Shivaji University 2010-7th Sem B.E Electrical Engineering Electrical (New) , Digital Control System(Elective-I) - Question Paper
Digital Control System - DCS is Elective subject for B.E. Electrical students in seventh semester of 2 sections, every of 50 marks i.e. total of 100 marks paper.
Illlimillllllllll 1-994
Seat
No,
B.E. (Electrical) (Semester -VII) (New) Examination, 2010 DIGITAL CONTROL SYSTEM (Elective-1)
Day and Date : Tuesday, 7-12-2010 Max. Marks: 100
Time : 230 p.m. to 5.30 p.m.
Instruction : Attempt any three questions from each Seaton,
SECTION - r
1. a) Deri ve with necessary mathematical equations the describing function for Backlash
nonlinearity. 9
b) S late and prove the mu 1 tip lication of two sequences property of z- transform. 8
2. a) A linear second order servo is described by the equation e + 2une + ta2e = 0
Where , = 0.15 0)=1 rad/sec e(o) = 1.5 & e(o) = G.
Determine ihe singular point, construct the phase trajectory using the method of isoclines. 9
b) Comment on the Lyapunov functions and stability criterion. 8
3. a) Find the system response in terms of
i) Zero input response
ii) Zero state response
iii) Total responce.
The system difference equation is given by y (n) = 1.5 y (n-1) - 0.5 y (n - 2) +x (n) with initial conditions y (-1) = 4 and y (-2) = 10 and x(n) = (0.25). 8
b) With the help of frequency response curves explain the characteristics of
ZOH. 8
P T.<X
4, Write short notes on (any two) :
a) Jurys stability criterion.
16
b) Designing using frequency response method.
c) Steady state errors and error constants.
SECTION - II
5. a) A linear time in variant system is described by the following state model.
|
O o |
"0" | ||||
|
X 2 |
= |
0 0 1 j |
x2 |
+ |
0 |
|
X- |
- 6 -11 - 6j |
_X3_ |
.2- |
and y = [) 0 0]
.*3 J
Transform this state model into a canonical state model. Also compute the state transition matrxi eAl. b) Obtain the pulse transfer function of the system if
|
i i ro o i |
"o~ | ||
|
a = |
0 -3 1 |
H = |
0 |
|
-3 -4 -Sj |
.1. |
c = [0 1 0]
6. a) C ommen I on conto Had i 1 i ty an d exp lai n po 1 e p lacemen t design ing.
b) Consider a linear system described by the transfer function
10
Y(S) = __
O(S) S(S + l)(S + 2)
Design a feedback controller with a state feedback so that the closed loop poles are placed at - 2, -1 j 1.
7 a) Explain state observer.
b) Consider the continuous time system given by
G{S) = _
U(S) SJ + 8S +12S + 9
obtain the controllable canonical form of state space
8. Write short notes on (any two):
a) State space representation of digital system .
b) Non linearity presented in physical systems,
c) Explain deka method for phase plane.
|
Attachment: |
| Earning: Approval pending. |
