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QUESTION ONE
Find the second order underdamped response specifications % OS, Tp, Ts, Tr, Wn, G (s), ζ of the
response graph below.
SOLUTION ONE
Form the response graph above we can see that;
Cmax = 13.5
Cfinal = 11
Peak time, Tp = 1 second
Percentage overshoot, % OS
max

final
final

 





= 22.727%
Damping ratio,
󰇛󰇜

󰇛󰇜
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
󰇛󰇜

󰇛󰇜



 
Peak time,



Natural frequency, Wn =





= 3.445 Hertz
Settling time, Ts =

=

= 2.845 seconds
Finding the rising time, Tr by using the table below.
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Rising time,


=





 =



0.0188 = Tr 1.463
Tr = 0.0188 + 1.463
Tr = 1.4818 seconds
Transfer function, G (s) =


Where k = Cfinal × 
= 11 × 
= 131
G (s) =


=


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Graph showing response specifications.
QUESTION TWO
Find the second order underdamped response specifications % OS, Tp, Ts, Tr, Wn, G (s), ζ of the
response graph below.
SOLUTION TWO
Form the response graph above we can see that;
Cmax = 1.4
Cfinal = 1.0
Cmax
Cfinal
Tr
Tp
Ts
Overshoot
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Peak time, Tp = 4 second
Percentage overshoot, % OS
max

final
final

 





= 40 %
Damping ratio,
󰇛󰇜

󰇛󰇜

󰇛󰇜

󰇛󰇜



 
Peak time,



Natural frequency, Wn =



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

= 0.852 Hertz
Settling time, Ts =

=

= 16.767 seconds
Finding the rising time, Tr by using the table below.
Rising time,


=





 =



0.0944 = Tr 1.203
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