Consider the control system has state space matrices as: -3 0 2] B-. c= 1 o 01, D = [0), The system A =0 5 1 Not completely state controllable but its completely observabity Not completely state controllable and observabiity 1 completely state controllable but not observability Can't decided
Consider the control system has state space matrices as: -3 0 2] B-. c= 1 o 01, D = [0), The system A =0 5 1 Not completely state controllable but its completely observabity Not completely state controllable and observabiity 1 completely state controllable but not observability Can't decided
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.1MCQ: For a set of linear algebraic equations in matrix format, Axy, for a unique solution to exist,...
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![Consider the control system has state space matrices as:
-3
21
Consider the control system has state space matrices as:
Consider the control systemn has state space matrices as:
A
1. B = 1, C = [1 0 0], D [0], The system is:
4.
5 a13
[2]
4
1
01
B
C = [1 0 0], D= [0], The system has
1
1.
A
-2
B =
A
-3
1
C = [1 0
0], D = [0], The system has
%3D
0 2]
Not completely state controllable but its completely observability
s2-5S+6
poles in right half side of S-plane.
transfer function
In this case the value of ( a3) is:
G(S)=
$3+4S²+9S+40
Not completely state controllable and observability O
One O
+12 O
1
completely state controllable but not observability O
Two
-3 O
Can' t decided O
Three
-2 O
Four
+4 O
Considering the root locus diagram for a system with (K-16) and T.F.
K(s+ 4)
Considering the Bode diagram for a system with (K=25) and T.F.
G(s)
s(s +1)(s + 3)(s? + 4s + 13)
K(s+2)
G(s) =
: The vahues of gain and phase margin at frequency
Considering a unity feedback control system with forward T.F.
%3D
s(s+5)(s+10s+21)
The break away and break in points at
(s + 4)
s(s + 1)(s+ 3)(s + 4s + 13)
(w=6.41 rad) as :
G(s)
-0,453 and -3.235
Gm=-26.4 dB and Pm= [-1771 o O
2
If we added to this system zero at (s+1), the stability of this system will
6.
-0.55 and -2.35 O
Gm=10.35 dB and Pm= [-29.51 o O
Deteriorate O
-0.45 and -3.5 O
9.
Gm=-23.53 dB and Pm= [-49.36) *o O
No impact O
Not all above O
Not all above O
Improves O
Considering the root locus diagram for a system with
Not all above O
20(s+ 4)
Consider the control system has state space matrices as:
G(s) =
s(s + 1)(s+3)(s² + 4s + 13)
1 01
-3 0 1
2.
4
A
B
C = [1 0 0], D= [0], The system has
%3D
%3D
The intersection points of root locus with imaginary axis by
1
±j2.54 with K=0.85 O
set conjugate zeros in the S-plane.
±j1.46 with K=1.26 O
One O
7
Not all above O
Two O
±j1.95 with K=2.46 O
Three O
Considering the Bode diagram for a system with (K-10) and T.F.
K(S+3)
G(S)=
S(S+10)(S+3)(S²+6S+8)
: G-37.502 dB and P49.76° : If the value of gain
is change to (K=50) the values of gain and phase margin as :
Gm=7.5 dB and Pm= [49.761 ^o O
4
Gm=1.35 dB and Pm= [9.751 ^o O
Gm=3.53 dB and Pm= [-44.361 ^o O
Not all above O
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Transcribed Image Text:Consider the control system has state space matrices as:
-3
21
Consider the control system has state space matrices as:
Consider the control systemn has state space matrices as:
A
1. B = 1, C = [1 0 0], D [0], The system is:
4.
5 a13
[2]
4
1
01
B
C = [1 0 0], D= [0], The system has
1
1.
A
-2
B =
A
-3
1
C = [1 0
0], D = [0], The system has
%3D
0 2]
Not completely state controllable but its completely observability
s2-5S+6
poles in right half side of S-plane.
transfer function
In this case the value of ( a3) is:
G(S)=
$3+4S²+9S+40
Not completely state controllable and observability O
One O
+12 O
1
completely state controllable but not observability O
Two
-3 O
Can' t decided O
Three
-2 O
Four
+4 O
Considering the root locus diagram for a system with (K-16) and T.F.
K(s+ 4)
Considering the Bode diagram for a system with (K=25) and T.F.
G(s)
s(s +1)(s + 3)(s? + 4s + 13)
K(s+2)
G(s) =
: The vahues of gain and phase margin at frequency
Considering a unity feedback control system with forward T.F.
%3D
s(s+5)(s+10s+21)
The break away and break in points at
(s + 4)
s(s + 1)(s+ 3)(s + 4s + 13)
(w=6.41 rad) as :
G(s)
-0,453 and -3.235
Gm=-26.4 dB and Pm= [-1771 o O
2
If we added to this system zero at (s+1), the stability of this system will
6.
-0.55 and -2.35 O
Gm=10.35 dB and Pm= [-29.51 o O
Deteriorate O
-0.45 and -3.5 O
9.
Gm=-23.53 dB and Pm= [-49.36) *o O
No impact O
Not all above O
Not all above O
Improves O
Considering the root locus diagram for a system with
Not all above O
20(s+ 4)
Consider the control system has state space matrices as:
G(s) =
s(s + 1)(s+3)(s² + 4s + 13)
1 01
-3 0 1
2.
4
A
B
C = [1 0 0], D= [0], The system has
%3D
%3D
The intersection points of root locus with imaginary axis by
1
±j2.54 with K=0.85 O
set conjugate zeros in the S-plane.
±j1.46 with K=1.26 O
One O
7
Not all above O
Two O
±j1.95 with K=2.46 O
Three O
Considering the Bode diagram for a system with (K-10) and T.F.
K(S+3)
G(S)=
S(S+10)(S+3)(S²+6S+8)
: G-37.502 dB and P49.76° : If the value of gain
is change to (K=50) the values of gain and phase margin as :
Gm=7.5 dB and Pm= [49.761 ^o O
4
Gm=1.35 dB and Pm= [9.751 ^o O
Gm=3.53 dB and Pm= [-44.361 ^o O
Not all above O
3.
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