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. 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. With the leadcompensated transfer function in 4, the step response has an overshoot of 19. In most of the cases the actual closed loop response will differ from the that predicted from these designs. A lead compensator is one which adds a zero the system and is used to improve the transient response of the system. 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. Then design the lag compensator to meet the sse specifications. The text is organized around the concept of control systems theory in the context of frequency and time domains. The root locus returns the closedloop pole trajectories as a function of the feedback gain k assuming negative feedback. 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.
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. A firstorder lead compensator cs can be designed using the root locus. The frequency response of the control system or the root locus plot are traditionally used to tune the. The poles on the root locus plot are denoted by x and the zeros are denoted by o. Design of lead and lag compensators using frequency. Pdf complex lead and lag compensators are new additions to the repertoire of compensator structures for loop shaping. The bode plots of the system in both cases, uncompensated and. This is a section in the chapter on classical control analysis techniques. Sample matlab mfile for root locus analysis txt format bode lead compensator design matlab mfile bode lag compensator design matlab mfile chapter 6.
Problem of root locus design root locus design can locate poles only on the root locus. 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. Keywords compensator design, frequency response, control systems. 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. Design via root locus solutions to case studies challenges antenna control. The phaselead compensation transfer function can be obtained with the net. Create a new mfile and add the following matlab code. 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 simple lead compensator realized using op amps is shown. A method for plotting the complementary root locus using the. Discrete transfer function rootlocus in zplane compensation using a digital controller. This requires moving the dominant branches of the root locus to the left. We can choose a value of s on this locus that will give us good results.
Write the transfer function of lag compensator and draw its polezero plots. Ic8451 syllabus control systems regulation 2017 anna university. 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. Develop a plc program for an automatic control system of a medium degree of complexity and select the right hardware for a given application. Designing a rootlocus compensator to attain design requirements. Without them, it is impossible to comprehensively analyze and design electrical systems.
Design of nonlinear lead andor lag compensators amir nassirharand and seyed reza mousavi firdeh abstract. Root locus compensator design me475 objectives design discrete lead and lag compensators for the servo table that yields a. Sometimes, proportional control with a carefully chosen value of k is. Relative stability, gain and phase margins 7 video lecture 24. In the root locus design approach presented here, these two tasks are approached separately. Compensator design to improve transient performance using root locus. 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. With this computer aided design, compensator can be obtained of any control system to meet the desired response specification. Designing a lead compensator with root locus youtube. One way to do this is to employ a lead compensator, refer to the lead and lag compensators page for details. Design of lead and lag compensators using frequency domain techniques prof. Use the left hand toolbar to access the other chapters and themes. Export the model to clead using the export option and convert the continuous compensator into a discrete one.
A lead compensator in root locus form is given by 1 where the magnitude of z0 is less than the magnitude of p0. So, please note that the poles on the root locus plot are denoted by x and the zeros are denoted by o. 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. The siso design tool allows you to iterate rapidly on your designs and perform the following tasks. From the settling time spec, we see that the real part of the dominant poles must be to the left of 10. Polar plots and the nyquist stability criterion 7 21. Also, the root locus of the laglead compensated system shifts.
Lag compensator design using bode plots objectives. A compensator that introduces a phase lag to an input signal is called a lag compensator. For instance, if a certain crossover frequency is desired, the examination of the bode plot would determine the type of the compensator. Ee2253 control systems previous year question papers ee2253 control systems aprmay 2018 regulation 2008 question paper. There are two schools in designing laglead compensators. They used 2 design strategies for a double integrator and a second order system with a very lightly damped resonance. Root loci are used to study the effects of varying feedback gains on closedloop pole locations. Bode diagram, polar plot, nichols plot, nyquist stability criterion. A phaselead compensator tends to shift the root locus toward to the left in the complex splane.
It improves the steady state performance of the system, but reduces the bandwidth and results in a slower transient response too. Guidelines for matlabs siso design tool gui siso design tool. Be familiar with the design of lead and lag compensators using root locus and bode plot. Design a lag compensator for the above system to satisfy the following. Depending on the effect desired, one or more lead and lag compensators may be used in various combinations.
Three di erent compensators are designed and analyzed based on phase and gain. Ic6501 control systems previous year question papers auhippo. Like pi compensation, lag compensation uses a closely. We specifically need to shift the root locus more to the left in the complex plane to get it inside our desired region. A method of selecting one or two parameters using the root locus method. 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 root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. 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. By following the foregoing design procedure, we determine the zero and pole of the lead compensator, as shown in figure 715, to be 5. We include a variable gain k in a unityfeedback con. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics.
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. Compensator design using the root locus mit opencourseware. There is one further consideration to do with the sampling rate. 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. Computeraided implementation of graphical root locus design recipes. However, it has certain advantages, especially in reallife situations such as modeling transfer functions from physical data. Design g cs using root locus or frequency response techniques. A lead compensator provides phase lead positive phase in the frequency response of system.
