Consider an openloop system which has a transfer function of 4 how do we design a feedback controller for the system using the rootlocus method. We include a variable gain k in a unityfeedback con. Interactive bode, root locus, and nichols graphical editors for adding, modifying, and removing controller poles, zeros, and gains. Effect of adding poles integrators lecture 22, frequency response. Design g cs using rootlocus or frequency response techniques. Designing a lag compensator with root locus youtube. In the editor, you can adjust the openloop bandwidth and design to gain and phase. Some case studies on compensator design through the created gui have been discussed below. The transfer function for a lag compensator is the same as the lead compensator, and is as follows. Rlocus analysis design nyu tandon school of engineering. To interactively shape the openloop response using control system designer, use the bode editor. There are practical limits as to how large the gain can be made. Controller design based on root locus general effects of addition of pole and zero lead lag compensator realization with op amp lead compensator design lead compensator improves stability and transient response. System also stable for all k, but when poles become complex.
They used 2 design strategies for a double integrator and a second order system with a very lightly damped resonance. Analyze and interpret stability of the system through root locus, bode plot and nyquist plot. Aug 01, 2015 design of lead, lag, and lag lead compensators with the root locus method is included. Analyze toque speed characteristics of dc and ac servomotors. Modern control lec 04 analysis and design of control. Then design the lag compensator to meet the sse specifications. Compensator design to improve steadystate error using root locus. Lead and lag compensator design using root locus yumpu. Laglead compensation chapter 6 control systems design by rootlocus method 2 laglead compensation techniques based on the rootlocus approach.
Root locus design the root locus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. An alternative to pd compensation is lead compensation. Design via root locus elec304alper erdogan 1 1 lecture. State space root locus sketching rules negative feedback rule 1. Phase lead compensators help to shift the poles of the transfer function to the left, which is beneficial for stability purposes. Sample matlab m file for root locus analysis txt format bode lead compensator design matlab m file bode lag compensator design matlab m file chapter 6. Performance criteria, lag, lead and laglead networks, compensator design using bode plots. By following the foregoing design procedure, we determine the zero and pole of the lead compensator, as shown in figure 715, to be 5. The nyquist stability criterion is presented in an easily understandable manner. International journal of advanced trends in computer science.
Pdf design of leadlag compensators for robust control. Then look at the root locus window and see how it changed once the compensator was added. Figure 1 shows the uncompensated and lead compensated root locus plots and closedloop step responses. Characteristics equation, location of roots in s plane for stability, routh hurwitz criterion, root locus construction, effect of pole, zero addition, gain margin and phase margin, nyquist stability criterion. You can again see how the step response changes with the compensator by c licking on the closed. The method cannot change the root locus and locate poles desired locations if they are outside the existing root locus. Using the root locus for the uncompensated system, the. For an unstable uncompensated system, lead compensation provides fast response but does not provide enough phase margin whereas lag compensation stabilize the system but does not provide enough bandwidth. You can add dynamics and modify compensator parameters using the compensator editor or using the graphical bode editor, root locus editor, or nichols editor plots. Chapter 6 control systems design by, 1, 1 2 c root.
Mar, 2012 gain a better understanding of root locus plots using matlab duration. A compensator that introduces a phase lag to an input signal is called a lag compensator. Lead mechanics ii adding a lead to the ltf changes both the magnitude and phase, so it is di. The steps for designing a lead compensator using root locus. The bode di agram approach to the design of lead, lag, and lag lead compensators is discussed. Rootloci 9 worked examples using all the 5 sketching rules. The compensator can be defined as a lag compensator if p a. Apr 29, 2017 lead compensation techniques based on the rootlocus approach the designing a lag compensator for the system shown by the root locus method may be stated as follows. Oct 23, 2019 with single lag or lead compensation may not satisfied design specifications. The root locus as generated by matlab is shown in figure 5.
It is a combination of both the lag and the lead compensators. This paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. A special case of the lag compensator is the pi controller when the pole is place at the zero i. Enter the transfer function and the command to plot the root locus. Bode diagram design is an interactive graphical method of modifying a compensator to achieve a specific openloop response loop shaping. From given specifications determine the damping ratio and the natural frequency. The root locus as generated by matlab is shown in figure 6. Rootlocus design the rootlocus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior.
Determine the desired pole location based on speci. In this section we introduce their structures and indicate their main properties. Once configured, you can tune a custom masked subsystem in the same way as any supported blocks in simulink control design. Graphically tune the compensator poles, zeros, and gains using openclosedloop bode, root locus, or nichols editor plots. Figure 1 shows the uncompensated and leadcompensated root locus plots and. How do we design a feedback controller for the system by using the root locus method. At the end, root locus design will not prove to be the best technique. Sometimes, proportional control with a carefully chosen value of k is. Chapter 9 solutions control systems engineering 7th. Problem of root locus design root locus design can locate poles only on the root locus. Im writing a book on the fundamentals of control theory. Design via root locus elec304alper erdogan 1 33 lag lead compensation. Gain a better understanding of root locus plots using matlab. Generic compensators cs are used in such situations in order to change the existing root locus.
