Be familiar with the design of lead and lag compensators using root locus and bode p. We include a variable gain k in a unityfeedback con. The root locus gives information about the stability and transient response of feedback control systems. Lag compensators reduce the gain crossover frequency of the system. A comparative analysis of pid, lead, lag, leadlag, and. The root locus of an openloop transfer function hs is a plot of the locations locus of all possible closed loop poles with proportional gain k and unity feedback. A lag compensator in root locus form is given by the following. Pdf tuning of a laglead compensator used with a first. Pdf computer aided design of lead compensator using root. The first part is the design of a phase lead compensator using the bode analysis in the frequency domain. May 23, 2012 if no output argument is specified, a plot of the response is made. This is called the proportional compensator or proportional controller and provides gradual response to deviations from the set point.
The point s s 1 shown in the root locus plots is the desired closedloop pole location s 1. Lead compensation techniques based on the root locus approach and design. Root locus techniques root locus is a graphical presentation of the closedloop poles as a system parameter k is varied. If root locus does not pass the desired location, then reshape the root locus by adding poleszeros to cscs. View notes 12 lead compensator design root locus from ece 382 at purdue university. D6 frequency response approach to compensator design information about the performance of the closedloop system, obtained from the openloop frequency response. In this lab you will explore the use of the root locus controller design methodology. Designing lead and lag compensators simon fraser university. Design of laglead compensator using root locus method.
Can be implemented using passive components simple rlc circuit as an alternative to the. Design via root locus elec304alper erdogan 1 1 lecture 1. Sometimes, proportional control with a carefully chosen value of k is. Design g cs using root locus or frequency response techniques. A number of matlab function are developed for the compensator design. A phase lead compensator tends to shift the root locus toward the left half plane. Designing lead and laglead compensators with bode plots. Lead compensation techniques based on the rootlocus. The plot on the left is the standard root locus plot. The dominant closedloop poles on the root locus plot are located. Zanasi, cuoghi and ntogramatzidis 2011 presented the dynamic structure of a new form of lead lag compensator with complex. Root locus plots of negativefeedback and positive feedback systems. The syntax for the function in transfer function and in system formats are.
The time constant \t\ of the lag compensator should not be unnecessarily large. Lead design using the root locus the design of the phase lead compensation network can also be readily accom plished using the root locus. Setiawan 2010 presented the evaluation of closedloop controller responses of a tini sma gripper using lag, lead and lag lead compensators. 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. A systematical procedure for lead compensator design max max max. Design via root locus elec304alper erdogan 1 1 lecture. Section 63 discusses generating root locus plots with matlab. Can be implemented using passive components simple. Abstract this paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. Webb mae 4421 3 introduction consider the following unity.
Mark the relevant stability margins on these graphs by choosing characteristics all stability margins. They are known as pd, pi, pid, phase lag,phase lead,and phase lag leadcontrollers. If you have learned the basics then please move on to the next post. 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. The following steps outline the procedure that will be used to design the special lag compensator using root locus methods in. Closedloop design by root locus place closedloop poles at desired location by tuning the gain csk.
Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. The root locus indicates the achievable closedloop pole locations of a system as a parameter usually the controller gain varies from zero to infinity. The design process of phase lead, lag, lead lag, and cascaded lead controllers is performed by applying the principles of the root locus technique 2628, using matlab sisotool 2931. Then design the lag compensator to meet the sse specifications. Section 6 root locus design college of engineering. Hence, the high frequency noise attenuation becomes better. 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. Section 65 presents general aspects of the root locus approach to the. Sep 09, 2019 in both cases the compensator will change the open loop poles and zeros, which creates a new root locus that goes through the desired closed loop pole locations which you are designing for. By using this method, the designer can predict the effects on. A proportional controller design for 8% overshoot use root locus to determine.
