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[Total No. of Questions: 12] [Total No. of Printed Pages: 2] 

UNIVERSITY OF PUNE

[4364]-540 

B. E. (Electrical) Examination - 2013 

DIGITAL CONTROL SYSTEMS (2008 Course)

[Time: 3 Hours] [Max. Marks: 100]

SECTION -IQ.1 A Draw a configuration of a basic digital control scheme in block diagram

and explain the function of each block.

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B Explain Linearity property of a system and determine whether the

following systems are linear or not with proper justification.i)  Y(n) = X(n) + n X(n+1)

ii)  Y(n) = n X2 (n)

iii)  Y(n) = 13 [X(n) + X(n-1) + X(n-2)]

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C Explain various types of Analog to digital converters. 5

OR 

Q.2 A Discuss the advantages and limitations of Digital Control Systems. 6

B Explain the sampling and reconstruction process, state the sampling

theorem and give its importance.

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C Explain Digital to Analog converter with block diagram. 5

Q. 3 A State and prove important properties of Z-transform. 5

B Determine the Z-transform and ROC of the following signals. Alsomention the particular property, which you will use.

i)  X(n) = (an + a-n) u (n)

ii)  X(n) = (cos 0n) u (n) ----use Euler’s identity 

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OR 

Q. 4 A State and prove the initial and final value theorems for X(z). 5

B Determine inverse Z-transform of the following

i)  X(z) =4

(+0.5)2  for |Z| > 0.5

ii)  Z2

/0.5 – 1.5Z + Z2

for |Z| < 0.5

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Q. 5 A Show how a mapping of Left Half of the S-plane is done into the Z-plane

with Stable and unstable regions.

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B Examine the stability of the system by Bilinear transformation method,

whose characteristic equation is:

F(z) = Z3+3Z

2+2Z-3=0

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OR 

Q. 6 A Describe the general rules for constructing the Root Loci in designing LTI

discrete time control system.

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B The characteristic equation of discrete time unity feedback control system 8

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is given by : Z +(3K)Z +(K+2)Z + 4=0. Determine the range of gain K for 

stability of the system by use of Jury’s stability test. 

SECTION IIQ. 7 A Explain discretization of continuous-time state space equation

X0

= Ax + Bu; y = Cx + Du

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B Determine the pulse transfer function of a system

X(K+1) = 0.8 1

0 0.5 X (k) + 1

0.5 

Y(k) = [1 0] X (k)

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OR 

Q. 8 A Discuss the various methods used for STM 8

B Determine STM by Cayley-Hamilton theorem

X(K+1) = 1 −1

0 2 X(k) Take X(0) = 1−1

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Q. 9 A What is the principle of duality? Also explain effect of pole zero

cancellation on the system with suitable example.

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B Investigate controllability and observability for the following system.

A= 0 1 0

0 0 1−6 −11 −6

B= 0

01

C=4 5 1 8

OR 

Q. 10 A What is Full order observer? With the help of a block diagram explain it. 8

B For the system

X (K+1) = G X(k) + H U (K) ; Y(k) = C X (k) whereG = 0 20.6

1 0, H= 1

0 AND C = [1 0] 

Design a full state observer for the desired eigen values of observer matrix

As Z1 = -1.8 + j2.4 & Z2 = -1.8 – j2.4

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Q. 11 A Draw a neat block diagram of digital temperature control scheme and

explain the function of each block.

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B Consider the system defined by

G (z) = +1

2++0.16 Obtain state space representation for this system in Controllable canonicalform.

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OR 

Q. 12 A Explain control algorithm for temperature control scheme. 8

B Consider the system defined by

G (z) =z3+8z2+17Z + 8+1+2(+3)

 

Obtain state space representation for this system in Jordan canonical form.

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