Characteristics equation routh hurwitz criterion nyquist stability criterion performance criteria effect of lag, lead and lag lead compensation on frequency responsedesign of lag, lead and laglead compensator using bode plots. Pdf complex lead and lag compensators are new additions to the repertoire of compensator structures for loop shaping. Draw the bode magnitude and phase plots determine the required phase margin from the. For instance, if a certain crossover frequency is desired, the examination of the bode plot would determine the type of the compensator. Pdf lead and lag compensators with complex poles and. Lag compensator design using bode plots objectives. Without them, it is impossible to comprehensively analyze and design electrical systems.
Bode diagram, polar plot, nichols plot, nyquist stability criterion. Compensator design to improve transient performance using root locus. In addition, csadp provides coefficients required to implement the compensator using selected digital algorithms. The following years witnessed the appearance of several graphical recipes for compensator design based on root locus plots which are standard material in most control texts see for example 2, 3. The following steps outline the procedure that will be used to design the special lag compensator using root locus methods in order to satisfy steadystate speci. Design a lag compensator for the above system to satisfy the following. However, it has certain advantages, especially in reallife situations such as modeling transfer functions from physical data. Ic6501 control systems previous year question papers auhippo. Develop a plc program for an automatic control system of a medium degree of complexity and select the right hardware for a given application.
The following steps outline the procedure that will be used to design either a lead or a lag compensator using root locus methods in order to. A lead compensator is one which adds a zero the system and is used to improve the transient response of the system. Ecomputer eee department,third year 5th semester ic6501 control systems previous year question papers for the regulation 20. There is one further consideration to do with the sampling rate. This requires moving the dominant branches of the root locus to the left. It improves the steady state performance of the system, but reduces the bandwidth and results in a slower transient response too. Find materials for this course in the pages linked along the left.
Then design the lag compensator to meet the sse specifications. The phaselead compensation transfer function can be obtained with the net. It is a combination of both the lag and the lead compensators. Discrete transfer function rootlocus in zplane compensation using a digital controller. Use the left hand toolbar to access the other chapters and themes. Interactive design with root locus and bode diagrams. In this page, you will learn how to design digital lead and lag compensators using the rootlocus design method.
With this computer aided design, compensator can be obtained of any control system to meet the desired response specification. Lag and lead compensators using op amp ece tutorials. Essentially, with a pi compensator, you add a pole at s0 to make the system type1 add a zero to cancel a pole. Be familiar with the design of lead and lag compensators using root locus and bode plot. Jongeun choi department of mechanical engineering michigan state university lecture 20 root locus. Lagcompensator the transfer function p z km p z the objective.
A lead compensator provides phase lead positive phase in the frequency response of system. Polar plots and the nyquist stability criterion 7 21. The purpose of compensator design generally is to satisfy both transient and steadystate speci. Like pi compensation, lag compensation uses a closely. With the leadcompensated transfer function in 4, the step response has an overshoot of 19. The steps to design the lead compensator are with root locus are. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of leadlag compensator with complex.
This is the only website,where you can download the previous year anna university question papers in pdf format with good quality and with out any water marks. We must attempt a dynamic compensator with poles andor zeros in order to reshape the root locus. Topics of interest include shape optimization, multidisciplinary design, trajectory optimization, feedback, and optimal control. By following the foregoing design procedure, we determine the zero and pole of the lead compensator, as shown in figure 715, to be 5. Analysis and design of control systems using matlab. Pdf this paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. A method of selecting one or two parameters using the root locus method. So far we have discussed on an introduction to matlab and lag compensator design with bode plot. A lead compensator in root locus form is given by 1 where the magnitude of z0 is less than the magnitude of p0. Pdf design and analysis of a control system using root locus. First we will introduce the nyquist stability diagram and nyquist plots when we discuss the design of lead, lag and lead lag compensators we will use bode plots frequency domain design tool 5.
We can choose a value of s on this locus that will give us good results. 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. The process is slightly simpler if we target the lead compensator design. The laglead compensator circuit in the s domain is shown in the following figure. This video walks through a phase lead compensator example using the root locus method. In this digital control version of the cruise control problem, we are going to use the rootlocus design method to design the digital controller. In most of the cases the actual closed loop response will differ from the that predicted from these designs. The main types of compensators are the lag, lead and lag lead.
