Root locus design pdf

A graphical representation of closed loop poles as a system parameter varied. Tuesday, april 06, 1999 root locus design examples here we give a few design examples of the root locus technique. 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. Each plot starts at a location equal to the location of a root of the plant transfer function. Root locus design the root locus can be used to determine the value of the loop gain, which results in a satisfactory closedloop behavior. Based on rootlocus graph we can choose the parameter for stability and the desired transient response. Bwr pressure control hard control problems a brief introduction the root locus design method is an iterative, graphical procedure for selecting and tuning compensators. Bwr pressure control hard control problems a brief introduction the root locus design method is an iterative, graphical procedure for. In the root locus design approach presented here, these two tasks are approached separately. To predict a systems performance by an analysis that does not require the actual solution of the differential equations.

The purpose of compensator design generally is to satisfy both transient and steadystate speci. Root locus 2 root locus observations because we have a 3rdorder system, there are 3 separate plots on the root locus, one for each root. Tries to differentiate a step input into an impulse not likely. Pid and root locus pid control design yvery common and classical control technique ygood tools for choosing gains root locus yshow closed loop poles as function of a free parameter. Section 5 root locus analysis college of engineering. The root locus is the locus of the roots of the characteristic equation by varying system. This is because complex roots occur in conjugate pairs. A proportional controller design for 8% overshoot use root locus to determine. It is an approach to select the gain as to achieve desired transient behavior. Root locus elec304alper erdogan 1 1 lecture 1 root locus what is rootlocus. Sometimes, proportional control with a carefully chosen value of k is. Consequently, the root locus plot will be symmetric about the real axis rule 2. Root locus design oklahoma state universitystillwater.

We include a variable gain k in a unityfeedback con. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Rlocus analysis design nyu tandon school of engineering. Using rootlocus ideas to design controller we have seen how to draw a root locus for given plant dynamics. Design via root locus elec304alper erdogan 1 1 lecture. To know if the system is absolutely stable and the degree of stability. The breakaway point is midway between the two openloop poles at z b 0. Sunday, march 28, 1999 root locus design feedback control design techniques include statevariable feedback, outputfeedback, root locus, bode design, nyquist design, polynomial design, and other techniques.

The root locus method typically focuses on the gain parameter. The root locus is obviously a very powerful technique for design and analysis of control systems, but it must be used with some care, and results obtained with it should always be checked. Using root locus rules gives the root locus plot in figure 6. Apr, 2014 a walk through of a typical homework problem using the root locus method to tune a pid controller. A walk through of a typical homework problem using the root locus method to tune a pid controller. The root locus plot indicates how the closed loop poles of a system vary with a system parameter typically a gain, k. Controls design techniques can be basically divided into statespace techniques vs. In this tutorial, we will introduce the root locus, show how to create it using matlab, and demonstrate how to design feedback controllers that satisfy certain performance criteria through the use of the root locus. Webb ese 499 3 introduction consider the following unityfeedback system assume. For free materials of different engineering subjects use my android application named engineeri. The poles on the root locus plot are denoted by x and the zeros are denoted by o. In the limit as k infinity, the poles of the closedloop system are bs 0 or the zeros of hs. Youll have to consider how your differentiator will actually handle a step input and how your amplifier will saturate.

The critical gain now occurs at the intersection of the root locus with the unit circle. Root locus design drexel university information technology. First design the minor loop then design the major loop. For free materials of different engineering subjects use my android application named engineering funda with following link. The minor loop is designed to change the open loop poles and open loop transientresponse. Root locus example 1 in control engineering by engineering. In this technique, we will use an open loop transfer function to know the stability of the closed loop control system. There are practical limits as to how large the gain can be made. The shape of the locus can also give us information on design of a more complex leadlag, pid controller though. After studying these materials, you should be able to create a root locus and use the locus to understand the closedloop system behavior given an openloop system and a feedback controller. Example the root loci start at the poles and at the zeros. Hence, we can identify the nature of the control system. Damping ratio and pole location recall 2ndorder underdamped sustem.

The root locus rules of behavior provides insight for adjusting additional compensator parameters. Consider compensation as adding poles and zeros to feedback section for the equivalent system. The root locus is a powerful technique as it brings into focus the complete dynamic response of the system and further, being a graphical technique, an approximate root locus can be made quickly and designer can be easily visualize the effect of varies system. Locus segments now, determine if point 6is on the root locus again angles from complex poles cancel always true for real. Pdf root locus design using matlab matlabassignment. They are known as pd, pi, pid, phaselag,phaselead,and phaselagleadcontrollers.

In this section we introduce their structures and indicate their main properties. This is the first in what may be a series of homework style problems ill cover. 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. Root locus elec304alper erdogan 1 7 real axis segments which parts of real line will be a part of root locus.

Root locus design imag axes real axis waterbed reduced sensitivity. The root locus structure also yields ideas for adding elements to the compensator. In the root locus diagram, we can observe the path of the closed loop poles. It can be drawn by varying the parameter generally gain of the system but there are also other parameters that can be varied from zero to infinity. To show potential pitfalls of this method, consider the two systems g1s and g2s. Design via root locus elec304alper erdogan 1 1 lecture 1. No matter what we pick k to be, the closedloop system must always have n poles, where n is the. Lecture abstract ee c128 me c4 feedback control systems. Oct 18, 2017 in this session, i have explained example of root locus plot. In this session, i have explained example of root locus plot. The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. We can choose a value of s on this locus that will give us good results.