Well learn how to use rootlocus techniques to design. May 25, 2012 the steps to design the lead compensator are with root locus are. This document is intended to give you an example of using matlab and root locus to design controllers compensators in the zplane. Computeraided implementation of graphical root locus design. Lec30 compensator design using root locus plots youtube. In each case gain k is chosen such that percent overshoot is same. By following the foregoing design procedure, we determine the zero and pole of the lead compensator, as shown in figure 715, to be 5. General root locus is hard to determine by hand and requires matlab tools such as. Guy beale, msn 1g5, electrical and computer engineering. The matlab root locus tool kit can then be used to finish off the design.
Lookingattheunderdampedpolesk25, the real parts of the complex poles stay the same. Describe root locus diagram and show how to use it to choose loop gain. Now lets design a controller using the root locus method. Consider compensation as adding poles and zeros to feedback section for the equivalent system. Design compensator for plant model with time delays 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. Do the zeros of a system change with a change in gain. Pd controller design the resulting root locus takes on the form shown here we need to verify the second order. The setting time is inversely proportional to the real parts for this second order. You can use the rldesigngui to design the controllers for the remaining examples.
Computeraided implementation of graphical root locus. In this digital control version of the cruise control problem, we are going to use the rootlocus design method to design the digital controller. Computeraided implementation of graphical root locus design recipes. Series compensation design using the root locus application. The lead compensator zero location is placed over the left. Based on rootlocus graph we can choose the parameter for stability and the desired transient. In the root locus design approach presented here, these two tasks are approached separately. A unified approach for teaching root locus and bode.
This can be accomplished by combining proportional with integral action or. The purpose of compensator design generally is to satisfy both transient and steadystate speci. Lead compensator design fall 2008 2 course roadmap laplace transform transfer function models for systems electrical mechanical electromechanical block diagrams linearization modeling analysis design time. Design via root locus ideal derivative compensation pd lead compensation pid controller design feedback compensation physical realization of compensation 1 ideal derivative compensation pd 1 lead compensation 1 pid controller design 1 feedback compensation 1 physical realization of compensation engi 5821 unit 8. The pole and zero will appear to merge at the root. Designing a lag compensator with root locus brian douglas.
Design via root locus elec304alper erdogan 1 18 ideal derivative compensation pd observations and facts. Root locus elec304alper erdogan 1 1 lecture 1 root locus. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. The minor loop is designed to change the open loop poles and open loop transientresponse. Pdf robust root locus application in design and analysis of. Simulation of networked control system based on smith. A lead compensator in root locus form is given by 1 where the magnitude of z0 is less than the magnitude of p0. Each tool in control system designer provides a warning pane to indicate when timedelays are approximated. Design compensator for plant model with time delays.
In the followupsections procedures for designing these controllers by using the root locus technique such that the given systems have the desired speci. In this post we will deal with lag compensator design with time domain specifications and using the root locus technique. A plot of the possible closedloop pole locations as some parameter varies from 0 to 1. Root locus elec304alper erdogan 1 1 lecture 1 root locus what is rootlocus. 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. 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. I am also using matlab sisotool to see where is the feasible region in which i should have the root locus to fulfill the design requirements. Design an ideal derivative compensator for the following system. Design a feedback compensator to reduce the settling time by a factor of 4 while continuing to operate the system with 20% overshoot. Define pid controllers and describe how to use them. The frequencyresponse design method therefore by applying the lead compensator. Root locus compensator design me475 objectives design discrete lead and lag compensators for the servo table that yields a. Designing a pid controller using the root locus method duration. So far we have discussed on an introduction to matlab and lag compensator design with bode plot.
Introduction design via root locus activecircuit realization in. The method cannot change the root locus and locate poles desired locations if they are outside the existing root locus. Draw the root locus of the given open loop uncompensated system with k1. Designing a lag compensator with bode plot duration. Sometimes, proportional control with a carefully chosen value of k is sufficient for the closedloop system to meet. The examples and plots presented here are all done in matlab. Computer aided design of lead compensator using root locus method. By adding zeros andor poles to the original system adding a compensator, the root locus and thus the closedloop response will be modified. In this example we placed the zeros of our compensator in order to reshape the root locus so that the closedloop poles could be placed in the. Lec34 compensator design using root locus plots contd. Pdf this paper presents an approach to controller design in the complex plain. Where are the zeros of the closedloop transfer function. Compensated poles have more negative real and imaginary parts.
Pdf root locus design using matlab matlabassignment. Ee 43435329 control system design project lecture 6 updated. Draw a line from origin making an angle with the negative real axis. From given specifications determine the damping ratio.
