Lead lag compensator design using root locus plots pdf file

Design lag, lead, leadlag compensators and verify experimental results using matlab. 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. They are known as pd, pi, pid, phase lag,phase lead,and phase lag leadcontrollers. 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. Pdf control systems notes, ebook download for eeeee. This is called the proportional compensator or proportional controller and provides gradual response to deviations from the set point. Once configured, you can tune a custom masked subsystem in the same way as any supported blocks in simulink control design. Lag compensator example prop vs lead vs lag concluding. This page is going to discuss using matlab for control systems design and analysis. Rlocus analysis design nyu tandon school of engineering.

In the previous lectures we laid the groundwork for design techniques based on root locus analysis. In this section we introduce their structures and indicate their main properties. Graphically tune the compensator poles, zeros, and gains using openclosedloop bode, root locus, or nichols editor plots. A special case of the lag compensator is the pi controller when the pole is place at the zero i. Like pi compensation, lag compensation uses a closely. Computeraided implementation of graphical root locus. Plot actual closed loop poles on the locus asterisks. 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. Evaluate the steady state performance of the lead compensated system to. For more details on pi compensation schemes, please see this article.

Compensator design to improve transient performance using. 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. Lead mechanics ii adding a lead to the ltf changes both the magnitude and phase, so it is di. Design via root locus elec304alper erdogan 1 33 laglead compensation. Design a laglead compensator such that the system will operate. Designing a lag compensator with root locus youtube. Then design the lag compensator to meet the sse specifications. For more information, see tune simulink blocks using compensator editor. Pdf computer aided design of lead compensator using root. Analyze and interpret stability of the system through root locus, bode plot and nyquist plot. Step response of the uncompensated system for the phase lead design example.

How to plot the root locus of transfer function in matlab. At the end, root locus design will not prove to be the best technique. Enter the transfer function and the command to plot the root locus. Figure 1 shows the uncompensated and lead compensated root locus plots and closedloop step responses. Optimizationbased tuning requires simulink design optimization software. 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. 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. They used 2 design strategies for a double integrator and a second order system with a very lightly damped resonance. If root locus does not pass the desired location, then reshape the root locus by adding poleszeros to by adding poleszeros to. So, the second order approximation is valid since higher order pole is much left to the. We include a variable gain k in a unityfeedback con.

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. D6 frequency response approach to compensator design information about the performance of the closedloop system, obtained from the openloop frequency response. 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. International journal of advanced trends in computer science. Compensator design using the root locus mit opencourseware. International journal of advanced trends in computer science and engineering, vol. In the root locus design approach presented here, these two tasks are approached separately. Root locus design the root locus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. 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. Lecture 21, root locus, lag compensator, leadlag compensator design. An alternative to pd compensation is lead compensation. The bode di agram approach to the design of lead, lag, and lag lead compensators is discussed. Compensator design to improve transient performance using root. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator.

This is simply a compensator with a single pole at s 0 and a gain. Manually tune the parameters of the leadlag controller using the compensator editor. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. Jun 14, 2015 gain a better understanding of root locus plots using matlab. Im writing a book on the fundamentals of control theory. Lead example the process is slightly simpler if we target the lead compensator design at a particular desired. Design via root locus elec304alper erdogan 1 1 lecture. The laglead compensator circuit in the s domain is shown in the following figure. Comparison of root locus plots with two lag compensator designs. To open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator.

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. The root locus as generated by matlab is shown in figure 6. Daniel gebbran compensator design in frequency domain there are 3 basic. 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. 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. Chapter 7 treats the frequencyresponse analysis and design of control systems. Aug 01, 2015 design of lead, lag, and lag lead compensators with the root locus method is included. Pdf design of leadlag compensators for robust control. 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. May 25, 2012 the steps to design the lead compensator are with root locus are. In the editor, you can adjust the openloop bandwidth and design to gain and phase. Control systemsmatlab wikibooks, open books for an open world. Locus controller design using the matlab sisotool toolbox. Get the bookinprogress with any contribution for my work on patreon.

