APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER M.TECH DEGREE EXEvf1NATI1ON, APRIL MAY 2017
Electrical & Electronics Engineering
(Control Systems, Guidance & Navigational Control)
O1EE6104 Nonlinear Control Systems

60 Duration: 3 Hours
Answer any two full questionsfrom each module

Max. Marks
PART A
10

1. For the system having a closed loop transfer itimction ' plot
the phase trajectory by the

32 +2S+5
method of isoclines originating from the initial (9 marks)
condition (-1 0 )

(4 marks)
2. (a) State and explain Poincare-bendixon criteria (5 marks)
for the existence of limit cycle
(4 marks)
(b) State and explain Locally and Globally
Lipchitz finctions
3. (a) Show that Rx) = 2x + 3 is continuous at x
= -5.
(b) Check the stability of limit cycle
ofthe system given below
1) = X2 —X1(X12 + 1)

+ X22 - 1) (5 marks)
(9202-18 marks)

PART B

4. Construct a Lyapunov fianction for the following system
using Variable Gradient Method

X= —h(xl) - 352

Given h(O) ©, yh(y) OV, ye (-b,c), ( (9 marks)
1

5. (a) Determine the stability ofthe system* = Ax,where AZ
3 using Lyapunov's direct
method. Hence find the Lyapunov Function (5 marks) (b)

State and explain Circle Criteria (4marks)