Jawaharlal Nehru Technological University Anantapur 2010-1st Sem B.Tech Code :R7411008 3 IV ester(R07)Regular s, ember/ember DIGITAL CONTROL SYSTEMS - Question Paper

Code :R7411008 3
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) Distinguish ranging from analog control systems and digital control systems.
(b) With the help of a block schematic, discuss the con¯guration of a digital control system.
2. (a) find the z-transforms of
i. Sine function
ii. Cosine function
(b) obtain the inverse z-transform of the function F (z) = z
(z+0:1)(z+0:2)(z+0:3)
3. obtain the transfer functions corresponding to the subsequent di®erence equations with input u(k)
and output y(k).If no transfer function is de¯ned, discuss why.
(i) y (k + 2) = y (k + 1) y (k) + u (k)
(ii) y (k + 3) ¡ 2y (k) = 0
(iii) y (k + 4) + y (k ¡ 1) = u (k)
4. find the discrete-time state equations of the subsequent analog state formula for a sampling
period of 0.1s. Solve the discrete- time state formula for the initial condition x (0) = £ one 0 ¤T
and unit step input. · :
x1
:
x2 ¸= · 0 1
¡2 ¡3 ¸24
x1
x235 + · 0
1 ¸u
5. (a) What do you understand by `Duality' ranging from controllability and observability? provide the
necessary proof for duality.
(b) discuss the concepts of `controllability' and observability.
6. obtain the range of the gain k for unity feedback system having the subsequent loop transfer
functions;
(a) 1:9412£10¡2k
z¡0:9418
(b) 1:0653£10¡2k(z+0:8467)
(z¡1)(z¡0:6065)
7. Design a proportional controller for the unity feedback, digital control system with analog
process.G(s) = 1
S(S+5) and a sampling period T=0.04s to obtain,
(a) A steady state fault of 10% due to a ramp input.
(b) A damping ratio of 0.7
8. (a) With the help of a block schematic, discuss `full order state estimator.'
(b) Distinguish ranging from `full order observers' and `reduced order observer.' Draw the block
diagram of reduced- order observer.

Earning:   Approval pending.