootlocus method 2 laglead compensation techniques based on the rootlocus approach.
Rlocus analysis design nyu tandon school of engineering. Indicates how rootloci can be used to analyse the impact of lag compensators on achievable closedloop poles positions. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Several common dynamic controllers appear very often in practice. Because the siso design tool shows both root locus and bode diagrams, you can also choose to combine elements of both perspectives in making your design. A graphical representation of closed loop poles as a system parameter varied. In this page, you will learn how to design digital lead and lag compensators using the rootlocus design method.
Based on rootlocus graph we can choose the parameter for stability and the desired transient. Chapter 6 control systems design by, 1, 1 2 c root. Once the compensator gains have been designed, one should always test the closed loop system using simulink before hardware implementation. Compensated poles have more negative real and imaginary parts. In the followup sections procedures for designing these controllers by using the root locus technique such that the given systems have the desired speci. In control theory and stability theory, root locus analysis is a graphical method for examining. Madan gopal, department of electrical engineering, iit delhi. Apr 12, 2020 design of controller using root locus method notes edurev is made by best teachers of. Additional root locus notes root locus analysis for. This paper shows that complementary root locus can be plotted using only the wellknown construction rules to plot root locus. Root locus analysisoutline motivational example desired pole region simple controller design using desired poleregion construction of root loci magnitude condition stability range from root loci phase condition properties of root loci effects of addition of poles and zeros classical dynamic compensation1.
Sometimes, proportional control with a carefully chosen value of k is. In the root locus design approach presented here, these two tasks are approached separately. This matlab function calculates and plots the root locus of the siso model sys. Root locus design using matlab a compensator design using the root locus method can be done completely in matlab with the tool rltool. 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. In each case gain k is chosen such that percent overshoot is same. Examples functions and other reference release notes pdf documentation.
221 1188 790 276 963 31 1103 667 36 1248 759 1267 859 1459 420 1548 925 1532 259 842 1389 680 849 1483 1254 115 530 111 193 1079 1112 646 708 1404 1011