MAR8067 Marine Machinery Systems - Desklib

MAR8067 MARINE MACHINERY SYSTEMS
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Question 1
(a) closed-loop block diagram for this mechanical system
In problem statement it is provided that from geometry
∆ z=k l1−l2
l1
( x− y )−l2
l1
y ... ... ... ... ... .....(1)
The flow rate balance gives
A dy
dt p . ∆ z
Applying Laplace transform

AsY ( s )= p ∆ z (s )
Y ( s )= ∆ z (s)
As
Substituting equation 1in the equation above
Y ( s )= p
As [ l1−l2
l1 ( X ( s )−Y ( s ) ¿ −l2
l1
Y (s )
) ]
Input to system is X(s)
Output to system is Y(s)
The signal flow graph of the system is as shown
(b) closed-loop transfer function
The transfer function Y (s)
X (s) may be obtained using the Mason’s gain formula
Gain= ∑
i
Pi ∆i
∆
in which
P is the forward path gain
I is the number of forwards paths

Loops in the signal flow graph is
L1= p l2
A sl1
L2= k (l1−l2 )
l1 As
The value of ∆ in Mason’s Gain formula (to get the transfer function) is provided by
∆=1−(l1+ l2)
∆=1+ p l2
A sl1
+ k (l1−l2)
l1 As p
Forward paths from X(s) to Y(s)
p1= k (l1−l2 )
l1 As p
∆1=1 For P1
The transfer function is T = Pi ∆i
∆
X (s)
Y (s) =
k (l1−l2 )
l1 As p
1+ p l2
A sl1
+ k (l1−l2 )
l1 As p
X (s)
Y (s) = k (l1−l2 ) p
l1 As + p l2 +k (l1−l2) p