This paper introduce the lead, lag, lag lead compensator design of root locus using single composite matlab programme. Lead compensator example draw bode plot of l1s using approximated bode plot pm is found to be 17o. Madan gopal, department of electrical engineering, iit delhi. A number of matlab function are developed for the compensator design method. Pdf lead and lag compensators with complex poles and zeros. The graph of all possible roots of this equation k is the variable parameter is called the root locus. Lec30 compensator design using root locus plots youtube. In this section we introduce their structures and indicate their main properties. State space root locus sketching rules negative feedback rule 1. Root locus lead compensator design example polezero. Figure 1 shows the uncompensated and lead compensated root locus plots and closedloop step responses.
For both compensators can be implemented with the following transfer function. A contribution of a lead compensator is that it moves the closed loop poles. School of electrical engineering and computer science. 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. Phaselead and phaselag compensator by bode and root locus. 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.
The positive root locus is the set of all points s in the complex plane for. The point s s1 shown in the root locus plots is the desired closedloop pole location s1. Phase lead compensator design using bode plots, a slightly di. Determine the desired pole location based on speci. Pdf control of dc motor using different control strategies. 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. In particular, since the phase of a negative real number is 180 degrees or.
Plot the bode, nyquist and root locus plots for your open loop system, csgs. In practice the rootlocus plot of a system may indicate that the desired performance cannot be achieved. The lag lead compensator can meet multiple design requirements. The polezero plot for the complex lead compensator of figure 3. Root locus design the root locus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. Lag compensators reduce the high frequency gain of the system. A lead compensator design example is worked based on improving transient time domain specifications. A firstorder lead compensator can be designed using the root locus. The graph of all possible roots of this equation k is the variable parameter is called the root. For a given plant it may or may not be possible to. Draw the root locus of the given open loop uncompensated system with k1. The simulation study is based on the model developed by myers et al.
Lag example step 1 design a lag compensator for the above system to satisfy the following requirements a. A firstorder lag compensator can be designed using the root locus. Now, let us add the controller to the plant and view. Compensator design to improve transient performance using. They used 2 design strategies for a double integrator and a second order system with a very lightly damped resonance. In this post we will deal with lag compensator design with time domain specifications and using the root locus technique. Section 64 treats a special case when the closedloop system has positive feedback. Webb ese 499 3 introduction consider the following unityfeedback system assume. Plot the closed loop system performance using the feedback and step function in matlab. An introduction to compensator design with matlab geek peek. Evaluate the steady state performance of the lead compensated system to.
Bode design slide 20 lead compensation the lead compensator can be used to change. 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. 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. There are practical limits as to how large the gain can be made. Design of lag lead compensator using root locus method s. A phase lag compensator tends to shift the root locus to the right, which is undesirable. This is different from pure gain because we are actually adding poles and zeros to the system, not just moving along the root locus created by the open. He discussed the tuning of the used compensators 12. The second part is the design of a phase lead compensator, and a phase lag compensator in series with the first phase lead compensator using two different approaches of root locus. 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. 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 satisfy transient performance speci. Using root locus approach the procedure for designing the lag compensator using root locus approach is briefly discussed here 1.
May 23, 2012 so far we have discussed on an introduction to matlab and lag compensator design with bode plot. Design via root locus elec304alper erdogan 1 33 lag lead compensation. A firstorder lag compensator cs can be designed using the root locus. In 2 and 4, good descrbtion of the optimat control design, including llinear state regulator control, the output regulator control and linear quadratic trackerthe matlab siso design tool 1 can be used to design compensators by root locus, bode diagram, and nichols plot design techniques, and to analyze the resulting designs. The lag lead compensator is the analog to the pid controller. The root locus plot is a plot of the roots of the characteristic. Firstly by drawing the root locus plot for the uncompensated system based on the transientresponse specifications. Phase lead and phase lag compensator by bode and root locus.
A first order lead compensator tends to shift the root locus into the lefthand plane. In this page, you will learn how to design digital lead and lag compensators using the root locus design method. Design a lead lag compensator hs for this system as indicated in figure 2, to achieve the following design requirements for the closed loop. Compensator design using the root locus each part specifies what to submit in your hw. Lead compensators design using frequency response techniques. Using root locus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Using a p compensator results in the loop gain k phs. Based on the transientresponse specifications, locate the dominant closedloop poles on the root locus. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci.
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