# Questions tagged [root-locus]

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### Is it possible to find the point at which the root locus crosses the damping ratio line?

I am aware of how the intersection of the root locus plot can be found with a second order system; however, I was wondering how would you find the intersection by hand (without MATLAB) of a higher ...
• 11
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### 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, ...
• 361
1 vote
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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(...
51 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
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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 ...
35 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 ...
• 1
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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 ...
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### Root Locus of the system

How can I plot root locus like these system can you help me?
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### 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
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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!
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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,"...
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1 vote
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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 ...
245 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
347 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 ...
106 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 ...
2k 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: ...
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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 $\... 1 vote 1 answer 163 views ### Design a digital controller for minimize the settling time I have a system of digital control with unitary feedback, with the following transfer function: G(z)=2\frac{(z-0.5)(z-2)}{(z+0.2)(z+1.5)} I need to use a digital controller: C(z)=K\frac{z-\... 2 votes 1 answer 244 views ### Root Locus in a feedback loop I'm trying to draw Root Locus by hand from the following block diagram and confirm the result I got from Routh Hurwitz's table: The table of Routh Hurwitz that I got is the following: And from the ... 0 votes 1 answer 212 views ### Given desired overshoot graphically find k from the root locus (Scilab) I want to find$k_1$that leads to the feedbakc system having poles in the 53º line (to have overshoot$\leq 10\%$). From the root locus, the poles move along the vertical asymptote centered on -1.... 0 votes 1 answer 7k views ### find a point on root locus for specific damping ratio? Although I have seen many types of root locus plots which have some curved behavior. I cannot find the poles for which my system has a given damping ration of$ \zeta = 0.59 $. I need to somehow ... 2 votes 1 answer 268 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-... • 5,288 0 votes 2 answers 2k 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 ... • 437 0 votes 0 answers 1k 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 • 641 0 votes 2 answers 178 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 ... • 641 0 votes 1 answer 295 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 ... • 445 1 vote 0 answers 718 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 ... • 445 1 vote 2 answers 2k 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 ... • 11 0 votes 1 answer 228 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$which the closed-system loop is stable.... 0 votes 3 answers 1k views ### Root Locus, Gain in Feedback Loop. Need help So this is the system for which I have to draw a root locus if 'K' changes from 0 to infinity. The problem for me is that root locus is drawn for open loop transfer function but 'K' is in the feedback ... • 3 3 votes 1 answer 810 views ### Pole Zero Cancellation on a Root Locus Problem Design a controller in the feed-forward path to minimize the effects of the two pairs of dominant poles. Use the pole-zero cancellation technique via the root locus diagram. I have a 5$^{th}$... • 1,116 2 votes 2 answers 763 views ### Root Locus and Imaginary Axis I’m having some serious issues finding the point at which the root loci cross the imaginary axis for the following Open Loop Transfer Function (OLTF) ; We have been taught to substitute s = jw and ... 0 votes 1 answer 225 views ### How to calculate roots using root locus method? [closed] Find the roots of the following polynomial by use of the root locus method. 3s⁴ + 10s³ + 21s² + 24s + 30 = 0 (The root locus plot has not been given.) Can you please help me with this? This ... 0 votes 2 answers 302 views ### Root locus, where do they leave the line parallel to imaginary axis I know how to sketch by hand root locus of simpler systems. Consider the root locus which Matlab gives for: G(s) = \frac{1}{(s+4)(s+6)(s^2 + 10s + 100)} I've marked the points of interest P1 and ... 0 votes 1 answer 685 views ### Root locus for an open loop transfer function? The function, rlocus(), in MATLAB is used for closed loop system roots for variation in gain K. However, I am curious if there is a similar function for variation ... 1 vote 0 answers 584 views ### Designing PID controller for 2 servo motor synchronization I am trying to use a PID controller to synchronize wheel speeds in an arduino-bot so that I can get it to drive straight. I am unsure how to approach this problem without knowing the physical ... • 39 0 votes 2 answers 3k views ### How to find the intersection point in rootlocus diagram? Question: Sketch the root locus for the open loop transfer function of a unity feedback control sytem given below and determine the value of K for$\xi=0.5G(s)=\frac{K}{s(s+1)(s+3)}\$--... • 478 0 votes 0 answers 105 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}...
I have an equation $${\text{L}\left(s\right)=\frac{K}{s(s+4)(s^2+6s+64)}}$$ and I am trying to determine it's root locus by hand.When I try plotting it with matlab, the ...