Questions tagged [root-locus]
The root-locus tag has no usage guidance.
37
questions
1
vote
0answers
41 views
PID - Root Locus (Sisotool) for Transfer Function (TF) with Zero and Poles in Right Plane
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(...
0
votes
0answers
33 views
Which of the following methods tells Absolute stability & which method tells Relative Stability? Bode Plot, Routh Hurwitz, Root Locus, Nyquist PlotC
Which of the following methods tells Absolute stability & which method tells Relative Stability?
I. Bode Plot
ii. Routh Hurwitz
iii. Root Locus
iv. Nyquist Plot
What i think is the following ...
1
vote
1answer
42 views
Trouble with meeting design specifications of a second order system using Matlab
I am trying to solve the following question.
Consider the transfer function $$G(s) = \frac{1.247}{s^2+9.76s+23.8}$$ is in the forward path of a unity feedback control loop. Assume that it is ...
0
votes
0answers
27 views
How to move closed loop pole to meet the design requirements for settling time and overshoot?
I have tried adding a lead compensator as shown in the second image however am now confused as to how to move the closed loop pole on the right into the feasible region. The first image shows the ...
0
votes
1answer
40 views
Break away/Break in angle in Root Locus method
We are learning Root Locus in our introductory controls course, and one thing has really been confusing me.
When the poles are on real axis, is the breakaway angle always 90 degrees? Is there a simple ...
-1
votes
1answer
79 views
0
votes
0answers
32 views
Finding \$\small K\$ for a given \$\small\zeta\$ value when \$\omega_n\$ (frequency) is not given
Here \$\omega_n\$ (frequency) is not given.
Then upon plotting the Root Locus, how will we find \$\small K\$ at \$\small\zeta = 0.5\$ if we're not using a graph sheet and want to find everything ...
1
vote
0answers
35 views
Phase Lag Compensator
I have a question on lag compensators in general.
Why do they increase both the rise time and the settling time? Is it due to the introduction of a slow pole?
Much thanks!
-1
votes
1answer
74 views
What is meant by "T" and "aT" here?
https://ctms.engin.umich.edu/CTMS/index.php?example=BallBeam§ion=ControlFrequency
I am trying to learn about lead compensator from above link
But i have bit confusion regarding two terms,"...
1
vote
0answers
56 views
How do I plot the root locus when there are multiple controller gains?
I am trying to design a closed loop system with a PI controller. I have plotted root loci before, but in those, I had assumed that the controller was only Proportional. This gave a characteristic ...
0
votes
0answers
104 views
Determine range of proportional gain with given overshoot
I have given the open-loop transfer function
$$
G_{ol} = 1.42 \frac{(s+3)^2+6^2}{(s-1)(s+2)((s+4)^2+4^2)}
$$
The task I was given is determining the range of the proportional gain, which makes the ...
1
vote
1answer
140 views
Centroid from calculated root locus is different to the one from MATLAB
Hi all hope someone can help me here.
My problem involves the transfer function
G(s)=(s+32.8)/((s+2.8)(s+5)(s+27.8) )
As far as im concerned the centroid is ...
0
votes
0answers
68 views
No breakaway points , No imaginary axis crossing points and No angle of departure
G(s)H(s) = K(s+1)/[s^2(s+2)(s+4)]
According to my calculations there are 4 poles (0,0,-2,-4) and 1 zero (-1) in this system.No of branches
are 3.The centroid is -1.67 and the angles of asymptote ...
0
votes
1answer
994 views
How to find the gain K at break-in and breakaway points of a Root Locus Plot on MATLAB
I would like to know how to find the break-in and breakaway points of a transfer function using root locus on MATLAB.
MATLAB Code:
...
0
votes
1answer
77 views
Digital Root Locus in Scilab
I have the following digital plant:
\$G(z)=\cfrac{z+1}{(z-0.3)(z-1)}\$
I want to use root locus to design a system with:
(1) position error=0;
(2) overshoot \$\leq 10\%\$
(3) settling time \$\...
1
vote
1answer
113 views
Design a digital controller for minimize the settling time
I have a system of digital control with unitary feedback, with the following transfer function:
$$G(z)=2\frac{(z-0.5)(z-2)}{(z+0.2)(z+1.5)}$$
I need to use a digital controller:
$$C(z)=K\frac{z-\...
2
votes
1answer
149 views
Root Locus in a feedback loop
I'm trying to draw Root Locus by hand from the following block diagram and confirm the result I got from Routh Hurwitz's table:
The table of Routh Hurwitz that I got is the following:
And from the ...
0
votes
1answer
140 views
Given desired overshoot graphically find k from the root locus (Scilab)
I want to find \$k_1\$ that leads to the feedbakc system having poles in the 53º line (to have overshoot \$\leq 10\%\$). From the root locus, the poles move along the vertical asymptote centered on -1....
0
votes
1answer
4k views
find a point on root locus for specific damping ratio?
Although I have seen many types of root locus plots which have some curved behavior. I cannot find the poles for which my system has a given damping ration of \$ \zeta = 0.59 \$. I need to somehow ...