Lagcompensator the transfer function p z km p z the objective. Digital root locus design again weve seen analysis using root locus in the z plane design is very similar to s plane. Compensator design to improve transient performance using. Interactive design with root locus and bode diagrams. 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. Lag and lead compensators using op amp ece tutorials. Draw the bode magnitude and phase plots determine the required phase margin from the. The steps to design the lag compensator are draw the root locus of the given open loop uncompensated. Leininger the university of toledo, toledo, ohio 43606, u. If the branches need to be moved to the right, a phase lag compensator providing negative phase shift at s1 is used.
Use the control system designer app to interactively design and analyze siso control systems. We must attempt a dynamic compensator with poles andor zeros in order to reshape the root locus. Pdf lead and lag compensators with complex poles and. Lag compensators design using frequency response techniques ahmed abu. Design in the frequency domain nyquist stability criterion. May 01, 2015 20 analysis and design of control systems using matlab overshoot. Pdf design and analysis of a control system using root locus. 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. Adjust the gain until the gain cross over frequency is at 5 rads. What are the advantages and disadvantages in frequency domain design. 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. 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. Ee2253 control systems previous year question papers auhippo.
A phase lead compensator providing positive phase shift at s1 is used for this purpose. Major focus has been placed on controller design and how the. 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. 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. 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. In this page, you will learn how to design digital lead and lag compensators using the rootlocus design method. In this post we will deal with lag compensator design with time domain specifications and using the root locus technique. Find materials for this course in the pages linked along the left. The design of leadlag compensators using root locus youtube.
From given specifications determine the damping ratio and the natural frequency. 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. Jongeun choi department of mechanical engineering michigan state university lecture 20 root locus. Generic compensators cs are used in such situations in order to change the existing root locus. So far we have discussed on an introduction to matlab and lag compensator design with bode plot.
Direct expressions for ogatas leadlag design method using root. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of leadlag compensator with complex. Analysis and design of control systems using matlab. Rlocus analysis design nyu tandon school of engineering. 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. 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. The laglead compensator circuit in the s domain is shown in the following figure.
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. This paper successfully attempts to model a practical real control system using root locus time domain and frequency response bode plots techniques. It can be observed that as increases, the steady state errors decrease assuming systems asymptotic stability, but the maximum percent overshoot increases. Phase lead compensator design using bode plots, a slightly di. Control system design using bode plot lead, lag and leadlag controllers. Sketch the root locus of the lead compensated system.
In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. Locus controller design using the matlab sisotool toolbox. Lead and lag compensators with complex poles and zeros design formulas. Using the root locus for the uncompensated system, the. The main types of compensators are the lag, lead and lag lead. Design and analysis of a control system using root locus.
The method cannot change the root locus and locate poles desired locations if they are outside the existing root locus. The root locus plot indicates how the closed loop poles of a system vary with a system parameter typically a gain, k. The steps to design the lead compensator are with root locus are. Laglead compensator is an electrical network which produces phase lag at one frequency region and phase lead at other frequency region. 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.
Develop a plc program for an automatic control system of a medium degree of complexity. Lag compensator example prop vs lead vs lag concluding. Pdf lead and lag compensators with complex poles and zeros. A number of matlab function are developed for the compensator design method. Lecture notes principles of automatic control aeronautics. The frequency response method of controller design may be less intuitive than other methods you have studied previously. Interactive educational tool for the design of compensators using. Discretetime modeling and compensator design for digitally. Siams advances in design and control series consists of texts and monographs dealing with all areas of design and control and their applications.
Pdf computer aided design of lead compensator using root. 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. Pdf this paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. Designing a rootlocus compensator to attain design. Lead and lag compensator design using root locus yumpu. Wonhee kim energy system engineering, chungang university. To provide attenuation reduction in magnitude after z. The design of leadlag compensators using root locus. In addition, csadp provides coefficients required to implement the compensator using selected digital algorithms. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. The process is slightly simpler if we target the lead compensator design. State space root locus sketching rules negative feedback rule 1. Sometimes one is able to improve control system speci.
The shape of the locus can also give us information on design of a more complex leadlag, pid controller though. This results in an improvement in the systems stability and an increase in its response speed. Graphically tune common control components, such as pids, lead lag networks, and notch filters using root locus, bode diagrams, and nichols charts. Clear the sisotool design by selecting designclearc place a dominant zero at 2. 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. Pdf ic6501 control systems cs books, lecture notes. Design a laglead compensator such that the system will operate. Unit iv stability and compensator design 9 ic8451 cs syllabus control systems. Ecomputer eee department,third year 5th semester ic6501 control systems previous year question papers for the regulation 20. In this paper the basic concepts associated with the multivariable nyquist array mna methods are extended to the logmagnitudefrequency and phaseanglefrequency planes.
This lecture details on the design of leadlag compensators using root locus. Multivariable compensator design using bode diagrams and. 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. May 22, 2019 performance criteria lag, lead and lag lead networks compensator design using bode plots.
996 1269 1064 1319 11 1443 209 298 290 886 288 1021 1088 703 1142 792 1478 504 331 999 868 95 819 1307 329 522 1147 1231 540 1398 1538 479 45 447 321 1266 281 331 12 757 872 820 644 168 1367