Control systemsmatlab wikibooks, open books for an open world. Pdf control systems notes, ebook download for eeeee. I am also using matlab sisotool to see where is the feasible region in which i should have the rootlocus to fulfill the design requirements. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. The main types of compensators are the lag, lead and lag lead. Weclome to me451 control systems college of engineering. Manually tune the parameters of the leadlag controller using the compensator editor. A number of matlab function are developed for the compensator design method. 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.
International journal of advanced trends in computer science and engineering, vol. The point s s1 shown in the root locus plots is the desired closedloop pole location s1. Compensator design using the root locus mit opencourseware. Optimizationbased tuning requires simulink design optimization software. Chapter 7 treats the frequencyresponse analysis and design of control systems. Root locus and step response of lagcompensated system.
Li, sheng and chen 2010 derived the impulse response of the distributed order leadlag compensator using matlab and compared with the numerical inverse laplace transformation method 10. We can attempt to reduce the oscillation by using a lead or a lag compensator, which is a component used in a control system to improve an undesirable plant response. Designing a pid controller using matlabs siso tool august 19, 2015 by adolfo martinez control systems engineering requires knowledge of at least two basic components of a system. You can add dynamics and modify compensator parameters using the compensator editor or using the graphical bode editor, root locus editor, or nichols editor plots compensator editor. Evaluate the steady state performance of the lead compensated system to. The laglead compensator circuit in the s domain is shown in the following figure.
Design a laglead compensator such that the system will operate. The following steps outline the procedure that will be used to design the special lag compensator using root locus methods in. Aug 19, 2015 technical article an introduction to control systems. Control systemscontrollers and compensators wikibooks. Lead example the process is slightly simpler if we target the lead compensator design at a particular desired. They are known as pd, pi, pid, phase lag,phase lead,and phase lag leadcontrollers. The purpose of compensator design generally is to satisfy both transient and steadystate speci. Lead compensator lag compensator o high pass o low pass o approximates derivative plus proportional control. Analyze the effect of p, pi, pd and pid controllers on a control system. G cs g c0 s 5 although the plain integral compensator could be used for this purpose, it is di cult to obtain good performance using this type of compensator. Pdf computer aided design of lead compensator using root. Daniel gebbran compensator design in frequency domain there are 3 basic. Design a lag controller where plant actual plant and lead controller. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator.
This page is going to discuss using matlab for control systems design and analysis. If root locus does not pass the desired location, then reshape the root locus by adding poleszeros to by adding poleszeros to. Design of lead compensator using bode plots youtube. Like pi compensation, lag compensation uses a closely. Matlab is a programming language that is specially designed for the manipulation of matrices.
We will employ the root locus to design our controller to place our systems closedloop poles in locations that will result in behavior that satisfies our given requirements. Comparison of root locus plots with two lag compensator designs. Get the bookinprogress with any contribution for my work on patreon. Step response of the uncompensated system for the phase lead design example. From the root locus, for a damping ratio of the dominant pole pair is, write the corresponding gain of the uncompensated system. For more details on pi compensation schemes, please see this article. This is called the proportional compensator or proportional controller and provides gradual response to deviations from the set point. Laglead compensator is an electrical network which produces phase lag at one frequency region and phase lead at other frequency region. 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. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of leadlag compensator with complex.
How to plot the root locus of transfer function in matlab. Lets assume our design criteria are 5% overshoot and 1 second rise time. Design via root locus elec304alper erdogan 1 33 laglead compensation. A firstorder lag compensator cs can be designed using the root locus. Computeraided implementation of graphical root locus. So, the second order approximation is valid since higher order pole is much left to the. Pdf this paper introduce the lead,lag,laglead compensator design of root locus using single. This example shows how to enable custom masked subsystems in control system designer. A comparative analysis of pid, lead, lag, leadlag, and. May 25, 2012 the steps to design the lead compensator are with root locus are. Lecture 21, root locus, lag compensator, leadlag compensator design. In designing laglead compensators, we consider two cases where and. Because of its computational power, matlab is a tool of choice for many control engineers to design and simulate control systems. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics.
A lag compensator in root locus form is given by the following. How to design a leadlag compensator using bode plot. Lag compensator example prop vs lead vs lag concluding. Compensator editor to open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. In the previous lectures we laid the groundwork for design techniques based on root locus analysis. In the root locus design approach presented here, these two tasks are approached separately.
Compensator design to improve transient performance using. For more information, see tune simulink blocks using compensator editor. Thus, the figure shows multiple root locus plots whose color varies according to the parameter value. The compensator improves the transient performance of the. Design lag, lead, leadlag compensators and verify experimental results using matlab.
This is simply a compensator with a single pole at s 0 and a gain. Design g cs using root locus or frequency response techniques. To open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. Plot actual closed loop poles on the locus asterisks. 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. Interactive educational tool for the design of compensators. Compensator design to improve transient performance using root. Compensation in control system lag lead compensation. In this video i go through various ways to use matlab to plot and visualize the root locus. Designing a rootlocus compensator to attain design.
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