# JNTU Kakinada B-Tech 4-2 ADVANCED CONTROL SYSTEMS R13 April 2018 Question Paper

IV B.Tech II Semester Regular/Supplementary Examinations, April – 2018
ADVANCED CONTROL SYSTEMS (Electrical and Electronics Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) State the significance of state transition matrix. [4]
b) What do you mean by principle of duality? [4]
c) Explain the effect of inherent nonlinearities on static accuracy. [4]
d) What are the different types of stability? [3]
e) State the fundamental theorem of the calculus of variations. [4]
f) What is the difference between the LQR and LQG? [3]

PART ?B (3×16 = 48 Marks)2. a) Explain the concept of state? Write the observable canonical form? [6]
b) The following facts are known about the linear system
If

then

If

then

Find

and hence A

[10]

3. a) Describe the controllability tests for continuous time systems. [6]
b) Convert the following state model into the Jordan canonical form and there
from comment on controllability and observability.

,

[10]

4. a)Draw a phase plane portrait of the following system,

.
[8]
b) Determine the describing function for the nonlinear element described by

where x=input to the nonlinear element (Sinusoidal signal) y=output of
the nonlinear element.

[8]

5. a) State and explain the Lyapunovs instability theorem. [7]
b) Find a Lyapunovs function for the following system

[9]

6. a) With suitable diagrams illustrate the one point is fixed end, terminal time t 1 is
specified and x(t 1) free end problem and derive the necessary conditions of
variational calculus.

[8]
b) Find the extremals for the functional

[8]

7. How LQG frame work can be used to design optimal controller? Explain with
mathematical equations.
[16]
Code No: RT42022A
Set No. 1
R13
1 of 1

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