It improves the steady state performance of the system, but reduces the bandwidth and results in a slower transient response too. Compensation in control system lag lead compensation. Rootlocus design the rootlocus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. Chapter 6 control systems design by, 1, 1 2 c root. 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. How to design a leadlag compensator using bode plot. Interactive bode, root locus, and nichols graphical editors for adding, modifying, and removing controller poles, zeros, and gains. The root locus as generated by matlab is shown in figure 5.

Matlab is a programming language that is specially designed for the manipulation of matrices. A compensator that introduces a phase lag to an input signal is called a lag compensator. 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 method cannot change the root locus and locate poles desired locations if they are outside the existing root locus.

From the root locus, for a damping ratio of the dominant pole pair is, write the corresponding gain of the uncompensated system. In designing laglead compensators, we consider two cases where and. Designing a rootlocus compensator to attain design. Rootloci 9 worked examples using all the 5 sketching rules. Control systemscontrollers and compensators wikibooks. The point s s1 shown in the root locus plots is the desired closedloop pole location s1. 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. Mar, 2012 gain a better understanding of root locus plots using matlab duration. Design via root locus elec304alper erdogan 1 33 lag lead compensation. In this case, the design process is a combination of the design of the lead compensator and that of. This paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. Oct 23, 2019 with single lag or lead compensation may not satisfied design specifications. Effect of adding poles integrators lecture 22, frequency response. The compensator improves the transient performance of the.

If the location of the zero is fixed, then the location of the pole can be determined. This example shows how to enable custom masked subsystems in control system designer. Sometimes, proportional control with a carefully chosen value of k is. The transfer function for a lag compensator is the same as the lead compensator, and is as follows. Aug 19, 2015 technical article an introduction to control systems. Design g cs using root locus or frequency response techniques. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of leadlag compensator with complex. Root locus and step response of lagcompensated system. A firstorder lag compensator cs can be designed using the root locus. Interactive educational tool for the design of compensators. Then look at the root locus window and see how it changed once the compensator was added.

Lets assume our design criteria are 5% overshoot and 1 second rise time. Analyze toque speed characteristics of dc and ac servomotors. The steps for designing a lead compensator using root locus. Laglead compensation chapter 6 control systems design by rootlocus method 2 laglead compensation techniques based on the rootlocus approach. Chapter 9 solutions control systems engineering 7th. Designing a lead compensator with root locus youtube. Thus, the figure shows multiple root locus plots whose color varies according to the parameter value. From given specifications determine the damping ratio and the natural frequency. The main types of compensators are the lag, lead and lag lead. Because of its computational power, matlab is a tool of choice for many control engineers to design and simulate control systems. For a lead design, we require the angle at the zero q z numerator angleand the angle at the poleq p denominator angle to satisfyq z q p f. 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. State space root locus sketching rules negative feedback rule 1. Weclome to me451 control systems college of engineering.

The following steps outline the procedure that will be used to design the special lag compensator using root locus methods in. Pdf this paper introduce the lead,lag,laglead compensator design of root locus using single. Lead compensator lag compensator o high pass o low pass o approximates derivative plus proportional control. Design g cs using rootlocus or frequency response techniques. There are practical limits as to how large the gain can be made. Compensator editor to open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. In this video i go through various ways to use matlab to plot and visualize the root locus. It is a combination of both the lag and the lead compensators.

Design of control systems cascade root locus design this is the first lecture devoted to the control system design. Laglead compensator is an electrical network which produces phase lag at one frequency region and phase lead at other frequency region. System also stable for all k, but when poles become complex. Problem of root locus design root locus design can locate poles only on the root locus. Analyze the effect of p, pi, pd and pid controllers on a control 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. Design a lag controller where plant actual plant and lead controller. The nyquist stability criterion is presented in an easily understandable manner. Bode diagram design is an interactive graphical method of modifying a compensator to achieve a specific openloop response loop shaping.

Design of lead compensator using bode plots youtube. Performance criteria, lag, lead and laglead networks, compensator design using bode plots. Lead and lag compensator design using root locus yumpu. Gain a better understanding of root locus plots using matlab. Phase lead compensators help to shift the poles of the transfer function to the left, which is beneficial for stability purposes. Figure 1 shows the uncompensated and leadcompensated root locus plots and. The purpose of compensator design generally is to satisfy both transient and steadystate speci. Modern control lec 04 analysis and design of control. A comparative analysis of pid, lead, lag, leadlag, and.