Design and analysis of a control system using root locus and. Root locus elec304alper erdogan 1 1 lecture 1 root locus. Root loci are used to study the effects of varying feedback gains on closedloop pole locations. Root locus technique in control system electrical4u. Root locus means closed loop poles path by varying. Searching the real axis segments of the root locus yields higherorder poles at greater than 150 and at 1. Design constraints then either new to add new constraints or edit to edit existing constraints. Calculate the value of at which the locus crosses the imaginary axis, and find the. Save the step response, the root locus zoom in near the origin so you can see something, and the values of, and that produced the step response for your memo. In this handout we introduce the idea the root locus which as a graphical. Root loci inspection 8 points for each of the root loci shown below, tell whether or not the sketch can be a root locus. In my approach to root locus design, the purpose of compensator design using root locus methods generally is to establish a speci. Pdf the introduction to root locus method find, read and cite all the research you need on researchgate. We exploit the properties of rootlocus to do a rough sketch.
Root locus elec304alper erdogan 1 4 drawing the root locus how do we draw root locus for more complex systems, and without calculating poles. In turn, these locations provide indirect information on the time and. You can use the rldesigngui to design the controllers for the remaining examples. Consider an openloop system which has a transfer function of 4 how do we design a feedback controller for the system using the root locus method.
A comparison and evaluation of common pid tuning methods. Please print out this page and attach it with your solutions to other problems. By examining the root locus, we see that as the gain increases, the closedloop complex poles approach the zeros, while the other root stays real and moves to the left. Root locus plot for determining k corresponding to 0. Find the gain k so that the system responds with an overshoot of less than 1 percent and a settling time as fast as possible. Lets assume our design criteria are 5% overshoot and 1 second rise time. The matlab commands to nd and k are shown in the transcript below. Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear. Now, we choose a kfor which the root locus will cross into the desired region. For this example, an easier design canceling the pole at 3 may be superior. The rootlocus can be used to determine the value of the loop gain, which results in a. The root locus gives the closedloop pole trajectories as a function of the feedback gain k assuming negative feedback. The steadystate value is when t tends to infinity and thus yss k. The overshoot is often written as a percentage of the steadystate value.
Now we wish to select a gain that has a low overshoot but that produces a fast response. Locus controller design using the matlab sisotool toolbox. Therefore, lets explore the properties of root locus. Pdf the purpose of this project was to control the angular rate of the load shaft position of a dc motor by varying the applied input voltage. Ece382me482 spring 2004 homework 8 solution april 27, 2004 2.
Percentage overshoot an overview sciencedirect topics. Root locus for controller design in this lab you will explore the use of the root locus technique in designing controllers. Unfortunately, on the current root locus at the specified percent overshoot, we only can obtain the settling time represented by point a after a simple gain adjustment. Root locus is always to the left of an odd number of poles or zeros on the. Assume that the desired transient response, defined by percent overshoot and settling time, is represented by point b.
The system could be presented in state space form so we enter the system in state space form if we wont to draw the root locus for multi systems in the same graph write rlocussys1,sys2. Introduction the plant model represents a linearization of the heading dynamics of a 250,000 ton tanker ship under empty load conditions. The pole locations for this gain will be shown as small squares on the root locus plot, as shown in figure 3. Design via root locus elec304alper erdogan 1 25 lead compensation. Adding our settling time and percent overshoot requirements to the root locus plot produces the following figure. Design and analysis of a control system using root locus. In the discretetime case, the constraint is a curved line. Unfortunately,onthecurrentroot locus at the specified percent overshoot, we only can obtain the settling time. Use the root locus diagram of a to select a k that should satisfy the settling time requirement. Each plot starts at a location equal to the location of a root of the plant transfer function. 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. 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. It seems that values of kbetween about 20 and 35 can work for this setup.
Starting at a value of k 0 calculate the locations of the poles of hs and repeat for. The overshoot is the maximum amount by which the response overshoots the steadystate value and is thus the amplitude of the first peak. Introduction to root locus islamic university of gaza. Example design three lead compensators for the system to reduce the settling factor by a factor of 2 while maintaining %30 overshoot for the system solution. Root locus is always symmetric about the real axis. Root locus design oklahoma state universitystillwater.
Secondorder approximation is not valid because of the two zeros and no polezero cancellation. Root locus sketching the poles of the openloop transfer function gsks are given by. All response characteristics obtained from data, not analytical expressions. 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. For the following secondorder response specs, nd the corresponding pole locations. Massachusetts institute of technology department of. Now in order to determine the stability of the system using the root locus technique we find the range of values of k for which the complete performance of the system will be satisfactory and the operation is stable. How to enter a system transfer function or state space to labview. It can be observed that as increases, the steady state errors decrease assuming systems asymptotic stability, but the maximum percent overshoot increases. Design via root locus elec304alper erdogan 1 1 lecture 1. The step response that is shown will be for the default gain value of k. Pdf introduction to root locus method researchgate. 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.
A plot of the possible closedloop pole locations as some parameter varies from 0 to 1. Design and analysis of a control system using root locus and frequency response methods article pdf available august 2017 with 2,042 reads how we measure reads. The response should be simulated since there may not be polezero cancellation. Sketching root loci 6 points sketch the general shape of the root locus for each of the openloop polezero plots shown below. The reference input signal rs is the desired heading angle for the ship. You can add many design requirements including settling time, percent overshoot, damping ratio, natural frequency, and generic region constraint. This is also known as root locus technique in control system and is used for determining the stability of the given system. To determine the settling time i generated a step response for a time vector 0 to 20.
Draw a closeup of the root locus where the axes go from 2 to 0 on the real axis and 2 to 2 on the imaginary axis. Overshoot %os vsmaller compensator design achieving a desired transient with a given rl 2. Underdamped second order system university of alabama. From the examples we have seen so far, we can see that often is a point on the. To estimate the settling time and peak time, we have to know the damp ing ratio and. Overlay the 10% overshoot line on the closeup root locus. Find the gain k so that the system responds with an overshoot of 1 percent. At this point you can choose from settling time, percent overshoot, damping ratio, andal natur frequency constraints. This is because complex roots occur in conjugate pairs. The root locus is a curve of the location of the poles of a transfer function as. We can also use root locus to check the stability of the system. The root locus diagram should now be visible in one of the windows. The value of gain for which the closedloop transfer function will have a pole on the real axis at. Consider an openloop system which has a transfer function of 4 how do we design a feedback controller for the system using the rootlocus method.
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