6 votes
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What is the practical advantage of root locus method in control system engineering?

You might find it interesting to know that the PID controller was around long before root locus. Root locus was so popular when it was first discovered because it was one of the first methods that ...
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  • 2,124
4 votes

How to calculate roots using root locus method?

You could use Newton's method. Yeah I know, it's not the "root locus method", but hey, it works. Let \$F(s)=3s^4+10s^3+21s^2+24s+30\$ Clean it up by dividing everything by 3 so our largest s is ...
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4 votes
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What is meant by "T" and "aT" here?

These are time constants and the formula would more advantageously be written as \$C(s) = K\frac{1+\tau s}{1+\alpha\tau s}\$ where \$\tau\$ is a time constant and has a dimension of time while \$\...
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2 votes
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Root Locus in a feedback loop

Since you have the closed-loop system you need to put it into the from \$1+\frac{k n(s)}{d(s)}=0\ \$ to use the standard root locus techniques. The roots depend on only the denominator of the closed-...
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2 votes
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How to find the intersection point in rootlocus diagram?

The characteristic equation is: $$s(s+1)(s+3)=-K$$ Hence, plug in any point on the locus, and that will give the corresponding value of K. It appears that your selected point on the locus is ...
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  • 7,323
2 votes

Determining imaginary axis crossing of a root locus

I'm not sure about your calculation but Matlab yields the correct result. In this problem, the common approach is to use Routh-Hurwitz criterion and search for a row of zeros that yields the ...
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  • 328
2 votes

Determining imaginary axis crossing of a root locus

In order to determine \$K\$. We need to investigate: \$1+KF(s)=0\implies 1+L(s)=0 \implies s(s+4)(s^2+6s+64)+K=0.\$ We know that \$s=j\omega\$. Plugging this into the equation and collecting the ...
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  • 214
2 votes

Pole Zero Cancellation on a Root Locus

As long as build-ability is not a design requirement, why not place two pairs of conjugate zeroes? Place one pair next to each pair of conjugate open-loop poles. Use SISOtool to play around with ...
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1 vote

Root Locus of the system

With \$\small T=1\$, the Laplace transform of the sampler and ZOH is \$\large\frac{1-e^{-s}}{s}\$. This is partitioned into a \$z\$ term, \$\small (1-z^{-1})=\large \frac{z-1}{z}\$, and an \$s\$ term, ...
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  • 7,323
1 vote

Root locus for an open loop transfer function?

Ignoring the semantics of "root locus," you can certainly plot the roots of a polynomial as its coefficients change. The following script plots the set of poles of your system as \$RL\$ varies from 0 ...
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1 vote
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Centroid from calculated root locus is different to the one from MATLAB

I used Octave and I got that the asymptotes goes at -1.4, just as you calculated. You should double check the Matlab result. I think you might be misunderstanding the meaning of the centroid, it is ...
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  • 2,350
1 vote

How to find the gain K at break-in and breakaway points of a Root Locus Plot on MATLAB

s=tf('s'); GH=((s-4)*(s-3))/((s+1)*(s+2)); rlocus(GH)
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  • 328
1 vote

Design a digital controller for minimize the settling time

Looking at the root locus with the damping factor and natural frequency isolines, we can better see where the poles move. For continuous-time systems, we have that the settling time is given by $$ ...
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  • 2,350
1 vote

Determining imaginary axis crossing of a root locus

MATLAB is plotting the root locus only for positive values of \$K\$. Your analytical calculation may be considering both positive and negative values of \$K\$ and this is why you end up with two pair ...
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  • 205
1 vote
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Given desired overshoot graphically find k from the root locus (Scilab)

First, drawing two more lines with angles 53⁰ and -53⁰ should be easy, just do another plot while keeping the root locus. The lines should be, $$ y = \tan(53^\circ)x$$ and, $$ y = -\tan(53^\circ)x.$$ ...
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1 vote
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Does this Root Locus analysis contradict my understanding of Nyquist stability criteria?

The only thing you're misunderstanding is that those vertical root loci do, in fact, imply and ever-diminishing phase margin. They're describing a system that goes resonant, with a Q that increases (...
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1 vote

Confusion regarding root locus. Open loop or close loop?

The answer is relatively simple: From stability considerations we know that the poles of the closed-loop function H(s)=N(s)/D(s) must not enter the right side of the complex s-plane. The poles of ...
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1 vote

Root Locus, Gain in Feedback Loop. Need help

In order to draw the root locus, you need to convert the open-loop system into the closed-loop system. You can do this $$ \begin{align} T(s) &= \frac{ \frac{1}{(s+3)(s+4)} }{ 1+ \frac{1}{(s+3)...
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  • 328
1 vote
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Root Locus, Gain in Feedback Loop. Need help

No - the root locus is not drawn for the open-loop function. It is the main purpose of the root locus of a system with feedback to show if resp. for which constant gain values the CLOSED-LOOP ...
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1 vote

Root Locus, Gain in Feedback Loop. Need help

When you are working with root locus, you are making a figure about your characteristic equation behavior. So, the root locus of a negative-feedback loop is going to be the same at any point of the ...
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