This video walks through a phase lead compensator example using the bode plot method. May 22, 20 designing a lead compensator with bode plot brian douglas. Compensator design for a set of plant models matlab. The procedure for designing the lag lead compensator is presented in section ii. Pdf design of a leadlag compensator for position loop. A firstorder lead compensator cs can be designed using the root locus. Thus we can say in the lead compensator zero is more dominating than the pole and because of this lead network introduces positive phase angle to the system when connected in series. Setiawan 2010 presented the evaluation of closedloop controller responses of a tini sma gripper using lag, lead and lag lead compensators.
Depending on the effect desired, one or more lead and lag compensators may be used in various combinations. Design of phase lead and phase lag compensator for pitch. To see which one, consider the 5thorder system from our previous lecture. Phase lag compensator design using bode plots andphase lead compensator design using bode plots, theses notes will concentrate on the use of those two designs together. Using matlab sisotool 2016 part 1 university of sheffield. The root locus editor displays the root locus for the nominal model and the closedloop pole locations associated with the set of plants. Achieve your design goals by manually editing compensator poles, zeros. The procedure for designing the laglead compensator is presented in section ii. In this page, you will learn how to design digital lead and lag compensators using the rootlocus design method. Lead example the process is slightly simpler if we target the lead compensator design at a particular desired. Execute time response analysis of a second order control system using matlab 2. May 25, 2012 form the complete transfer function with the lead compensator added in series to the original system. To open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. From given specifications determine the damping ratio and the natural frequency find the dominant pole.
Pdf computer aided design of lead compensator using root. The syntax for the function in transfer function and in system formats are. Design compensator using automated pid tuning and graphical bode design. Introduction to matlab lag compensator with bode plot lag compensator with root locus so far we have seen the design of lag compensators, now we move on to lead compensators which help in improving the transient response. Designing a lead compensator with bode plot brian douglas. Nichols plot design is an interactive graphical method of modifying a compensator to achieve a specific openloop response loop shaping. Start with the design of the lead compensator neglect the lag compensator part for now lead compensator ch.
Lead compensators design using frequency response techniques. 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. It is more usual to use a proportionalintegral or pi compensator, as discussed in. Control system design by frequency response using matlab. Validate your compensator design by simulating the nonlinear simulink model with the tuned controller parameters. A lead compensator in root locus form is given by 1 where the magnitude of z0 is less than the magnitude of p0. Designing digital lead and lag compensators using the. 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. A number of matlab function are developed for the compensator design method.
The examples and plots presented in this paper are all done in matlab, and the various measurements that are presented in the examples are obtained from the. If you have learned the basics then please move on to the next post. Analyze and interpret stability of the system through root locus, bode plot and nyquist plot. If no output argument is specified, a plot of the response is made. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. A phaselead compensator tends to shift the root locus toward to the left in the complex splane. Equation12 10 8 6 4 2 0 2 415105 0 5 10 15 i m a g a x i s real axis j2 j2bca draw the root locus. Analysis of phase lead compensator design for laser. A phase lead compensator tends to shift the root locus toward to the left in the complex splane. G cs g c0 s 5 although the plain integral compensator could be used for this purpose, it is di cult to obtain good performance using this type of compensator. The reader is referred to those notes for details on the individual design procedures. We include a variable gain k in a unityfeedback con.
Design of a lead compensator with root locus in matlab. We calculate the required phase to be added using the lead compensator. Oct 23, 2019 clearly we have 1t which is a zero of the transfer function is closer to origin than the 1. Compensation in control system lag lead compensation. 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. This paper introduce the lead,lag,lag lead compensator design of root locus using single composite matlab programme. A bode plot of a phaselead compensator cs has the following form. Unlike bode diagram design, nichols plot design uses nichols plots to view the openloop frequency response. Compensator editor to open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. Finally, the result of phase lead and phase led compensator is presented by using matlab gui. To analyze the controller design, create a closedloop transfer function of the system, and plot its step response. It simply produces a design that meets the design speci cations.
