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Given the feed-forward pulse transfer function of a system, plot the root locus

and comment on the stability for the closed loop system with unity feedback.

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G(z) = ‏ل لل سنا اك‎ Assume T = 0.5 ऽ
(2 -1)(2 -€ )
PART C

Answer any two full questions, each carries 20 marks.
For the following transfer function, obtain
Y(z) +1
U(z) 22 +1.32+0.4

i. Controllable canonical form
11. Observable canonical form
iii. | Diagonal canonical from
Derive the expression for the pulse transfer function matrix of an LTI system
governed by the standard state space equations.
Obtain the discrete time state equation of the following continuous time system.

Assume sampling period 1515.

G(s) “5௬2

Find the pulse transfer function representation of the system defined by the
following state space equations.
x(k +1) 1 0.4323 | ×)۸( 0.2838
= + 1/(1)
x,(k +1) 0 0.1353 | x, (4) 0.4323
_ ‏ای‎
‏ناد ضا‎ 04.0൮)
Given the pulse-transfer function, determine whether the system is completely
state controllable and state observable.

20 2 ।(1+ 0.82 )

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Explain the concept of pole placement by state feedback.

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