Locate the openloop poles and zeros on the complex plane 2. Pdf the introduction to root locus method find, read and cite all the research you need. The projects are assigned around week 8 of the regular 16week semester and students work in three or fourmember groups. Compensated poles have more negative real and imaginary parts. We can find the value of k for the points on the root locus branches by using magnitude condition. 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. Root locus elec304alper erdogan 1 4 drawing the root locus how do we draw root locus for more complex systems, and without calculating poles. So, we can use the magnitude condition for the points, and this satisfies the angle. The primary objective of this experiment is to learn root locus using matlab. Make sure all necessary information is shown on the plot refer to item a until h in lab assignment section by clicking on the locus and moving your cursor accordingly. Determine the parts of the real axis that are 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. Rltool is a component of the broader siso design tool in matlab, which can also do bode and nyquist anal. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. By adding zeros andor poles to the original system adding a compensator, the root locus and thus the closedloop response will be modified.
It also describes how to choose the proportional gain to achieve a desired closedloop response, and how matlab figure 1. The primary mode of delivery consists of two 75minute lectures per week. Application of the many classical and modern control system design and analysis tools is based. Root locus elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus. 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.
A suitable value of \k\ can then be selected form the rl plot. The vector lengths from to the poles are marked on the diagram. The root loci are asymptotic to straight lines, for large values of s, with angles given by. The root locus structure also yields ideas for adding elements to the compensator. Rltool is a tool in matlab, that provides a gui for performing root locus analysis on single input single output siso systems, which are the class of systems we cover in e105. Matlab scripts for plotting root loci and simulating the system are provided.
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. Using matlab for root locus analysis as an example of how to use matlab to perform a root locus analysis, consider design problem dp6. Root locus design of digital controllers engineering. An example of the type of root locus well learn to sketch by hand, as well as plot in matlab. Using matlab for root locus analysis homepages at wmu. We exploit the properties of rootlocus to do a rough sketch. Sketch the root locus diagram for the parameter k for the closed loop system shown in the diagram. Stability analysis with a matlab root locus plot youtube. Pdf introduction to root locus method researchgate. Root locus plot of dynamic system matlab rlocus mathworks. 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.
Design via root locus elec304alper erdogan 1 1 lecture. Two approaches ideal derivative proportionalplusderivative pd. The block diagram of the closedloop system is shown. Closedloop poles plotting the root locus of a transfer function choosing a value of k from root locus closedloop response. The user may input m, c, and k values for a secondorder system and view the time response of the system to an initial displacement of 1, the frequency response, and the root locus. The first two software packages are free alternatives to matlab, and their use is encouraged. The root locus returns the closedloop pole trajectories as a function of the. With the aid of this toolbox, for example, the control engineer can draw the bode diagram, root locus or time response of. The block diagram of the closedloop system is shown below. There are practical limits as to how large the gain can be made. A graphical representation of the closed loop poles as a system parameter varies.
The plots are now empty because no model is imported yet. Design via root locus elec304alper erdogan 1 1 lecture 1. Ies3006 control systems cad tutorial 3 1 introduction this tutorial has the following objectives. How to plot the root locus using matlab first thing you need to do is to enter the open loop transfer function or the equivalent state space then in the command window write rlocussys like the following example sketch the root locus of the following system. Pdf root locus design using matlab matlabassignment. Where applicable, also explain the compensator the added poles andor zeros. 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. For an excellent tutorial on controlrelated functions, type democontrol. This tutorial illustrates how to use the rlocus command in matlab to quickly and easily sketch the root locus. This example is from the textbook process dynamics and control seb. The main idea of root locus design is to estimate the closedloop response from the openloop root locus plot. Pdf example problems and solutions ogata root locus. In the discretetime case, the constraint is a curved line.
Syde 352l control systems laboratory laboratory 0 matlab simulink workshop goals. This example shows how to design a compensator for an electrohydraulic servomechanism using root locus graphical tuning techniques. You will need to print one or more plots for each problem. In this tutorial, we will introduce the root locus, show how to create it using matlab, and demonstrate how to design. This is called the proportional compensator or proportional controller and provides gradual response to deviations from the set point. The root locus rules of behavior provide insight for adjusting additional compensator parameters. Sometimes, proportional control with a carefully chosen value of k is. Introduction to root locus semester 083 page 3 cise 316 control systems design lab experiment 1. Root locus plot in matlab complete tutorial todays. Root locus design the root locus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. Pdf an undergraduate control tutorial on root locusbased. The effects of gains on the system response, overshoot and the stability can be determined.