We show that many of the standard recipes for root locus compensator design can be easily adapted for computer implementation and. 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. It is even possible to obtain root locus plots using a handheld calculator 6. Design via root locus elec304alper erdogan 1 1 lecture. In the root locus diagram, we can observe the path of the closed loop poles. Then, combined with incomplete differential forward pid control. From given specifications determine the damping ratio and the natural frequency.
Overshoot %os vsmaller compensator design achieving a desired transient with a given rl 2. I am also using matlab sisotool to see where is the feasible region in which i should have the. Root locus lead compensator design example polezero. By using the rootlocus method, it is possible to determine the value of the loop gain k that will make the damping ratio of the dominant closedloop poles as prescribed. Compensator design to improve transient performance using root. A graphical representation of closed loop poles as a system parameter varied. The steps to design the lead compensator are with root locus are. A number of matlab function are developed for the compensator design method. Compensator design to improve transient performance using. Designing a rootlocus compensator to attain design. Rlocus analysis design nyu tandon school of engineering. Hence, we can identify the nature of the control system. The ideal transient response has 16% overshoot and a.
Essentially, with a pi compensator, you add a pole at s0 to make the system type1 add a zero to cancel a pole. Design via root locus ideal derivative compensation pd generally, we want to speed up the transient response decrease ts and tp. The rootlocus can be used to determine the value of the loop gain, which results in a. First, using root locus method and simulink simulation software, the influences of networks time delay on the system stability and dynamic performance are analyzed. This results in an improvement in the systems stability and an increase in its response speed. The steps to design the lag compensator are draw the root locus of the given open loop uncompensated. Design via root locus elec304alper erdogan 1 35 two approaches for feedback compensation 1. The main idea of root locus design is to estimate the closedloop response from the openloop root locus plot.
Guy beale electrical and computer engineering department george mason university fairfax, virginia correspondence concerning this paper should be sent to prof. In the most cases these controllers are placed in the. If the location of an openloop pole or zero is a system variable, then the rootlocus method suggests the way. Click tuning methods, and select root locus editor. Problem of root locus design root locus design can locate poles only on the root locus. Introduction to root locus islamic university of gaza. 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. A lead compensator design example is worked based on improving transient time domain specifications. The bolus dose, when merged with continuous infusion results in the.
First design the minor loop then design the major loop. Generic compensators cs are used in such situations in order to change the existing root locus. Jun 10, 20 designing a lag compensator with root locus brian douglas. In this technique, we will use an open loop transfer function to know the stability of the closed loop control system. Designing a lead compensator with root locus youtube. Using a p compensator results in the loop gain k phs. When using approximations, the results are not exact and depend on the validity of the approximation. Design via root locus using the systems poles and the pole and zero of the ideal integral compensator, the summation of angles to the design point is 225. Discrete transfer function rootlocus in zplane compensation using a digital controller. The method involves altering the root locus of a servo by suiting the networks poles and zeros in the. A first order lead compensator tends to shift the root locus into the lefthand plane. Comparison of root locus plots with two lag compensator designs.
Try to use the root locus method to design a lead compensator. Using overshoot and settlingtime relations 3 with the damping ratio and. Open a root locus editor plot for the openloop response. Designing a lag compensator with root locus youtube. A unified approach for teaching root locus and bode compensator design conference paper in proceedings of the american control conference 1. Leadlag compensator using root locus 504 chapter 9 1. A firstorder lead compensator cs can be designed using the root locus. Compensator design to improve transient performance using root locus prof. However, the root locus method never lost its popularity among control engineers and their computeraided design packages typically include commands to obtain root locus plots.
Controller design based on root locus general effects of addition of pole and zero lead lag compensator realization with op amplead lag compensator realization with op amp lead compensator design lead compensator improves stability and transient response. State space root locus sketching rules negative feedback rule 1. 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. This example shows how to design a compensator for a plant with time delays using control system designer. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a specified. In the followup sections procedures for designing these controllers by using the root. A comparative analysis of pid, lead, lag, leadlag, and. Pdf computer aided design of lead compensator using root. This worksheet illustrates a method for designing a seriescompensation network for a simple servo. Jongeun choi department of mechanical engineering michigan state university lecture 20 root locus. The root locus for this further reduced system with controller is shown below. Compensator design for speed control of dc motor by root locus. May 23, 2012 so far we have discussed on an introduction to matlab and lag compensator design with bode plot. Based on rootlocus graph we can choose the parameter for stability and the desired transient response.
Compensator design using the root locus mit opencourseware. The rootloci for such a case is called the rootcontour. This paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. Designing a rootlocus compensator to attain design requirements. May 07, 20 im writing a book on the fundamentals of control theory.