Design of lag compensator for process control using. These parameters would yield a fast, adequately damped transient performance of the closed loop servo. Ece 382 fall 2018 lead compensator design using root locus. Designing a pid controller using the root locus method duration. The stability of a process model is determined by its phase margin and gain margin. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Designing digital lead and lag compensators using the. Design of control systems cascade root locus design this is the first lecture devoted to the control system design. The minor loop is designed to change the open loop poles and open loop transientresponse. Introduction the purpose of compensator design using root locus methods generally is to establish a speci.
Lec30 compensator design using root locus plots duration. Design by rootlocus method the rootlocus approach to design is very powerful when the specifications are given in terms of timedomain quantities, such as the damping ratio and undamped natural frequency of the desired dominant closedloop poles, maximum overshoot, rise time, and settling time. For the robust design of a closed loop system, it is required to keep these margins to be greater than zero. It should be noted that this design method does not produce an optimal compensator design. Execute time response analysis of a second order control system using matlab 2. Pdf this paper introduce the lead,lag,laglead compensator design of. Modern control lec 04 analysis and design of control. Using the root locus for the uncompensated system, the intersection of the locus and the 20% overshoot line gives the operating point, 1. It can be observed that as increases, the steady state errors decrease assuming systems asymptotic stability, but the maximum percent overshoot increases. Pdf root locus design using matlab matlabassignment. In the previous lectures we laid the groundwork for design techniques based on root locus analysis. 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 and zero. Determine the location of the zero of the pd compensator. Root locus for integral compensation ndsu pid compensation ece 461 jsg 2 rev june 9, 2016.
Design g cs using root locus or frequency response techniques. By default, control system designer displays these responses when it opens. The steps to design the lead compensator are with root locus are. Analyze and interpret stability of the system through root locus, bode plot and nyquist plot. Series compensation design using the root locus application. Leadlag compensator using root locus 504 chapter 9 1. In this handout we introduce the idea the root locus which as a graphical. At the end, root locus design will not prove to be the best technique.
Pdf computer aided design of lead compensator using root. Design lead compensator to meet the transient response specifications. Introduce a lead compensator characteristic equation with the lead is and, at phase cond. The method cannot change the root locus and locate poles desired locations if they are outside the existing root locus. Zeros to the left of the locus pull it to the left.
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. From given specifications determine the damping ratio and the natural frequency. We include a variable gain k in a unityfeedback con. The laglead compensator circuit in the s domain is shown in the following figure.
Design of control systems cascade root locus control theory. This example shows how to design a compensator for an electrohydraulic. Webb ese 499 3 introduction consider the following unityfeedback system assume. For this example, graphically tune your compensator using the root locus editor and openloop bode editor, and validate the design using the closedloop step response. To achieve the required parameters of and, the root locus needs to be moved to the left along the real axis, so that the dominant poles can be at a radius of 30 from the origin and make an angle of 56. By default, the nominal model used for design is the first element in the lti array. 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. Using root locus ideas to design controller we have seen how to draw a root locus for given plant dynamics. You can use the rldesigngui to design the controllers for the remaining examples. The app opens with bode and root locus openloop editors open along with a step response plot. 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. Introduction design via root locus activecircuit realization in. In the root locus design approach presented here, these two tasks are approached separately. Discrete transfer function rootlocus in zplane compensation using a digital controller.
A lead compensator design example is worked based on improving transient time domain specifications. Getting started with the control system designer matlab. Design and analysis of a control system using root locus and frequency response methods. It is a combination of both the lag and the lead compensators. In this post we will deal with lag compensator design with time domain specifications and using the root locus technique. A proportional controller design for 8% overshoot use root locus to determine. 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. Consider compensation as adding poles and zeros to feedback section for the equivalent system. Lag compensator design using root locus eecs 460 lecture 27 necmiye ozay control design based on root locus g. Determine the location of the pole and zero of the lead compensator using, for example, the bisector method. D6 frequency response approach to compensator design information about the performance of the closedloop system, obtained from the openloop frequency response.