In each case gain k is chosen such that percent overshoot is same. The poles on the root locus plot are denoted by x and the zeros are denoted by o. This document is intended to give you an example of using matlab and root locus to design controllers compensators in the zplane. Root locus for uncompensated system zoomed for finding 20% overshoot searching for the 20% overshoot in figure 4 zoomed graph of figure 3, we find the dominant poles at 5. The root locus technique is the primary design method used in pr ojects to date. If you have a need for more information, refer to the simulink manual. Design via root locus elec304alper erdogan 1 18 ideal derivative compensation pd observations and facts. First we evaluate the performance of the uncompensated system in matlab.
Therefore, lets explore the properties of root locus. A root loci plot is simply a plot of the s zero values and. Pdf example problems and solutions ogata root locus sasi. It is an approach to select the gain as to achieve desired transient behavior. The plot on the left is the root locus, and the plots on the right are the magnitude and phase plots of the bode diagram. The root locus is the graphic technique that gives us that qualitative description of the performance of the control system we are designing.
Plot new root locus to see how close it comes to 1. Root locus can describe the performance of the system as varius parameters are changed. First we evaluate the performance of the uncompensated. The points on the root locus branches satisfy the angle condition. Section 5 root locus analysis college of engineering. On the homework web page, find the matlab tutorial in pdf form, siso tool tutorial starts on page 23.
In this video we will lean bout how to plot root locus in matlab and will study different control system parameters like. These problems should be done using matlab or some other program that creates root locus plots. The root locus of an openloop transfer function hs is a plot of the locations locus of all possible closed loop poles with proportional gain k and unity feedback. Matlab program 611 generates a root locus plot as shown in figure 650. To ensure closedloop stability, the closedloop roots should be confined to inside the unit circle. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Gnu octave is a numerical computation software package very similar to matlab. Control tutorials for matlab and simulink introduction. Note that the input argument is the openloop transfer function. The goal is to use matlab to draw a root locus diagram for the parameter k, given the parameter m 4. The projects are assigned around week 8 of the regular 16week semester and students work in three or fourmember. A proportional controller design for 8% overshoot use root locus to determine. Obtain root locus, step response and the timedomain specifications for the compensated system.
Hi everyone in this video, i am demonstrating how to obtain root locus plot of the transfer function in matlab software. The tutorial provides a brief introduction to the use of matlab with examples, and then describes the control system toolbox with examples. The pr imary mode of delivery consists of two 75minute lectures per week. The root locus plotted by using matlab on the figure window, click edit copy figure, and then paste to a word document. Using root locus ideas to design controller we have seen how to draw a root locus for given plant dynamics.
Control tutorials for matlab and simulink suspension. Using simulink, matlab, and lego mindstorms to teach a. The root loci must be symmetric about the real axis. The root loci may be found on portions of the real axis to the left of an odd number of open loop poles and zeros. Have matlab solve for the roots for each of a specified list of values for k and plot them. Design via root locus elec304alper erdogan 1 15 improving transient response with cascade compensation if the closed loop root locus doesnt go through the desired point, it needs to be reshaped. The root loci of the original and compensated systems are presented in figures 8. Sisotool quick tutorial to start, you type sisotool lower case in the command prompt. Locus segments now, determine if point 6is on the root locus again angles from complex poles cancel always true for real. In the previous example on the printer paper advance position control, t. This process is important and common enough that matlab has a way to do it automatically. The root locus technique is the primary design method used in projects to date. Plot root loci with a square aspect ratio so that a line with slope 1. We include a variable gain k in a unityfeedback con.
So, the angle condition is used to know whether the point exist on root locus branch or not. Root locus definition the rootlocusis the set of all points in the s. Closedloop stability can be analyzed with routh arrays, bode plots, or root locus plots. You can also make use of matlab s rlocfind function. In this method, the closedloop system poles are plotted against the value of a system parameter, typically the openloop transfer function gain. As an example of how to use matlab to perform a root locus analysis, consider design problem dp6. Each software package employs different methods to create, examine, print, and save transfer functions. 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. Root locus is a plot of closed loop poles as varies from. Matlab supplies its own set of gain values that are used to calculate a root locus plot. You can move the pink square around on the root locus to change the compensator gain. The root locus method typically focuses on the gain parameter. Evans, is widely used in control engineering for the design and analysis of control systems.
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