2
votes
1answer
206 views
Does this Root Locus analysis contradict my understanding of Nyquist stability criteria?
I have been trying to theoretically analyse the operation of a 741 op-amp from a stability point of view by firstly deriving its open-loop transfer function.
Here is the magnitude plot of a 741 op-...
0
votes
2answers
651 views
Confusion regarding root locus. Open loop or close loop?
Which transfer function ,open loop or close loop do we use/need as a pre req to perform root locus analysis?
I have also attached a snapshot of the relevant webpage of university of Michigan.
I have ...
0
votes
0answers
763 views
Root locus vs routh hurwitz criteria?
What is the difference between root locus and routh hurwitz criteria? As according to layman knowledge, both techniques are used somehow to determine
0
votes
2answers
112 views
How to identify branches of root locus from figure/plot?
How can we identify the branches in a root locus
For example How many branches do we have in this below root locus(i feel from its appearance to have one branch)
And how many branches in this below ...
0
votes
1answer
212 views
How can I prove that for any control system root locus plot starts from poles of OLTF and ends at zeroes of OLTF?
simulate this circuit – Schematic created using CircuitLab
G(s)H(s)=N/D
T(s)=KN/(D+KN)
Proof:
]
But
For K=0 T=0
For K=infinity T=infinity
then how can K=0 {condition where forward path ...
1
vote
0answers
398 views
Gain margin using Root locus plot
How can I find Gain margin of any control system given its polar plot In schaum's series I have read that Gain Margin=Ku/Ki but in given figure the system never becomes unstable so shouldn't Gain ...
0
votes
2answers
1k views
Relationship Between Root Locus Pole and Percent Overshoot and Gain in MATLAB
I have a peculiar confusion regarding the relationship between a closed-loop pole on a root locus plot and its gain and percent overshoot. I have found a point on the root locus plot that MATLAB ...
0
votes
1answer
170 views
Steady error control system sinusoidal disturbance
Consider the control system closed-loop represented such a block diagram below:
Given that: \$G_C(s) = K\$ and \$G(s) = 1/s\$
a) Determine the values of \$ K\$ which the closed-system loop is stable....
0
votes
3answers
887 views
Root Locus, Gain in Feedback Loop. Need help
So this is the system for which I have to draw a root locus if 'K' changes from 0 to infinity. The problem for me is that root locus is drawn for open loop transfer function but 'K' is in the feedback ...
3
votes
1answer
671 views
Pole Zero Cancellation on a Root Locus
Problem Design a controller in the feed-forward path to minimize the effects of the two pairs of dominant poles. Use the pole-zero cancellation technique via the root locus diagram.
I have a 5\$^{th}\$...
2
votes
2answers
546 views
Root Locus and Imaginary Axis
I’m having some serious issues finding the point at which the root loci cross the imaginary axis for the following Open Loop Transfer Function (OLTF) ;
We have been taught to substitute s = jw and ...
0
votes
1answer
175 views
How to calculate roots using root locus method? [closed]
Find the roots of the following polynomial by use of the root locus method.
3s⁴ + 10s³ + 21s² + 24s + 30 = 0
(The root locus plot has not been given.)
Can you please help me with this?
This ...
0
votes
2answers
261 views
Root locus, where do they leave the line parallel to imaginary axis
I know how to sketch by hand root locus of simpler systems. Consider the root locus which Matlab gives for:
$$G(s) = \frac{1}{(s+4)(s+6)(s^2 + 10s + 100)}$$
I've marked the points of interest P1 and ...
0
votes
1answer
551 views
Root locus for an open loop transfer function?
The function, rlocus(), in MATLAB is used for closed loop system roots for variation in gain K. However, I am curious if there is a similar function for variation ...
1
vote
0answers
531 views
Designing PID controller for 2 servo motor synchronization
I am trying to use a PID controller to synchronize wheel speeds in an arduino-bot so that I can get it to drive straight. I am unsure how to approach this problem without knowing the physical ...
0
votes
2answers
3k views
How to find the intersection point in rootlocus diagram?
Question:
Sketch the root locus for the open loop transfer function of a unity feedback control sytem given below and determine the value of K for \$\xi=0.5\$
\$G(s)=\frac{K}{s(s+1)(s+3)}\$
--...
0
votes
0answers
104 views
Question about the transfer function found from state space model
I'll make up a problem to explain what I'm having trouble with. $$\dot x=\begin{bmatrix}0&1\\-5&-6\end{bmatrix}x+\begin{bmatrix}0\\1\end{bmatrix}u=Ax+Bu\\\\y=\begin{bmatrix}0&1\end{bmatrix}...
3
votes
3answers
13k views
Determining imaginary axis crossing of a root locus
I have an equation \begin{equation}{\text{L}\left(s\right)=\frac{K}{s(s+4)(s^2+6s+64)}} \end{equation}
and I am trying to determine it's root locus by hand.When I try plotting it with matlab, the ...
