Visvesvaraya Technological University (VTU) 2006 B.E Fifth Semester , .06 / 07 Modern Control Theory - Question Paper

Fifth Semester B.E. Degree exam , Dec.06 / Jan. 07
Electrical and Electronics Engineering
Modern Control Theory
Time:3 hrs] [Max.Marks:100
Note: 1. ans any 5 full ques..
2. presume any missing data.
1. a. What is a controller? discuss P, I, PI and OPID controllers. (10 Marks)
b. find the state space representation model for the subsequent electrical circuit in
fig .1(b).Given R = one Ohm and C = one Farad.
2. a. discuss the terms : i) State ii) State Variable iii) State vector
iv) State space –with an example. (10marks)
b. find the state space representation of the subsequent system and draw its phase
variable diagram:
Y + six Y + 11Y + 6Y = 6u .
· · · · · ·
(10 Marks)
3. a. What is state transition matrix? List out the properties and advantages of state
Transition matrix. (10 Marks)
b. find the state transition matrix using:
i) Laplace Transformation matrix using:
ii) Cayley – Hamilton method
For the system define by,
4. a. State the conditions for completely controllability and complete observability.
Determine the state controllability and observability of the system defined by,
b. discuss common physical nonlinearities
in control systems (10 Marks)
5. a. elaborate the singular points? discuss various singular points adopted in
nonlinear
control systems. (08 Marks)
b. obtain out singular points for the subsequent systems:
i) + . five + two = 0
· ·
x o x x
ii) + three + two = 0
· · ·
y y y
iii) + three - 10 = 0
· ·
y y
(12 Marks)
6. a. find the necessary and sufficiency condition for arbitary pole placement .
(10 Marks)
b. find the gain matrix for the system:
provided :xwn =4.
7. a. Determine whether or not subsequent quadratic form is positive definite:
1 two 2 three one 3
2
3
2
2
2
1 two one Q ( x , x ) = 10 x + four x + x + two x x - two x x - four x x (10 Marks)
b. discuss with an example – i) Liapunov Main Stability theorem
ii) Liapunov 2nd Method and
iii) Krasovskii’s theorem (10 marks)
8. a. obtain the Liapunov function for the system:
b. Draw the phaseplane
trajectory for the subsequent formula using Isoline method:
+ two + two = 0
· ·
x xw x w x
Given, x = 0.5, w = 1, Initial point ( 0, 6) (10 Marks)

Earning:   Approval pending.