Export the model to clead using the export option and convert the continuous compensator into a discrete one. They used 2 design strategies for a double integrator and a second order system with a very lightly damped resonance. Clear the sisotool design by selecting designclearc place a dominant zero at 2. Compensator design to improve transient performance using. Root locus controller design using the matlab sisotool toolbox overview in this lab you will explore the use of the root locus controller design methodology. Unit iv stability and compensator design 9 ic8451 cs syllabus control systems. Design of lead and lag compensators using frequency. Lecture notes principles of automatic control aeronautics. Ee2253 control systems previous year question papers ee2253 control systems aprmay 2018 regulation 2008 question paper. The frequency response of the control system or the root locus plot are traditionally used to tune the.
Sketch the root locus of the lead compensated system. May 01, 2015 20 analysis and design of control systems using matlab overshoot. A number of matlab function are developed for the compensator design method. The design of leadlag compensators using root locus. It can be observed that as increases, the steady state errors decrease assuming systems asymptotic stability, but the maximum percent overshoot increases.
A compensator that introduces a phase lag to an input signal is called a lag compensator. Design a laglead compensator such that the system will operate. A phaselead compensator tends to shift the root locus toward to the left in the complex splane. Graphically tune common control components, such as pids, lead lag networks, and notch filters using root locus, bode diagrams, and nichols charts. Design in the frequency domain nyquist stability criterion. Sometimes one is able to improve control system speci. Three di erent compensators are designed and analyzed based on phase and gain. In this paper the basic concepts associated with the multivariable nyquist array mna methods are extended to the logmagnitudefrequency and phaseanglefrequency planes. Design of nonlinear lead andor lag compensators amir nassirharand and seyed reza mousavi firdeh abstract. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Locus controller design using the matlab sisotool toolbox. Pdf computer aided design of lead compensator using root.
Unit iv stability and compensator design characteristics equation routh hurwitz criterion nyquist stability criterion performance criteria lag, lead and laglead networks laglead compensator design using bode plots. Design g cs using root locus or frequency response techniques. Leininger the university of toledo, toledo, ohio 43606, u. A firstorder lead compensator cs can be designed using the root locus. Guidelines for matlabs siso design tool gui siso design tool. We specifically need to shift the root locus more to the left in the complex plane to get it inside our desired region. Relative stability, gain and phase margins 7 video lecture 24. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. Problem of root locus design root locus design can locate poles only on the root locus.
So, please note that the poles on the root locus plot are denoted by x and the zeros are denoted by o. State space root locus sketching rules negative feedback rule 1. Adjust the gain until the gain cross over frequency is at 5 rads. Pdf ic6501 control systems cs books, lecture notes. Compensator design using the root locus mit opencourseware. Lead and lag compensators with complex poles and zeros design formulas. Pdf lead and lag compensators with complex poles and zeros. This lecture details on the design of leadlag compensators using root locus.
This paper introduce the lead, lag, laglead compensator design of root locus using single composite matlab programme. It brings together the sections on bode and nyquist and use insights from these as a tool for feedback design using lead and lag compensation. The design of leadlag compensators using root locus youtube. 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. Csadp also allows the user to design compensators interactively using bode and root locus methods, and aids the user in selecting the required resistor and capacitor values needed for implementing the compensator using opamp circuits. The poles on the root locus plot are denoted by x and the zeros are denoted by o.
The design of the lead and the lag compensator root locus, bode and analytical techniques can be used. The siso design analyze and tune siso feedback control systems using the siso design tool, you can graphically tune the gains and dynamics of the compensator c and prefilter f root locus view to stabilize the feedback loop enforce some minimum damping and bode diagrams to adjust the bandwidth, check the gain and phase margins 6. Direct expressions for the design of a lead lag continuous compensator using the root locus method and the procedure described in the 1970 and 1990 books by ogata are presented. Write the transfer function of lag compensator and draw its polezero plots. Digital root locus design again weve seen analysis using root locus in the z plane design is very similar to s plane. This paper successfully attempts to model a practical real control system using root locus time domain and frequency response bode plots techniques. Computeraided implementation of graphical root locus design recipes. The shape of the locus can also give us information on design of a more complex leadlag, pid controller though. Major focus has been placed on controller design and how the. Wonhee kim energy system engineering, chungang university. Lag compensator example prop vs lead vs lag concluding.
Root locus compensator design me475 objectives design discrete lead and lag compensators for the servo table that yields a. Phase lead compensator design using bode plots, a slightly di. The bode plots of the system in both cases, uncompensated and. The siso design tool allows you to iterate rapidly on your designs and perform the following tasks. Guidelines for matlabs siso design tool gui the siso design tool is a graphical user interface gui that facilitates the design of compensators for singleinput, singleoutput feedback loops. 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. From the settling time spec, we see that the real part of the dominant poles must be to the left of 10.
