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Code No:D109115601JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY
HYDERABAD
M.Tech I Semester Regular Examinations March/April2010
ADVANCED CONTROL SYSTEMS
(COMMON TO POWER SYSTEMS (HIGH VOLTAGE), CONTROL SYSTEMS)
Time: 3hours Max.Marks:60
Answer any five questions
All questions carry equal marks
- - -
1. Explain the design procedure of lag-lead compensation by
using root locus
technique.
2.a) Compare PI, PD, and PID controllers.
b) A unity feed back system has an open loop transfer
function,
( )( 1)(0.2 1)
kG s
s s s=
+ +
Design phase-lag compensation for the system to achieve the
following
specifications:Velocity error constant kv = 8
Phase margin = 400.
3.a) Given the vector-matrix differential equation describing
the dynamics of the
system as
[ ]
0 1 0 0 0
0 0 1 0 0, ; ; 1 0 0 0
0 0 0 1 0
1 0 0 0 1
x Ax Bu where A B C
= + = = =
i) Determine the eigen values of A. Then obtain a transformation
matrix p suchthat the system state equation becomes in decoupled
form.
ii) Determine the transfer function from the state variable
formulation.
b) Write short notes on second-order eigen vector
sensitivities.
4.a) State the properties of Jordan canonical form.b) Given the
transfer function:
3 2
( ) 2 4 5 3( )
( ) ( 2) ( 2) ( 2) ( 1)
Y sG s
U s s s s s= = + + +
+ + + +
Write the state variable formulation in Jordan canonical
form.
5. Suppose you are given an n-dimensional linear-time invariant
system. How do
you transform it into controllability canonical form? State and
explain the
theorems used.
R09
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6.a) Consider a state model, ,x Ax Bu= +
and y = cx where
[ ]
0 1 0 0
0 0 1 ; 0 ; 3 4 1
40 34 10 1
A B C
= = =
i) Show that the eigen values of A are 3 1, 4.j
ii) Suggest a suitable transformation matrix M so that
1
3 1 0 0
0 3 1 0
0 0 4
j
M AM j +
= =
b) Check the observability of the above system.
7.a) State and explain different singular points
b) Obtain the describing function of a relay with dead zone and
hysteresis.
8.a) State and explain 2nd
method of Liapunov.
b) Consider a non-linear system described by the equations.
1 1 2
32 1 2 2
3x x x
x x x x
= +
=
Investigate the stability of equilibrium state by using
Krasovskiis method withP as identity matrix.
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