In these cases, it is necessary to use two lead networks in series, use more elaborate compensation networks, or use parallel compensation. This worksheet shows how systems with multiple free parameters. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. Lag example step 1 design a lag compensator for the above system to satisfy the following requirements a. Using bode plots determine the gain and phase margins for the closedloop system.
This shifts the root locus to the left, which enhances the responsiveness and stability of the system. 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. The 3d version of the plot helps to visualize not only where the poles are moving, but also how fast they move across the complex plane when we vary. Lec34 compensator design using root locus plots contd. Pdf tuning of a laglead compensator used with a first. The compensator can be defined as a lag compensator if a p.
Matlab can sketch the root locus for any gs easily using the rlocus command. Design a cascade compensator to yield zero steadystate error, a settling time of about 0. However, it is important to note that in a lead compensator as high. The procedure of lag lead compensator design is same as lead and lag compensators designed individually. It can be very challenging to reguate such a system. System also stable for all k, but when poles become. They are known as pd, pi, pid, phase lag,phase lead,and phase lag leadcontrollers. Ppt design with root locus powerpoint presentation. Evaluate the steady state performance of the lead compensated system to. For this system, let us sketch the root locus plot and then determine the value of k such that the damping ratio z of a pair of dominant complexconjugate closedloop poles. A phase lag compensator tends to shift the root locus to the right, which is undesirable. Design and implementation of control system for magnetic. Sometimes, proportional control with a carefully chosen value of k is. View notes 12 lead compensator design root locus from ece 382 at purdue university.
Root locus lead compensator design example polezero. The rootlocus plot of the uncompensated system reveals that it is not. In this article the lead and lag compensators will be briefly discussed. The positive root locus is the set of all points s in the complex plane for. In this page, you will learn how to design digital lead and lag compensators using the root locus design method. He discussed the tuning of the used compensators 12. Designing digital lead and lag compensators using the. From the root locus graph obtained from matlab simulation zoomed in figure 10, it is evident that the dominant pole for the lead compensated system with 30%. Both analog and digital control systems use lead lag compensators. Plot the closed loop system performance using the feedback and step function in matlab. Lead compensator example draw bode plot of l1s using approximated bode plot pm is found to be 17o. The plot on the left is the standard root locus plot. State space root locus sketching rules negative feedback rule 1.
To open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. The dominant closedloop poles on the root locus plot are located. Can be implemented using passive components simple rlc circuit as an alternative to the. Compensator design to improve transient performance using. The point s s1 shown in the root locus plots is the desired closedloop pole location s1. Design of laglead compensator using root locus method. A lag compensator in root locus form is given by where the magnitude of zo is greater than the magnitude of po. A firstorder lead compensator can be designed using the root locus. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. Following are the steps which give a sequential idea for designing lag lead compensator. The point s s 1 shown in the root locus plots is the desired closedloop pole location s 1. The following steps outline the procedure that will be used to design the special lag compensator using root locus methods in. Modern control lec 04 analysis and design of control.
More elaborate techniques of controller design using the root locus are available in most control textbooks. Now with an ideal integrator pi controller root locus. Apr 29, 2017 the effect of such control is to introduce a degree of anticipation into the system and speed up the transient response. Let us assume that the transfer function of the laglead compensator t. Lead and lag compensator design using root locus yumpu. Plot the bode, nyquist and root locus plots for your open loop system, csgs. Design a lag lead compensator for a unity feedback system with open loop 15 k transfer function g s to meet the following specifications s s 1s 4 i kv.
Although algebraic and trigonometric methods were used to determine the parameters of the compensation network kc, a, b and, semigraphical methods can be used instead. Like pi compensation, lag compensation uses a closely. The transfer function of the compensator takes the form of. Be familiar with the design of lead and lag compensators using root locus and bode plot methods. Pdf computer aided design of lead compensator using root. Design a lag controller where plant actual plant and lead. This is called the proportional compensator or proportional controller and provides gradual response to deviations from the set point. Design via root locus elec304alper erdogan 1 1 lecture 1. The transfer function is rearranged so that the output is expressed in terms of sums of terms involving the input, and integrals of the input and output. 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.
Using root locus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Design via root locus elec304alper erdogan 1 33 lag lead compensation. Using root locus approach the procedure for designing the lag compensator using root locus approach is briefly discussed here 1. Design via root locus intro lead compensator pid controllers design introduction readings. Webb ese 499 3 introduction consider the following unityfeedback system assume. A lag compensator in root locus form is given by the following. Bode design slide 20 lead compensation the lead compensator can be used to change. There are practical limits as to how large the gain can be made. For both compensators can be implemented with the following transfer function.
The technology used for the implementation is different in each case, but the underlying principles are the same. The bode plot indicates that the gain margin of the plant would be unaffected if a lead compensator is used but the phase margin would be improved. Nichols chart, and b a plot of the closedloop free. Lead compensators design using frequency response techniques. A number of matlab function are developed for the compensator design method. 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 response transient steady state frequency response bode plot stability routhhurwitz nyquist. A phaselag compensator tends to shift the root locus to the right, which is undesirable. A firstorder lag compensator can be designed using the root locus. In order to use the root locus method to design the lead compensator the root locus of the feedforward path of the the system has to be drawn same goes if we want to use the bode plot for the design process. Compensator design for speed control of dc motor by root.
