In control theory and stability theory, root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. This is a technique used as a stability criterion in the field of classical control theory developed by Walter R. Evans which can determine stability of the system. The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot).
A graphical method that uses a special protractor called a "Spirule" was once used to determine angles and draw the root loci.
I have used root locus before but my confusion now is that the input is the negative feedback. Usually when I have negative feedback I consider the the error between the input (ideal) signal and the observed signal.
Also, in this case what is the tranfer function since u = -k*y, and what does...
Hi everyone! I have a 8th order transfer function, you can see it in the first image:
% Transfer function
num = [2.091,0,203.3,0,-2151,0,-1.072e05];
den = [1,0,-830.4,0,-1.036e05,0,-5.767e05,0,2.412e07];
tf = tf(num, den)
I need to use a PID, so I'm trying to use a compensator, adding poles...
From my understanding, the root locus is only concerned with open loop gain. I figured this means you would ignore the negative feedback loop and calculate the root locus from just the plant's function
Workings:
zeros: -1
poles: 0, -2, -2,
relative degree = 2
=> 90-degree asymptotes
meeting...
Homework Statement
For an exam question i need to be able to sketch the root locus of a system, for example the following: g(S) = 200(S+3) / ((S+2)(S+4)(S+6)(S+8)(S+10)
The Attempt at a Solution
So i counted number of poles and zeroes and calculated no. of asymtodes: p-z = 4 and calculated the...
Good afternoon people; recently I decided to give a study break from control engineering; now I'm back. I'm studying again control theory and I see some good results. By the way I got stuck in a topic called root locus method. Now my issue is not about how to sketch the root loci graph (BTW I...
Homework Statement
[/B]
I am trying to answer two questions:
1. Solve part (b) in the image above by hand.
2. What are the differences between transfer function (a) and transfer function (b).
Homework Equations
cos(Im(s) / Re(s)) = ζ
The Attempt at a Solution
1. For part one given the...
Hi,
Having a bit of trouble with this question: "Assuming a proportional controller is used, determine the gain to achieve a damping ratio of 0.5, for the following transfer function. Hence calculate the associated natural frequency and oscillation period. G(s) = -4(s+0.4) / s^2+1.6s+14."
I...
QUESTION (2/2)
1) What are some alternatives to iterative design in control theory?
2) I have a certain plant transfer function PTF(s) that is higher order than two and non-unity numerator.
I want certain characteristics such as a certain damping ratio (zeta).
So I want approximate it as...
Homework Statement
I've been trying for a week to understand root locus and how it works but what i got is a big confusion that's why I'm asking here for help. Why do we only look at open loop transfer function of the system when we are supposed to know the stability of the closed loop system...
The characteristic equation is 1+K(S+1)/S2 Below is the root locus diagram. I don't get why there are two branches when there is only one pole, at 0. Does it count as having two poles even if it is the same because of s^2 ? If it does then why doesn't the angle of departure make sense?
number...
Hi guys. Firstly the answer to the requirement of the post is all in the picture (problem statement, relevant equations etc.). I'm just wondering if someone could tell me why they use the root -0.435 as the breakaway point? Like I know there's two real roots; -0.435 and -1.61, so obviously one...
Homework Statement
With unity position feedbck, i.e. make K2=0, plot root locus as a function of pitch gain (K1). By imposing 2nd order system approximation, estimate settling time, rise time, peak time of the closed-loop system with 20% overshoot.
Pic of system...
Hi,
In the attached image the roots are shown for the characteristic equation. I don't know how the roots were found. Anyone able to help?
Thanks
Splint
The root locus design method is used to locate poles at desired locations.
However, it is not possible to locate poles arbitrarily. Provide reasons for this statement.
K = 1/│G(s)H(s)│
K G(s)H(s) = (2k+1)π
I've formulated the answer for this as,
The root locus gives the path of...
Homework Statement
Homework Equations
See below
The Attempt at a Solution
Root Locus? Easy Peasy right? Based on provided equation G(s), i solved the coordinates of the root locus diagram using quadratic equation.
For the 2nd part of the question, i have to find gain at which rise time...
Hello guys, I need help to sketch the root locus of the system when K is varying from 0 to infinity. (K>=0)
The system:
http://www.freeimagehosting.net/newuploads/anspe.jpg
I'm stuck. I really don't know how proceed.
Thanks in advance.
Homework Statement
Given the transfer function:
R(s)=\frac{K}{s(s+2)(s^2+4s+5)}
Find the following (needed to sketch the root locus:
a) Number of branches
b) Symmetry
c) Starting and ending points
d) behavior at infinity (asymptotes)
e) Real axis breakaway and break-in points.
f)...
When sketching a root locus of a simple closed loop negative feedback system (with positive gain K)... if you have more poles than zeros, we know that they will tend towards infinity along some asymptotes. How do you know which pole will travel along which asymptote?
For example in the...
i just want to make sure I'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros)
the equation i have is s2 + 2s + 8 / s(s2 + 2s + 10)
so the zeros are -1 + i√7 and -1 - i√7
and the poles are 0, -1...
Hello,
I do not understand very well how to sketch a root locus plot. I am able to find poles/zeros, where the root locus exist on the real axis, the break away/in points, intersection of asymptotes, crossing of the imaginary axis, etc., but I do not understand how to actually draw the root...
Homework Statement
Re-arrange the open-loop transfer function and sketch the root locus for the system for variation of the parameter 'a' from 0 to infinity.
Homework Equations
G(s)H(s) = 10(s+a) / [s(s+1)(s+8)]
The Attempt at a Solution
my problem is that i don't know how to re-arrange...
I was told to plot a root locus(by hand) of the open loop transfer function:
H(s)G(s)= (s+2)/(s^2 + 2s + 3)
and for a value of k=1.33 determine the location of the root, then find the equivalent damping coefficient.
After several attempts i was able to draw the...
Hi everyone, I would please like some suggestions regarding where my error is, designing a lead compensator with the root locus method for a unity feedback control system where G = [12.5] / [2.5 1 2500]. I want to set the overshoot zeta = 0.5 for an overshoot of 16%, and settling time Ts =...
Homework Statement
I have to design a controller for "Cruise Control System" using Root Locus method.
Homework Equations
We havnt studied that method yet and nor do I think it is in the course outline. Actually that is why I selected root locus so that I can learn something beyond the...
I want a MATLAB code to draw the root locus for a characteristic equation of a transfer function of unity feedback, also what is the range of K that keeps the system stable , here is the characteristic equation:
s^5+600s^4+50000s^3+ks^2+24ks+80k=0
please help, thanks in previous
Homework Statement
I'm trying to analyze the root locus of this transfer function in Matlab to control a DC motor:
mysys=tf([0.022],[0.00000000007 0.0000000626 0.000493])
The Attempt at a Solution
Using:
%[Kp,P]=rlocfind(mysys)
%rltool(mysys)
rlocus(mysys)
I get a root locus...
I had to use state-variable feedback to design a position control system for a motor. I have to design the controller using root locus methods.
The gain that is varied is located in the feedback loop as shown in the picture.
I am completely lost as to how to generate a root locus with the...
I had to use state-variable feedback to design a control system for a motor. I first designed a deadbeat controller, which was pretty easy.
But now I have to design another controller using root locus methods.
The gain that is varied is located in the feedback loop as shown in the picture...