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

Code :R7411008 1
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) obtain the z- transform of the sampled ramp sequence f(k)= k, k=0,1,2, . . . .
(b) find the inverse z-transform of the function F (z) = (z+1)
z2+0:2z+0:1 .
2. (a) What do you understand by `primary strips' and 'complementary strips'? discuss.
(b) For every of the subsequent di®erence equations, determine the order of the formula. Is the
formula Linear and time invariant?
i. y (k + 2) + 0:8y (k + 1) + 7y (k) = u (k)
ii. y (k + 4) + sin (0:4k) y (k + 1) + 3y (k) = 0
3. The state formula of an armature controlled D.C. Motor is provided by
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
Where x1 is the angular position, x2 is the angular velocity, and x3 is the anmature current.
calculate the state transition matrix.
4. (a) Prove the rank condition for controllability.
(b) Determine the controllability of the subsequent state formula.
24
x1 (k + 1)
x2 (k + 1)
x3 (k + 1)
35
=24
¡2 ¡2 0
0 0 1
0 ¡0:4 ¡0:5
35
24
x1 (k)
x2 (k)
x3 (k)
35+
241
0
1
0
1
1
35
u (k)
5. (a) discuss about primary strips and complementary strips.
(b) Test the stability of the polynomial,F (z) = z5+2:6z4¡0:56z3¡2:05 z2+0:0775z+0:35 = 0
6. Design a digital controller for the D.C. motor speed control system
G(s) = 1
(S+1)(S+10) to find.
(a) A zero steady state fault due to a unit step.
(b) A damping ratio of 0.7 and
(c) A setting time of about 1s.
7. (a) discuss the concept of `pole placement'.
(b) obtain the state feedback matrix that assigns the Eigen values f0:3 § j0:2g to the pair
A = · 0 1
3 four ¸ b = · 0
1 ¸
8. (a) discuss any 2 examples for discrete data control system.
(b) find the transfer function of Zero Order Hold.

Earning:   Approval pending.