Anaylise and Design of Nonlinear System (MATLAB skills is required)

Q2 (20) Phase Plane ) 3 ,X,, U’ ) \~.\ w 0° I
Consider the Rayleigh differential equation OK-10 , i 3 lg
u .2 ‘ ~ A372.
3: 2((1 – as: )1. + 1.. ~- 0 :. odd it it
23 (8) Setg _-: an .~.~. Construct a phase plane plot
by the method of isoclines. ‘ti
2b (4) Set Q = -%,a = Construct a phase plane plot
using matlab. Discuss the nature of the plot and com- E,
pare to the plot in 55>”-“”““”“““”“:
2d (8) Carry out a linearized stabilit analysis. Be sure to T i
check validity of conditions. Does the result depend u _ t
Does the phase plane plot depend on a‘? ‘ _\\ :,_ i” ‘gt; -7
25. ‘7\ J 5′” ‘W 7
Q3 (20) Stability. 3( “” U 35x
y Consider the following nonlinear system, . it C y
C C54 y :21 = i :62 .- :13? C ;, . ii r f

Q3 (20) Stability. “- U” ‘5:’X )7? ‘ix’
Consider the following nonlinear system,
Ill} -7-” L172 – Cl‘?
Ilfjg T: 1’1
3a (4) Establish existence by showing that a Lipschitzy
condition holds in any bounded region,
e.g. {(:::1,ac2) : [1271] 3’ R, Li:-2} g R}.
3 1
‘R-9 3b (4) Find all equilibrium points.
3c (4) Using matlab, construct a phase plane plot in the
region {($1,322) 2 [$1] 5 ~;1,l;i‘.2l _<_ 4} and discuss its
features. ‘ H
-‘_”””‘”””-.-..o
3d (8) Do a linearized stability analysis of one equilib-
rium point and compare the result with the phase plane
plot. q‘(’,_ 73:0“ 0 [I
C[’S‘(D) ( -l

30‘, (“W 2 Y‘ Q
‘X2 7“ “XL

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