The purpose of compensator design generally is to satisfy both transient and steadystate speci. In this digital control version of the cruise control problem, we are going to use the rootlocus design method to design the digital controller. Tune electrohydraulic servomechanism using root locus graphical tuning. Problem of root locus design root locus design can locate poles only on the root locus. Designing a rootlocus compensator to attain design requirements. Oct 22, 2010 lec30 compensator design using root locus plots. Design lag, lead, leadlag compensators and verify experimental results using matlab. Lead, lag and leadlag compensators are used to ensure that the stability margins are at the desired levels. Cascade root locus design this is the first lecture devoted to the control system design. Design of lead compensator for process control using. In the limit as k infinity, the poles of the closedloop system are bs 0 or the zeros of hs. It simply produces a design that meets the design speci cations.
Well learn how to use rootlocus techniques to design compensators to do the following. May 07, 20 this video walks through a phase lead compensator example using the root locus method. In the frequency domain approach, the stability of the system is measured using its stability margins namely the phase margin p. Compensator design for a set of plant models matlab. From the examples we have seen so far, we can see that often is a point on the real axis at. State space root locus sketching rules negative feedback rule 1. Lec30 compensator design using root locus plots youtube. You can also store, compare, and export different control system designs. May 25, 2012 the steps to design the lead compensator are with root locus are. Then design the lag compensator to meet the sse specifications. In the limit as k 0, the poles of the closedloop system are as 0 or the poles of hs. The root locus indicates the possible location of the closed loop poles of a system as a parameter usually the gain k varies from small to large values. 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.
Ece 382 fall 2018 pd compensator design using root locus. Rlocus analysis design nyu tandon school of engineering. Design and analysis of a control system using root locus. These techniques are classified using the generic term classical control techniques. Analyze toque speed characteristics of dc and ac servomotors.
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. Sometimes, proportional control with a carefully chosen value of k is. From given specifications determine the damping ratio and the natural frequency find the dominant pole. Root locus sketching rules negative feedback rule 1. Design via root locus elec304alper erdogan 1 1 lecture. No matter what we pick k to be, the closedloop system must always have n poles, where n is the.
Evaluate performance of uncompensated system to determine how much improvement in transient response is required. Designing a lead compensator with root locus youtube. The root locus editor displays the root locus for the nominal model and the closedloop pole locations associated with the set of plants. Apr 29, 2017 design by root locus method the root locus approach to design is very powerful when the specifications are given in terms of timedomain quantities, such as the damping ratio and undamped natural frequency of the desired dominant closedloop poles, maximum overshoot, rise time, and settling time. The rootlocus can be used to determine the value of the loop gain, which. From given specifications determine the damping ratio. The design includes the zero location, pole location, and loop gain. Ppt design with root locus powerpoint presentation.
First design the minor loop then design the major loop. On the control system tab, you can select a compensator tuning method, and create response plots for analyzing your controller performance. 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. 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.
Designing a lag compensator with root locus duration. 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. Overshoot %os vsmaller compensator design achieving a desired transient with a given rl 2. Draw the root locus of the given open loop uncompensated system with k1.
In the previous lectures we laid the groundwork for design techniques based on root locus. In this chapter, let us discuss how to construct draw the root locus. A firstorder lag compensator cs can be designed using the root locus. A comparative analysis of pid, lead, lag, leadlag, and. Generic compensators cs are used in such situations in order to change the existing root locus. Because the open loop poles and zeros exist in the sdomain having the values either as real or as complex conjugate pairs. Now lets design a controller using the root locus method. Compensator design to improve transient performance using. Design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. May 23, 2012 in this post we will deal with lag compensator design with time domain specifications and using the root locus technique.
The root locus is a graphical representation in sdomain and it is symmetrical about the real axis. Laglead compensator is an electrical network which produces phase lag at one frequency region and phase lead at other frequency region. A lag compensator in root locus form is given by the following. This circuit looks like both the compensators are cascaded.