Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. EE 1st Semester 75224 OPTIMAL AND ADAPTIVE CONTROL Question Paper.

1 | M-75224 (S35)-2218

Roll No. Total No. of Pages : 02
Total No. of Questions : 08
M.Tech (EE) El-II (2018 Batch) (Sem.-1)
Subject Code : MTEE-104D-18
M.Code : 75224
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWELVE marks.

Q1. (a) Define optimal control problem.
(b) Find the curve with the minimum arc length joining the point (0, 0) and line ?
? (t) = 2 ? t.
Q2. (a) Discuss the steps in solving optimal control problem using Hamilton-Jacobi method.
(b) Consider the system
1
x ? = x
2
2
x ? = u
Is to be controlled to minimize the performance index
2
2
0
1
2
J u dt ?
?

Find a set of necessary conditions for optimal control problem.
Q3. (a) Discuss various performance indices used in optimal control.
(b) Find the trajectory in the (t, x) plane that will extremize
1 2
0
( )
t
J t x x dt ? ?
?
? ? ; x (0) = 1, x (1) = 5
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1 | M-75224 (S35)-2218

Roll No. Total No. of Pages : 02
Total No. of Questions : 08
M.Tech (EE) El-II (2018 Batch) (Sem.-1)
Subject Code : MTEE-104D-18
M.Code : 75224
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWELVE marks.

Q1. (a) Define optimal control problem.
(b) Find the curve with the minimum arc length joining the point (0, 0) and line ?
? (t) = 2 ? t.
Q2. (a) Discuss the steps in solving optimal control problem using Hamilton-Jacobi method.
(b) Consider the system
1
x ? = x
2
2
x ? = u
Is to be controlled to minimize the performance index
2
2
0
1
2
J u dt ?
?

Find a set of necessary conditions for optimal control problem.
Q3. (a) Discuss various performance indices used in optimal control.
(b) Find the trajectory in the (t, x) plane that will extremize
1 2
0
( )
t
J t x x dt ? ?
?
? ? ; x (0) = 1, x (1) = 5
2 | M-75224 (S35)-2218

Q4. What is Hamiltonian? What is the use of Hamiltonian in solving optimal control
problem?
For given plant equation x x u ? ? ? ? with boundary conditions x (0) = 0, x (1) = 1 and
performance index
1
2 2
0
1
(3 )
2
J x u dt ? ?
?
find the optimal control using Hamiltonian
method.
Q5. What is Pontryagin?s minimum principle? Discuss the procedure for finding optimal
control using pontryagin minimum priniciple with control variable and state variable
inequality constraints.
Q.6. (a) Discuss Dynamic programming and its use in control.
(b) Discuss the model reference adaptive control and draw one scheme.
Q7. (a) Discuss MRAC using Lyapunov method.
(b) For the process and reference models respectively described by x Ax Bu ? ? ? ,
? ? ?
m m m m
x A X B r , obtain MRAC with state feedback using Liapunov method.
Q8. (a) The transfer function of a second order plant is
2
1 0
( )
( )
( )
s b
G s
s a s a
?
?
? ?

With normal values a
1
= 3, a
0
= 10 and b = 2. Use a suitable control law and
determine the response of the MRAC scheme with unit step input r(t) = u (t), if the
desired response is specified by the reference models
1
( )
( 1)
m
G s
s
?
?
.
(b) Discuss design of variable structure and adaptive model following control.

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