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Q 7 Control Fall 2015

1. The document contains a quiz with multiple questions about determining properties of root loci for different open-loop transfer functions. 2. Question 1 involves calculating properties like the number of asymptotes, asymptote angles, breakaway points, and stability for a given open-loop transfer function. 3. Question 2 asks to sketch the root locus on the back page for a different open-loop transfer function, identifying properties like asymptotes. 4. Question 3 asks to prove whether a given point is on the root locus using angle relationships. 5. Question 4 asks to determine whether two given points are on the root locus.

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Fahad Siddiq
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41 views1 page

Q 7 Control Fall 2015

1. The document contains a quiz with multiple questions about determining properties of root loci for different open-loop transfer functions. 2. Question 1 involves calculating properties like the number of asymptotes, asymptote angles, breakaway points, and stability for a given open-loop transfer function. 3. Question 2 asks to sketch the root locus on the back page for a different open-loop transfer function, identifying properties like asymptotes. 4. Question 3 asks to prove whether a given point is on the root locus using angle relationships. 5. Question 4 asks to determine whether two given points are on the root locus.

Uploaded by

Fahad Siddiq
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOC, PDF, TXT or read online on Scribd
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Roll Number = Marks =

(Feedback Control) Page 1 of 1


Air University Quiz–7 Time : 10 Min
Electrical Engineering Deptt. (EE …..) Marks : 10
Instructor: Dr. Fida Date: 15.12.2015

Question:1 Figure:1 Let Gc(s)=K and the root locus is sketched. Find the following. (write and use
proper equations from the table given below )
K
G p (s) 
2 s(s  3)(s  2)
 number of asymptotes.......... +
-
K
s3 + 4s2 + 5s + 2 C(s) K
 
R (s) s(s  3)(s  2)  K
K= ? at imaginary axis
 angles of asymptotes..........
Figure: 1

 centre of asymptotes..........
X X X
S=-3 S=-2 S=0

 breakaway point: simply write equation with values and do the necessary:……….

 for what value K the system is Unstable(use given RH table):…………….

s3 1 6
 value of s at imaginary axis (use auxiliary equation from given RH table)
s2 5 K

 value of K at s=-2 …….. s1 (30-K)/5

 do we need to calculate angle of departure/arrival? YES/ NO Why?...................... s K

1
Question:2 Figure:1 Sketch root locus on back page: follow the given steps where Gp (s)  and Gc (s)  K
s2
number of asymptotes.......... angles of asymptotes..........

-2+j0.707
centre of asymptotes.......... breakaway point if exist ……….

0  35.260 p1  144.740


Question:3 Is the point s=-2+j0.707 in the given figure part of the  z 2  19.468 z1 p 2  900

root locus? H int s :          180 0 the po int to be on RL z z1 p2 p1


p1 p2 z1 z2
2 x x
Prove: (put all angle values-no need to calculate). -4 -3 -2 -1

Rules to help locate the root locus

1. Indicate the finite poles and zeros of the open-loop transfer


function (OLTF) on the s-plane.
2. Number of asymptotes (): =n-m n,m = number poles &zeros;
Question:4 For the system with open-loop function.
r180
3. Angle(s) of Asymptotes ()  ; r  1,  3, ..

(sum of poles )  (sum of zeros)
Determine if the following points are on the root locus. 4. Center of asymptotes () 
  nm

(a) s= - 0.5 5. Breakaway Real-axis and break-in points (If any): ND  ND  0 ;

6. Angles of departure and Arrivals of the root locus:


 d    z   p  r(1800 ) r  1, 3

(b) s=-1+j 7. Intersection of loci with Imaginary axis can be found by the
Routh Criterion.

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