Download PTU M.Tech. EE 2nd Semester 76102 ADVANCE CONTROL SYSTEM Question Paper

Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. EE 2nd Semester 76102 ADVANCE CONTROL SYSTEM Question Paper.

1 | M-76102 (S35)-1333

Roll No. Total No. of Pages : 03
Total No. of Questions : 08
M.Tech. (EE) (2018 Batch) (Sem.?2)
ADVANCE CONTROL SYSTEM
Subject Code : MTEE-203A-18
M.Code : 76102
Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :
1.Attempt any FIVE questions out of EIGHT questions.
2.Each question carries TWELVE marks.


SECTION-A
Q1 Obtain the state space representation of the system shown below :

Fig.1
Q2 Consider the following state space representation of a system:
1 1
2 2
3 3
0 1 0 0
0 0 1 0
6 11 6 6
x x
x x u
x x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
?

? ?
1
2
3
1 0 0
x
y x
x
? ?
? ?
?
? ?
? ?
? ?

Obtain the eigen values of the matrix A. Also develop the system in diagonal canonical
form.
m
1
m
2
y
2
y
1
k
b
u
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1 | M-76102 (S35)-1333

Roll No. Total No. of Pages : 03
Total No. of Questions : 08
M.Tech. (EE) (2018 Batch) (Sem.?2)
ADVANCE CONTROL SYSTEM
Subject Code : MTEE-203A-18
M.Code : 76102
Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :
1.Attempt any FIVE questions out of EIGHT questions.
2.Each question carries TWELVE marks.


SECTION-A
Q1 Obtain the state space representation of the system shown below :

Fig.1
Q2 Consider the following state space representation of a system:
1 1
2 2
3 3
0 1 0 0
0 0 1 0
6 11 6 6
x x
x x u
x x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
?

? ?
1
2
3
1 0 0
x
y x
x
? ?
? ?
?
? ?
? ?
? ?

Obtain the eigen values of the matrix A. Also develop the system in diagonal canonical
form.
m
1
m
2
y
2
y
1
k
b
u

2 | M-76102 (S35)-1333

Q3 Define Observability. For the system defined by :
X AX BU ? ?
?

Derive the condition for complete state Observability.
Q4 Discuss the properties of Lyapunov function. Discuss any two methods for finding out the
Lyapunov function.
Q5 Consider the system given by:
X AX BU ? ?
?

y CX ?
? ?
1 0 1 0
A 1 2 0 , B 0 , C = 1 1 0
0 0 3 1
? ? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ? ?
? ? ? ?

Transform the system equations into observable and controllable canonical form.
Q6 Discuss the concept of an observer in control theory. Consider a system defined by :
1 1
2 2
3 3
0 1 0 0
0 0 1 0
1.244 0.3956 3.145 1.244
x x
x x u
x x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
?

? ?
1
2
3
1 0 0
x
y x
x
? ?
? ?
?
? ?
? ?
? ?

Given the set of desired poles of the observer to be
5 5 3, 5 ? 5 3, 10 s j s j s ? ? ? ? ? ? ?
design a full order observer.
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1 | M-76102 (S35)-1333

Roll No. Total No. of Pages : 03
Total No. of Questions : 08
M.Tech. (EE) (2018 Batch) (Sem.?2)
ADVANCE CONTROL SYSTEM
Subject Code : MTEE-203A-18
M.Code : 76102
Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :
1.Attempt any FIVE questions out of EIGHT questions.
2.Each question carries TWELVE marks.


SECTION-A
Q1 Obtain the state space representation of the system shown below :

Fig.1
Q2 Consider the following state space representation of a system:
1 1
2 2
3 3
0 1 0 0
0 0 1 0
6 11 6 6
x x
x x u
x x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
?

? ?
1
2
3
1 0 0
x
y x
x
? ?
? ?
?
? ?
? ?
? ?

Obtain the eigen values of the matrix A. Also develop the system in diagonal canonical
form.
m
1
m
2
y
2
y
1
k
b
u

2 | M-76102 (S35)-1333

Q3 Define Observability. For the system defined by :
X AX BU ? ?
?

Derive the condition for complete state Observability.
Q4 Discuss the properties of Lyapunov function. Discuss any two methods for finding out the
Lyapunov function.
Q5 Consider the system given by:
X AX BU ? ?
?

y CX ?
? ?
1 0 1 0
A 1 2 0 , B 0 , C = 1 1 0
0 0 3 1
? ? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ? ?
? ? ? ?

Transform the system equations into observable and controllable canonical form.
Q6 Discuss the concept of an observer in control theory. Consider a system defined by :
1 1
2 2
3 3
0 1 0 0
0 0 1 0
1.244 0.3956 3.145 1.244
x x
x x u
x x
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
?

? ?
1
2
3
1 0 0
x
y x
x
? ?
? ?
?
? ?
? ?
? ?

Given the set of desired poles of the observer to be
5 5 3, 5 ? 5 3, 10 s j s j s ? ? ? ? ? ? ?
design a full order observer.

3 | M-76102 (S35)-1333

Q7 Determine the optimal control signal U for the system defined by:
X AX BU ? ?
?

Where
0 1 0
0 1 1
A and B
? ? ? ?
? ?
? ? ? ?
?
? ? ? ?

Such that the following performance index is minimized:

2
0
( )
T
J X X U dt
?
? ?
?

Q8 Write a short note on :
(a) Similarity transformation
(b) Kalman filter










NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.

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