Questions tagged [root-locus]
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34
questions
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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
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1answer
73 views
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29 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 ...
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25 views
Phase Lag Compensator
Good evening,
I have a question on lag compensators in general. Why do they increase both the rise time and the settling time? Is it because due to the introduction of a slow pole?
Much thanks
-1
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1answer
72 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
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0answers
43 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 ...
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73 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
71 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 ...
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46 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 ...
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0answers
39 views
How can we plot Non minimum Phase system Root Locus?
I have a closed-loop transfer function
$$ H(s)=\frac{K(2-s)}{s(s+18)}.$$
I know that this is Non-Minimum Phase system, but I could not determine the points that cut through the real axis, the ...
0
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1answer
506 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
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1answer
63 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
92 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
110 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
92 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 53Āŗ line (to have overshoot \$\leq 10\%\$). From the root locus, the poles move along the vertical asymptote centered on -1....
0
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1answer
3k 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
176 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-...
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2answers
233 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 ...
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0answers
437 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
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2answers
74 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
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1answer
139 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 ...
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0answers
230 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
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2answers
902 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
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1answer
126 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....
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3answers
614 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 ...
2
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1answer
528 views
Pole Zero Cancellation on a Root Locus
Question: ...design a controller in the feedforward path to minimise the effects of the two pairs of dominant poles. Use a pole-zero cancellation technique on a root locus diagram....
I have a 5th ...
2
votes
2answers
376 views
Root Locus and Imaginary Axis
Iām 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
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1answer
168 views
How to calculate roots using root locus method? [closed]
Find the roots of the following polynomial by use of the root locus method.
3sā“ + 10sĀ³ + 21sĀ² + 24s + 30 = 0
(The root locus plot has not been given.)
Can you please help me with this?
This ...
0
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2answers
204 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)}$$
I've marked the points of interest P1 and ...
0
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1answer
419 views
Root locus for an open loop transfer function?
The function, rlocus(), in MATLAB is used for closed loop system roots for variation in gain K. However, I am curious if there is a similar function for variation ...
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0answers
513 views
Designing PID controller for 2 servo motor synchronization
I am trying to use a PID controller to synchronize wheel speeds in an arduino-bot so that I can get it to drive straight. I am unsure how to approach this problem without knowing the physical ...
0
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2answers
3k views
How to find the intersection point in rootlocus diagram?
Question:
Sketch the root locus for the open loop transfer function of a unity feedback control sytem given below and determine the value of K for \$\xi=0.5\$
\$G(s)=\frac{K}{s(s+1)(s+3)}\$
--...
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0answers
102 views
Question about the transfer function found from state space model
I'll make up a problem to explain what I'm having trouble with. $$\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
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3answers
11k 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 ...