Ic8451 syllabus control systems regulation 2017 anna university. Lag compensators design using frequency response techniques ahmed abu. Create a new mfile and add the following matlab code. Complete design performed in the frequency domain design oriented analysis based on intuitive relationships between frequency response and system specifications extensive design experience and existing, proven designs available. Lead and lag compensator design using root locus yumpu. Depending on the effect desired, one or more lead and lag compensators may be used in various combinations. In the root locus design approach presented here, these two tasks are approached separately. Develop a plc program for an automatic control system of a medium degree of complexity.
Computeraided implementation of graphical root locus. 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. Interactive educational tool for the design of compensators using. Comparison between lead and lag compensators lead compensator lag compensator o high pass o low pass o approximates derivative plus proportional control o approximates integral plus proportional.
Control system design using bode plot lead, lag and leadlag controllers. Generic compensators cs are used in such situations in order to change the existing root locus. Discretetime modeling and compensator design for digitally. There are two schools in designing laglead compensators. Design tools we will use two different graphical representations to design compensators in the frequency domain. Design via root locus solutions to case studies challenges antenna control. This is a section in the chapter on classical control analysis techniques. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci.
Design and analysis portland state university department of electrical and computer engineering portland, oregon, usa december 30, 2009 abstract this paper discusses the design of a compensator for the buck dc switching converter. Using the root locus for the uncompensated system, the. Multivariable compensator design using bode diagrams and. 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. A known nonlinear compensator design approach is adapted to allow design of nonlinear lead andor lag compensators, and a number of matlab functions are developed that automate the compensator design procedure. The steps to design the lag compensator are draw the root locus of the given open loop uncompensated. Design and analysis of a control system using root locus. Design feedback compensators to achieve a set of desired closed loop system characteristics and design a compensator in the frequency domain to meet specific design requirements using a lead compensator, lag compensator, or lead lag compensator. 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. Root loci are used to study the effects of varying feedback gains on closedloop pole locations. Designing a lead compensator with root locus youtube.
Students will be exposed to block diagram analysis, analysis using laplace transforms, modeling of dynamical systems, linearization, transient analysis, sinusoidal steady state analysis, stability, design specifications, internal model principle, root locus and bode plot analysis, polar plots, stability margins, and computer aided design. We include a variable gain k in a unityfeedback con. Also, the root locus of the laglead compensated system shifts. Designing a rootlocus compensator to attain design requirements. To be able to design a lead compensator using bode plot techniques, design a lag compensator using bode plot techniques definitions.
This results in an improvement in the systems stability and an increase in its response speed. Designing a rootlocus compensator to attain design. To provide attenuation reduction in magnitude after z. Ee2253 control systems previous year question papers auhippo. What are the advantages and disadvantages in frequency domain design. The text is organized around the concept of control systems theory in the context of frequency and time domains.
Written to be equally useful for all engineering disciplines, it covers topics such as classical control, employing root locus design, frequency and response design using bode and nyquist plots. A method for plotting the complementary root locus using the. Siams advances in design and control series consists of texts and monographs dealing with all areas of design and control and their applications. In this post we will deal with lag compensator design with time domain specifications and using the root locus technique. The method cannot change the root locus and locate poles desired locations if they are outside the existing root locus. Keywords compensator design, frequency response, control systems. A simple lead compensator realized using op amps is shown. From given specifications determine the damping ratio and the natural frequency. Sometimes, proportional control with a carefully chosen value of k is. Laglead compensator is an electrical network which produces phase lag at one frequency region and phase lead at other frequency region. The frequency response method of controller design may be less intuitive than other methods you have studied previously.
The root locus plot indicates how the closed loop poles of a system vary with a system parameter typically a gain, k. One way to do this is to employ a lead compensator, refer to the lead and lag compensators page for details. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. Sample matlab mfile for root locus analysis txt format bode lead compensator design matlab mfile bode lag compensator design matlab mfile chapter 6. Direct expressions for ogatas leadlag design method using root. 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 of lead and lag compensators using frequency domain techniques prof. Use the control system designer app to interactively design and analyze siso control systems. Download link is provided and students can download the anna university ic6501 control systems cs syllabus question bank lecture notes syllabus part a 2 marks with answers part b 16 marks question bank with answer, all the materials are listed below for the students to make use of it and score good maximum marks with our study materials. If the branches need to be moved to the right, a phase lag compensator providing negative phase shift at s1 is used. Rlocus analysis design nyu tandon school of engineering. A phase lead compensator providing positive phase shift at s1 is used for this purpose. May 22, 2019 performance criteria lag, lead and lag lead networks compensator design using bode plots.1508 778 922 113 1131 1219 874 494 46 328 43 862 400 508 1270 32 990 850 1003 1206 111 1547 29 112 701 1272 1132 146 362 1401