Jawaharlal Nehru Technological University Anantapur 2010-1st Sem B.Tech Code :R7411008 2 IV ester(R07)Regular s, ember/ember DIGITAL CONTROL SYSTEMS - Question Paper

Code :R7411008 2
IV B.Tech I Semester(R07)Regular Examinations, November/December 2010
DIGITAL CONTROL SYSTEMS
(Electronics & Control Engineering, Electronics & Instrumentation Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
? ? ? ? ?
1. (a) discuss the advantages and disadvantages of digital control systems.
(b) define in detail the `sample and hold' operation.
2. (a) find the inverse z-transform of the function F (z) = z+1
z2+0:3z+0:02
(b) Verify the ¯nal value theorem using the z-transform of a decaying exponential sequence
and its limit as k tends to in¯nity.
3. (a) provided the discrete - time system, y (k + 1) ¡ y (k) = u (k + 1). obtain the system transfer
function and its response to a sampled units step.
(b) provided the discrete- time system,y (k + 1) ¡ 0:5 y (k) = u (k) ; y (0) = 0. obtain the impulse
response h(k) of the system.
4. find the discrete- time state equations for
24
:
x1
:
x2
:
x3
35
=24
0 one 0
0 0 1
0 ¡10 ¡11
35
24
x1
x2
x3
35
+24
0
0
10
35
u for a sampling period T=0.01 s.
5. (a) Prove the Rank condition for observability.
(b) Determine the observability of the system.
24
x1 (k + 1)
x2 (k + 1)
x3 (k + 1)
35
=24
¡0:4 0 0
0 three 0
0 0 ¡2
35
24
x1 (k)
x2 (k)
x3 (k)
35
+24
1
0
1
0
0
1
35
u (k)
yk = £ one 1 0 ¤[x1; (k) x2 (k) x3 (k)]T
6. (a) elaborate 'primary strips' and 'complementary strips'? discuss.
(b) obtain stability conditions for
i. The ¯rst -order polynomial a1z + a0 ; a1 > 0
ii. The 2nd - order polynomial a2z2 + a1z + a0; a2 > 0
7. Design a digital controller for the analog plant transfer function G(s) = 1
(S+1)(S+3) for a time
constant of less than 0.3 second, a dominant pole damping ratio of at lowest 0.7, and zero steady
- state fault due to a step input.
8. Design a feedback controller for the pair A =24
0:1 0 0:1
0 0:5 0:2
0:2 0 0:4
35
b =24
0:01
0
0:005
35
to find
the eigen values f0:1; 0:4 § j0:4g.

Earning:   Approval pending.