Download PTU M.Tech. EE 2nd Semester 76107 ROBUST CONTROL Question Paper

Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. EE 2nd Semester 76107 ROBUST CONTROL Question Paper.

1 | M-76107 (S35)-1771

Roll No. Total No. of Pages : 02
Total No. of Questions : 08
M.Tech. (EE) (2018 Batch) (Sem.?2)
ROBUST CONTROL
Subject Code : MTEE-204B-18
M.Code : 76107
Time : 3 Hrs. Max. Marks : 60

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


l. Check definiteness of the scalar function applying Sylvester?s criterion-
2 2 2
1 2 3 1 2 1 2 2 3
( ) 4 5 8 4 4 . V x x x x x x x x x x ? ? ? ? ? ?
2. Apply the vectorization method to solve the Lyapunov equation.
A
T
P + PA = ? I
With
0 1 1
2 5 1
3 1 2
A
? ? ?
? ?
? ? ?
? ?
? ? ?
? ?

3. Determine the optimum input using Riccati equation when the performance index is :
0
1 0 1 0
0 1 0 1
T T
X X M M dt
?
? ? ? ? ? ?
?
? ? ? ? ? ?
? ? ? ? ? ?
?

Where M is the input and the system equation is :
0 1 1 0
.
0 0 0 1
X X M
? ? ? ?
? ?
? ? ? ?
? ? ? ?
?

4. Given the system with state-space matrices :
? ?
0 1 0
; ; 1 1
3 2 1
A B C
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?

Design the linear quadratic regulator with Q = C
T
C and r = 5.
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1 | M-76107 (S35)-1771

Roll No. Total No. of Pages : 02
Total No. of Questions : 08
M.Tech. (EE) (2018 Batch) (Sem.?2)
ROBUST CONTROL
Subject Code : MTEE-204B-18
M.Code : 76107
Time : 3 Hrs. Max. Marks : 60

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


l. Check definiteness of the scalar function applying Sylvester?s criterion-
2 2 2
1 2 3 1 2 1 2 2 3
( ) 4 5 8 4 4 . V x x x x x x x x x x ? ? ? ? ? ?
2. Apply the vectorization method to solve the Lyapunov equation.
A
T
P + PA = ? I
With
0 1 1
2 5 1
3 1 2
A
? ? ?
? ?
? ? ?
? ?
? ? ?
? ?

3. Determine the optimum input using Riccati equation when the performance index is :
0
1 0 1 0
0 1 0 1
T T
X X M M dt
?
? ? ? ? ? ?
?
? ? ? ? ? ?
? ? ? ? ? ?
?

Where M is the input and the system equation is :
0 1 1 0
.
0 0 0 1
X X M
? ? ? ?
? ?
? ? ? ?
? ? ? ?
?

4. Given the system with state-space matrices :
? ?
0 1 0
; ; 1 1
3 2 1
A B C
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?

Design the linear quadratic regulator with Q = C
T
C and r = 5.

2 | M-76107 (S35)-1771

5. Distinguish between H
2
and H
inf
control.
Given the system
1 1
1
1
2
2 2
x x u w
y x w
z x u
? ? ? ?
?
? ?
?
?
? ?
?
?

Calculate analytically the compensator C(s) with the H
?
control technique.
6. Using the LMI approach, find the control law that stabilizes simultaneously the two
systems :
A
1
=
1 2 2
2 0 0 0 5 0 0 0
0 1 0 ; 1 0 6 0 ; 1
0 0 5 1 0 0 3 3
B e A B
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?

7. Give the system with transfer function G(s)
4
3 s
?
?
determine the coprime factorization.
Then determine the class of stabilizing compensators with unit step response equal to 1.
Finally, calculate the energy associated to the impulse response for the closed-loop
system.
8. Given the continuous-time system with transfer function G(s) =
3 2
4 4 s s s
?
? ? ?
calculate
for which values of ? is the system bounded real.




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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