Questions tagged [root-locus]

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Control engineering: how to design a system for desired impulse response

I've designed a system to get a desirable step response. However, I think the impulse response of my system is more important. There are many methods for designing a system for transient response ...
Mr Phase Locked Loop's user avatar
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The center and radius of root locus

With this opened-loop transfer function, $$ \begin{align*} L(s) & = \dfrac{K(s+2)}{s(s+1)} \end{align*} $$ I would like to plot the root locus of this system. Based on the textbook,...
Sonamu's user avatar
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What does the root locus tell us exactly?

More specifically what information can one extract from a root locus drawing without calculating the transfer function and then using Routh Hurwitz or other techniques? Essentially, what information ...
Ahsan Yousaf's user avatar
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1 answer
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Unable to determine transfer function to obtain root locus

This one is pretty straightforward. We set K1 = 4 and want to bring out K2 as a common factor so we can plot the root locus for the system. The correct answer is: $$\small G_{new}(s)=4K_2\frac{(s+6)}{(...
Or Perez's user avatar
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How are break-away point and break-in points related to damping factor 'd' of a system?

I have to determine gain of P-Controller when damping factor = 1. So in the solutions it is mentioned that damping factor and break-away point are related. Please can anyone clarify how damping factor ...
Tejas Kondhalkar's user avatar
3 votes
1 answer
282 views

What is the practical advantage of root locus method in control system engineering? [closed]

Recently I learned about the topic. Decades ago, when no computational power was available for engineers, it was surely helpful in some way. But I do not understand what the advantage is nowadays, ...
MichaelW's user avatar
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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(...
Brian1776's user avatar
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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 ...
Husnain Afzal's user avatar
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1 answer
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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 ...
Michio Kaku's user avatar
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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 ...
Max's user avatar
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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 ...
user_9's user avatar
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Root Locus of the system

How can I plot root locus like these system can you help me?
Hans Muller's user avatar
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146 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 ...
Safin Rahman's user avatar
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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!
aid846's user avatar
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What is meant by "T" and "aT" here?

https://ctms.engin.umich.edu/CTMS/index.php?example=BallBeam&section=ControlFrequency I am trying to learn about lead compensator from above link But i have bit confusion regarding two terms,"...
DSP_CS's user avatar
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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 ...
Francis Vellara's user avatar
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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 ...
Th2mas's user avatar
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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 ...
dorudrakky's user avatar
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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 ...
Malsha Ranasinghe's user avatar
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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: ...
Ind's user avatar
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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 \$\...
Carmen González's user avatar
1 vote
1 answer
310 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-\...
Carmen González's user avatar
2 votes
1 answer
481 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 ...
Carmen González's user avatar
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1 answer
455 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....
Carmen González's user avatar
1 vote
1 answer
11k 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 ratio of \$ \zeta = 0.59 \$. I need to somehow find ...
Will's user avatar
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1 answer
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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-...
user avatar
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2 answers
4k 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 ...
DSP_CS's user avatar
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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
DSP_CS's user avatar
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2 answers
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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 ...
DSP_CS's user avatar
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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 ...
SUNITA GUPTA's user avatar
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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 ...
SUNITA GUPTA's user avatar
2 votes
2 answers
4k 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 ...
Rando's user avatar
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1 answer
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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....
miguel747's user avatar
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3 answers
2k 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 ...
Ibnc's user avatar
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3 votes
1 answer
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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}\$...
rrz0's user avatar
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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 ...
JakeNorms's user avatar
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1 answer
280 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 ...
Nishanth Rao's user avatar
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2 answers
355 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 ...
user1949350's user avatar
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1 answer
964 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 ...
Mostafa Mekawy's user avatar
1 vote
0 answers
699 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 ...
NLhere's user avatar
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2 answers
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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)}\$ --...
Rohit's user avatar
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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}...
John Katsantas's user avatar
4 votes
3 answers
22k 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 ...
Ca01an's user avatar
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