Jawaharlal Nehru Technological University Anantapur 2010-1st Sem B.Tech Code :R7411008 4 IV ester(R07)Regular s, ember/ember DIGITAL CONTROL SYSTEMS - Question Paper

Code :R7411008 4
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 role of analog to digital conversion and digital to analog conversion in digital control systems.
(b) Why is `Sample and Hold' operation needed in digital control systems?
2. (a) What is `modi¯ed' z-transform'? Why is it required?
(b) Use the `multiplication by exponential' property to find the transforms of the discrete- time functions.
(i) e¡®KT Sin (kwT)
(ii) e¡®KTCos (wT)
3. Solve the subsequent di®erence equations
(a) y (k + 1) ¡ 0:8y (k) = 0; y (0) = 1:
(b) y (k + 1) ¡ 0:8y (k) = one (k) ; y (0) = 0
4. (a) What is `State Transition Matrix'? What is its signi¯cance? elaborate its properties?
(b) Solve the state formula · :
x1 :
x2 ¸ = h 0 1
¡2 ¡3 i" x1
x2 # + h 0
1 iu for a unit step input and the initial
condition vector x (0) = [ one 0 ]T . Use the solution to find the discrete - time state equations for a
sampling period of 0.1s.
5. Show that the subsequent state formula is uncontrollable, and determine the uncontrollable mode. Then find
the discrete- time state formula and verify that it is also uncontrollable.
· :
x1 (t)
:
x2 (t) ¸= h 0 1
0 0 i· x1 (t)
x2 (t) ¸+ h ¡1
0 iu (t) .
6. (a) discuss `constant damping Loci'.
(b) Determine the asymptotic stability of the subsequent systems:
i. H (z) = 4(z¡2)
(z¡2)(z¡0:1)
ii. H (z) = 4(z¡0:2)
(z¡0:2)(z¡0:1)
iii. H (z) = 5(z¡0:3)
(z¡0:2)(z¡0:1)
iv. H (z) = 8(z¡0:2)
(z¡0:1)(z¡1)
7. A closed loop control system is to be designed for a steady state fault not to exceed five percent, a damping ratio
of about 0.7, and an undamped natural frequency of 10 rad/s. choose a suitable sampling period for the system
if the system has a sensor delay of
(a) 0.02s.
(b) 0.03s.
8. (a) Derive Ackerman's formula for design via pole placement.
(b) What is `State observer'? discuss with the help of a block schematic. Distinguish ranging from full order
observer and decreased order observer.

Earning:   Approval pending.