They used 2 design strategies for a double integrator and a second order system with a very lightly damped resonance. A method for plotting the complementary root locus using. You can again see how the step response changes with the compensator by c licking on the closed. In the analysis and design for stable systems and gives information about transient response of control systems. Designing digital lead and lag compensators using the. Root locus design using matlab a compensator design using the root locus method can be done completely in matlab with the tool rltool. Root locus elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus. Computeraided implementation of graphical root locus. Design a lead compensator to decrease the settling time by three times. 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. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci.
In this page, you will learn how to design digital lead and lag compensators using the rootlocus design method. In the root locus design approach presented here, these two tasks are approached separately. The minor loop is designed to change the open loop poles and open loop transientresponse. May 23, 2012 in this post we will deal with lag compensator design with time domain specifications and using the root locus technique. May 07, 20 this video walks through a phase lead compensator example using the root locus method. The root locus gives information about the stability and transient response of feedback control systems. Then look at the root locus window and see how it changed once the compensator was added. Root locus techniques root locus is a graphical presentation of the closedloop poles as a system parameter k is varied. Designing a lead compensator with root locus duration. If that is insufficient o determine dc, the frequency at which the uncompensated open loop, kpgjw, has a phase margin equal to the desired phase margin plus 5.
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. The lag compensator circuit in the s domain is shown in the following figure. This paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. Specifically, if you click on the openloop pole at 3 marked by a red x you can then slide the pole along the real axis and observe how the root locus plot changes. Design via root locus elec304alper erdogan 1 1 lecture 1. In the analysis and design for stable systems and gives information about transient response of. First design the minor loop then design the major loop. In this post we will deal with lag compensator design with time domain specifications and using the root locus technique. However, the pole caused by the motors shunt field time constant at sec is of no interest, so the horizontal and vertical ranges for the plot are chosen to. Ees42042 fundamental of control systems controller. The industrial operations hierarchy supervision supervision control control process 1 process 2 management, coordination, optimization low layer high layer. 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. Root locus design slide 6 specifications in the splane recall that the transient system specifications can be formulated in the splane t r.
The method cannot change the root locus and locate poles desired locations if they are outside the existing root locus. Exercise 3 lead compensator a unity feedback system with the forward transfer function is operating with a closedloop step response that has 15% overshoot. Design control systems using root locus techniques 1 design control systems using root locus techniques 2 no transcript 3 no transcript 4 if you equate the characteristic polynomial to zero, you can get the system poles 5 a value of s will be a closed loop pole if 6 the next question is for what k this will happen 7 no transcript 8. We include a variable gain k in a unityfeedback con. The root locus of the compensated servos openloop transfer function is now plotted, with the poles and zeros of the compensated servos closed loop transfer function superimposed.
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 measure angle contributed by each pole. The lag compensator is an electrical network which produces a sinusoidal output having the phase lag when a sinusoidal input is applied. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. From given specifications determine the damping ratio. Designing a rootlocus compensator to attain design requirements. In this digital control version of the cruise control problem, we are going to use the rootlocus design method to design the digital controller. Consider compensation as adding poles and zeros to feedback section for the equivalent system. Introduction the purpose of compensator design using root locus methods generally is to establish a speci. It is an important topic in introductory undergraduate engineering control disciplines.
The root locus method is a wellknown and commonly used tool in control system analysis and design. Here, the capacitor is in series with the resistor r2 and the output is measured across this combination. May 25, 2012 the steps to design the lead compensator are with root locus are. This video walks through a phase lead compensator example using the root locus method. Design a feedback compensator to reduce the settling time by a factor of 4 while continuing to operate the system with 20% overshoot. Alternatively, you can tune the compensator graphically directly from the root locus plot. Design via root locus elec304alper erdogan 1 1 lecture. Design a lag compensator for the above system to satisfy the following requirements a. Sometimes, proportional control with a carefully chosen value of k is.
Generic compensators cs are used in such situations in order to change the existing root locus. We show that many of the standard recipes for root locus compensator design can be easily adapted for computer implementation and. Frequency domain techniques updated 18 march 2020 lead and lag compensator design using frequency domain techniques lectures 3437. Design of lead and lag compensators using frequency. Evaluate the phase margin, analytically, or using a bode diagram. It is even possible to obtain root locus plots using a handheld calculator 6. Root locus compensator design me475 objectives design discrete lead and lag compensators for the servo table that yields a. Using the root locus for the uncompensated system, the intersection of the locus and the 20% overshoot line gives the operating point, 1. 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. Csadp allows the user to analyze and manipulate measured frequency response data, design control systems using.
The graph of all possible roots of this equation k is the variable parameter is called the root locus. Plot the root locus for the compensated system with pd controller. Root locus based control design university of illinois. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of leadlag compensator with complex. Draw the root locus of the given open loop uncompensated system with k1. A number of matlab function are developed for the compensator design method. The rootlocus method is a wellknown and commonly used tool in control system analysis and design. Root locus for integral compensation ndsu pid compensation ece 461 jsg 2 rev june 9, 2016.
Designing a rootlocus compensator to attain design. Using rlocf indg find the compensated closed loop poles and gain. Here, the capacitor is in series with the resistor r2. The steps to design the lead compensator are with root locus are. Compensator design to improve transient performance using. Root locus design 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. Discrete transfer function rootlocus in zplane compensation using a digital controller. Locate the openloop poles and zeros on the complex plane 2. Using the systems original poles and assuming a lead compensator zero at 1.
Locus controller design using the matlab sisotool toolbox. Lead and lag compensator design using root locus lectures 20, 21, 23, 24. Ppt design control systems using root locus techniques. Jongeun choi department of mechanical engineering michigan state university lecture 20 root locus. The control system analysis and design package csadp is a computeraided design package for applying classical control system analysis and design tools to experimental frequency response measurements. Compensator zero will change the root locus placement of the zero allows us to move the locus to place closedloop poles where we want them one less asymptote to. Jun 10, 20 designing a lead compensator with root locus duration. Sometimes one is able to improve control system speci. Root locus sketching rules negative feedback rule 1. Design via root locus elec304alper erdogan 1 35 two approaches for feedback compensation 1.
A method for plotting the complementary root locus using the. 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. Introduction and state variables pdf or pptformat pdf file if you cant view the file in your browser, download the file right mouse click, select save target as and view the downloaded file. Computeraided implementation of graphical root locus design. The roots corresponding to a particular value of the system parameter can then be located on the locus or value of the parameter for a desired root location can be determined from the locus. From given specifications determine the damping ratio and the natural frequency. State space root locus sketching rules negative feedback rule 1. Overshoot %os vsmaller compensator design achieving a desired transient with a given rl 2. If root locus does not pass the desired location, then reshape the root locus by adding poleszeros to by adding poleszeros to. Designing a lead compensator with root locus youtube.
From given specifications determine the damping ratio and the natural frequency find the dominant pole. Problem of root locus design root locus design can locate poles only on the root locus. Computeraided implementation of graphical root locus design recipes. 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. 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. In this page, you will learn how to design digital lead and lag compensators using the root locus design method. Finding the gain at a point on the root locus we can. Root locus elec304alper erdogan 1 1 lecture 1 root locus. It can be observed that as increases, the steady state errors decrease assuming systems asymptotic stability, but the maximum percent overshoot increases.
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