5)

6)

b)

a)

b)

a)

b)

a)

b)

00000AE407121906

Obtain the modified Z transform of
i. x(t) = e@u(t), where w(t) represents the unit step signal.
1. G(S)= = where G(S) represents the Laplace Transform of g(t)

Check the stability of the system with the following characteristic equation
using Jury’s stability test.
F(Z) = ജ്‌ —1.223+ 0.0722 + 0.32 - 0.08 = 0
Explain the gain margin and phase margin.
Draw the root locus diagram for the system with following characteristic
equation (For T = 0.5 sec.)

ச(1-௪ 7)

PART C
Answer any two full questions, each carries 20 marks.
Derive a state space representation of the following pulse transfer function

system in the observable canonical form and draw the block diagram
[2] _ z 744273
एदा 1+ 62 1+ 117 2 ‏و6‎
‎Determine whether the following system with state space representation is
completely controllable or not and observable or not.
ಜ್‌ 2 _ [ 0 7
‏)يو‎ + 1) 0 -210டி()
x(k)
x2(k)
Derive the state space representation of the following pulse transfer function
system in controllable canonical form and diagonal canonical form and draw the
block diagram.
Y[Z] _ 2711
212] 22 + 1.32 + 0.4

Obtain the transfer function of the system with the following state space

= 51|

1 + 1) | [2 -1 01൨൪ 0
representation |x2(k + 1) ۲ -3 பு ८2 (८) | + | u(k)
x3(k+1)| 1-3 ‏یہ‎ விரு ‏ا‎
‎൫0
‎1) = [0 0 11൧൧
x3(k)

Write short notes on:
i. Pole placement using state feedback
ii. Dynamic Output feedback
Effects of finite word length on controllability and closed loop pole placement

اد ‎मं मैप‏ اد

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