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Gujarat Technological University: Instructions

This document is an exam for a Modern Control Systems course. It contains 5 questions assessing various concepts related to state space representations, state transition matrices, transfer matrices, matrix properties, and stability analysis. Question 1 asks students to explain state, state variables, and state models, and obtain the state equations for a DC motor model. Question 2 covers steps for constructing state space representations and representing discrete time systems. Question 3 covers state transition matrices and their properties, or transfer matrices and observability. Question 4 covers inverse and rank of matrices, expressing a matrix as a sum of symmetric and skew-symmetric matrices, and types of matrices. Question 5 covers solving a differential equation using matrices or explaining asymptotic stability and Liapunov's stability

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63 views2 pages

Gujarat Technological University: Instructions

This document is an exam for a Modern Control Systems course. It contains 5 questions assessing various concepts related to state space representations, state transition matrices, transfer matrices, matrix properties, and stability analysis. Question 1 asks students to explain state, state variables, and state models, and obtain the state equations for a DC motor model. Question 2 covers steps for constructing state space representations and representing discrete time systems. Question 3 covers state transition matrices and their properties, or transfer matrices and observability. Question 4 covers inverse and rank of matrices, expressing a matrix as a sum of symmetric and skew-symmetric matrices, and types of matrices. Question 5 covers solving a differential equation using matrices or explaining asymptotic stability and Liapunov's stability

Uploaded by

be6351
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Seat No.: _____ Enrolment No.

______

GUJARAT TECHNOLOGICAL UNIVERSITY


M.E Sem-I Remedial Examination April 2010

Subject code: 710703 Subject ame: Modern Control System


Date:08 /04 /2010 Time: 12.00 noon 02.30 pm
Total Marks: 60

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q:1 a) Explain the concept of state, state variables and state model (06)

b) Obtain the state equations for the field controlled D.C motor shown in
fig 1(b) (06)
Rf Ia (Constant)

If m,Jm,fm
Ef Lf Kf

fig 1(b)

Q:2 a) List the steps for constructing state space representation using canonical
variables. (06)

b) How the state variables method can be used to represent discrete-time


system? (06)
OR

b) Explain : Controllability (06)

Q:3 a) Explain : State Transition Matrix (06)

b) List the properties of state transition matrix. (06)

OR

Q:3 a) Explain the concept of Transfer Matrix for state space representation. (06)

b) Define : Observability (06)

Q:4 a) Find the inverse of matrix. (06)


.

1 3 3
A= 1 4 3
1 3 4

1
b) Find the rank of the matrix. (06)

A= 3 -1 2
-6 2 4
-3 1 2

OR

Q:4 a) Express the matrix A as a sum of a symmetric and a skew symmetric


matrix; where (06)

4 2 -3
A= 1 3 -6
-5 0 -7

b) List various types of matrices with illustration. (06)

Q:5 a) Solve the following different equation by matrix method. (10)

d2x / dt2 - 5dx/dt + 6x = 0 , x(0) = 1, x(0) = 2

b) Is the rank of a matrix , affected by elementary transformation? (02)

OR

Q:5 a) By neat diagram explain : Asymptotic stability (04)

b) Explain : Liapunovs stability criteria (08)

**********

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