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. He discussed the tuning of the used compensators 12. It can be observed that as increases, the steady state errors decrease assuming systems asymptotic stability, but the maximum percent overshoot increases. Dec 05, 2017 lead compensator design using bode plot enggs tech. Plot the closed loop system performance using the feedback and step function. In this lecture we would revisit the continuous time design techniques using frequency domain since these can be directly applied to design for digital control system by transferring the loop transfer function in z plane to wplane. Design via root locus elec304alper erdogan 1 1 lecture 1. It can be very challenging to reguate such a system.
The steps to design the lead compensator are with root locus are. Bode diagram design is an interactive graphical method of modifying a compensator to achieve a specific openloop response loop shaping. Pdf this paper introduce the lead,lag,laglead compensator design of root locus using single. Design of a leadlag compensator for position loop control of a gimballed payload. Phase lag compensator design using bode plotsandphase lead compensator design using bode plots, theses notes will concentrate on the use of those two designs together. Lecture 19 compensator design using bode plot, control systems. Design example 1 design a lead compensator for the digital control system below so that the pm is 50, the gm is at least 10 db. Using matlab to generate a bode plot for the closedloop system for gs 2.
Designing a lead compensator with bode plot youtube. Lead mechanics ii adding a lead to the ltf changes both the magnitude and phase, so it is di. In this particular system the feedforward path includes only the transer function. Setiawan 2010 presented the evaluation of closedloop controller responses of a tini sma gripper using lag, lead and laglead compensators. To interactively shape the openloop response using control system designer, use the bode editor. In the editor, you can adjust the openloop bandwidth and design to gain and phase margin specifications. The app opens with bode and root locus openloop editors open along with a step response plot. Design via root locus elec304alper erdogan 1 33 laglead compensation. 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. Like pi compensation, lag compensation uses a closely. Phase lead compensator design using bode plots the gmu ece.
To tune the parameters of your compensator directly, use the compensator editor. It should be noted that this design method does not produce an optimal compensator design. Create a transfer function in matlab for your model of the xaxis. Design lag, lead, leadlag compensators and verify experimental results using matlab. We will start from the frequency domain design using bode plot. In the editor, you can adjust the openloop bandwidth and design to gain and phase. Design a lead compensator using bode plot sketches so that kv 20sec. Using matlab sisotool 2016 part 4 resources in control education. Using the expressions given on the bode plot, the value of g. Lead compensator example draw bode plot of l1s using approximated bode plot pm is found to be 17o.
An introduction to compensator design with matlab geek peek. To cope with uncertainties in our model, we can design for stability. Make a bode plot of kghjw, including logmagnitude and phase plots. Design of lead compensator using bode plots duration. Design via root locus elec304alper erdogan 1 1 lecture.
Lecture 19 compensator design using bode plot electrical. In the compensator editor dialog box, on the parameter tab, tune the pid. The proposed phase lead and phase lag compensator design can be used for any system that the mathematical model have been known to meet desired specifications. He purpose of phase lead compensator design in the frequency domain generally is to satisfy specifications. Evaluate the steady state performance of the lead compensated system to. Focus is on students doing a single course in classical control methods such as bode, nyquist, gain and phase margins and lead and lag design.
This paper introduce the lead,lag,laglead compensator design of root locus using single composite matlab programme. By default, the nominal model used for design is the first element in the lti array. 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. Design of lead compensator for process control using. The root locus editor displays the root locus for the nominal model and the closedloop pole locations associated with the set of. Lec41 compensator design using frequency response plots duration. Sometimes, proportional control with a carefully chosen value of k is.
Analyze toque speed characteristics of dc and ac servomotors. 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. The lead compensator achieves the desired results through the merits of its phaselead contribution. The last compensator discussed will be the combination of the lead and proportionalintegral compensators to obtain the bene ts of both. Design compensator using automated pid tuning and graphical. Note the attenuation by 1 this accounted for by increasing the forward gain k by a factor of the compensators. A lead compensator increases the bandwidthspeed of response good if you want the system to react fast a lag compensator decreases the bandwidthspeed of response good if your model is bad at high frequencies good to reduce the impact of mostly highfrequency noise. Determine the desired pole location based on speci. Introduction to root locus semester 083 page 4 root locus the root locus of an openloop transfer function hs is a plot of the locations locus of all. Lead compensator design take 1 to design a lead compensator, the first trick is to determine which pole to cancel.
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