Lead or lag compensation the transfer function is where 57 58. Figure 1 shows the uncompensated and lead compensated root locus plots and closedloop step responses. The typical bode plot of a lead compensator is as shown below for an example compensator of. 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. The frequency response of the control system or the root locus plot are traditionally used to tune the compensator in a lengthy procedure. At the end, root locus design will not prove to be the best technique. Then design the lag compensator to meet the sse specifications.
They have 4 parameters to be adjusted tuned for proper operation. The conversions page explains how to convert a statespace model into transfer function form. Use matlab or any other computer program to simulate the system to check your design. Design three lead compensators for the system to reduce. Two common types of compensators are lead and lag compensators. This paper introduce the lead, lag, lag lead compensator design of root locus using single composite matlab programme. The plot on the left is the standard root locus plot, while the plot on the right is a 3d version incorporating the control gain, as the zaxis. Both the compensators introduce a pole and a zero the system. D6 frequency response approach to compensator design information about the performance of the closedloop system, obtained from the openloop frequency response. School of electrical engineering and computer science. Design of a lead compensator with root locus in matlab. Series compensation design using the root locus application. Rcs gc cs gp s ccs controllers in the feedforward path are called cascade compensator and pid controllers and its variants are one type. Design of laglead compensator using root locus method s.
Design g cs using root locus or frequency response techniques. Section 64 treats a special case when the closedloop system has positive feedback. Section 63 discusses generating root locus plots with matlab. Design with root locus lecture 9 a free powerpoint ppt presentation displayed as a flash slide show on id. Setiawan 2010 presented the evaluation of closedloop controller responses of a tini sma gripper using lag, lead and lag lead compensators. Lead, lag, and lead lag compensators are usually designed for a system in transfer function form. In this particular system the feedforward path includes only the transer function. A lead lag compensator consists of a lead compensator cascaded with a lag compensator.
The dominant closedloop poles on the root locus plot. We can attempt to reduce the oscillation by using a lead or a lag compensator, which i. Example 61 consider the negative feedback system shown in figure 63. In this section we introduce their structures and indicate their main properties. Ppt design with root locus powerpoint presentation free. Example ziegler nichols pid tuning using root locus the ziegler nichols technique can be used on actual industrial processes, but also allows design using the root locus. Pdf lead and lag compensators with complex poles and. The use of simple lag compensation one pole at 1, no zero to alter the. Lead design using the root locus the design of the phase lead compensation network can also be readily accom plished using the root locus. The rootlocus plot of the uncompensated system reveals that it is not possible to. Step 5 plot the root locus of the compensated system dg dtf1 z,1 p. Sketch the root locus with respect to k for the equation. Pdf lead and lag compensators with complex poles and zeros.
Root locus plots can provide a great deal of information about a. Using a p compensator results in the loop gain k phs. Determine the desired pole location based on speci. In particular, since the phase of a negative real number is 180 degrees or. Lead and lag root locus design application center maplesoft. Section 65 presents general aspects of the root locus approach to the. The bode plot for a lead compensator looks like this the frequency of the phase increase can be designed to meet a particular phase margin requirement the high frequency magnitude is now limited dr. Mark the relevant stability margins on these graphs by choosing characteristics all stability margins. In the previous lectures we laid the groundwork for design techniques based on root locus analysis.
A highly oscillating secondorder process has a time response to a unit step input of 85. Lag lead compensators are well known in automatic control engineering. 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. Use matlab to verify your answer by plotting the roots of the polynomial in the s plane. A firstorder lag compensator cs can be designed using the root locus. A comparative analysis of pid, lead, lag, leadlag, and. Design of lag lead compensator using root locus method s. If root locus does not pass the desired location, then reshape the root locus by adding poleszeros to by adding poleszeros to c. Firstly by drawing the root locus plot for the uncompensated system based on the transientresponse specifications. Root locus design the root locus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. A phase lead compensator tends to shift the root locus toward the left half plane.
Design of control systems cascade root locus design this is the first lecture devoted to the control system design. Pdf cl7101 control system design question bank ayyar. Designing lead and lag compensators simon fraser university. The polezero plot for the complex lead compensator of figure 3.
If root locus does not pass the desired location, then reshape the root locus by adding poleszeros to cscs. Design via root locus elec304alper erdogan 1 1 lecture. Rootlocus design mcgrawhill education access engineering. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of lead lag compensator with complex. We include a variable gain k in a unityfeedback con. Pdf this paper introduce the lead, lag, lag lead compensator design of root locus using. Closedloop design by root locus place closedloop poles at desired location by tuning the gain csk. A contribution of a lead compensator is that it moves the closed loop poles. This transfer function was used to analyze the performance of the system and to design proper controllers lag compensator and pid to meet the design criteria.
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