B.Tech. VI Semester (Main/Back) Examination, May-June 2015

Electrical Engineering

6EEIA Modern Control Theory(Common for EE, EX)

t-r,(f-.\ori\o

Time : 3 Hours Maximum Marks : 80

Min. Passing Marks : 24

Instructions to Candidates:

Attempt any five questions, selecting one question from each unit. Allquestions carry equal marks. (Schematic diagrams must be shown wherevernecessary. Any data you feel missing suitably be assumed and stated clearly.Units of quantities used/calculated must be stated clearly.

Unit - I1. Give concept of linear vector space. Describe state model of linear systems.

(16)

OR

1. Derive state model of mechanical system given in Fig. I

LxttlII

Fv(t)

Fig. I Mechanical system

Take z,(t) and 4O as new variables given by

z,(t):2x(t)+v(t)zr(t):x(t)+v(t)

Write state equations for z,(t) & zr(t). (16)

[Contd....6E 6071 lzus (1)

Unit-II

2. a) , Diff.erentiatebetweenphysical&phasevariables' (6)

b) For a transfer function given below, write state equations'

71.1=r(r)= , b (10)' t" - u(J) sn + a,s' ' + """an.f + a,t '

.oR2. a) Describe Jordan canonical form in detail'

b) Consider the transfer function

f(s) b.s' + b,s2 +brs +b,

uul =;;;;.,*a

(6)

Derive state sPace equations.(10)

Unit - III3.a)Defineeigenvalues.Describepropertiesofstatetransitionmahix.(12)

b) DescribeconhollabilitY.

OR

3. a) For a matrix A given as,

(4)

6E 6071

to l oltlA=1 3 0 2l

l-rz -t -o)

Prove that L-- M-t AM

Where,^isadiagonalmatrixwitheigenvaluesofAasitsdiagonalelements.(12)

b) Describe state transition matrix . @)

Unit - IV

4. a) Describe how signal is reconstructed from sampled data signal. (8)

b)Describez-transferfunction.Definepropertiesofonesidedz-transform-(8)

OR

4. a) Define sampled data control system'

(2\

(4)

b) Completethefollowingtable,

(t)

a)

(3)

(4)

(s)

(6)

(7)

(8)

F(s)

1/s

?

1

s

1

(s + a)2

?

w ,s- + 14.,-

s+ao

(s + a)2 +w2 !

1

=- 'ls+a

F(z)

?

Tz

(z - l)'

?

?

z(l - e-'r )(z -1)(z - e-'r )

(12)

Unit- V5. what do you mean by stability criterion. Describe Jury stability criteria in detail.

(16)

OR5. Write short notes on :

a) Digital PID controller

b) Adaptive control. (16)

6E 6071 (3)