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K.S.RANGASAMY COLLEGE OF TECHNOLOGY, TIRUCHENGODE 637 215

An Autonomous Institution, Affiliated to Anna University CoimbatoreApproved by AICTE, New Delhi, Accredited by NBA and an ISO 9001: 2000 Certified

Institution

END SEMESTER EXAMINATION (R -2010)[ACADEMIC YEAR 2010-11 (ODD SEMESTER)]

DEG / BRANCH ME- POWER ELECTRONICS & DRIVES

SEMESTER FIRST SUBJECT CODE 10PPE102SUBJECT NAME LINEAR AND NONLINEAR SYSTEM THEORY

MAX. MARKS /DURATION

100 / 3Hours EXAM DATE

Descriptive (Essay type) 5 20 Marks = 100Marks

Instruction: Answer all the Questions

1. a i)Consider a linear time invariant system described by the equation(12)

X = Ax+ Bu, Y= Cx where

[ ]001

1

0

0

6116

100

010

=

=

= CBA

Design a full order state observer assuming that the desired Eigenvalues of the observer matrix are 1, 2= -2 j3.464, 3= -5.

a ii)Obtain the canonical state for a system whose transfer function is

given by (8)

6116

8178

)(

)(23

23

+++

+++=

sss

sss

sU

sY

(OR)1. b i) Given a system

uxX

+

=

1

0

0

320

100

010

(10)Determine new state vector W such that equations are diagonalized.

b ii) Check whether the system given below is completely controllable andcompletely observable.

[ ]513

7

41

21=

=

= CBA

(10)

2. a i)Consider a system with ideal real as intentional non linear element asshown below (12)

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5. b) How neural network is used in adaptive controllers. Explain with anexample. (20)