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Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
book

Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

by Harold Klee, Randal Allen
April 2016
Intermediate to advanced content levelIntermediate to advanced
815 pages
31h 29m
English
CRC Press
Content preview from Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
The integrals in Equation 1.7 can be approximated by assuming F
1
(t) and F
0
(t) are constant over the
interval t to t þDt (see Figure 1.4). Hence,
ð
tþDt
t
F
1
(t)dt F
1
(t)Dt (1:8)
ð
tþDt
t
F
0
(t)dt F
0
(t)Dt (1:9)
Equations 1.8 and 1.9 are reasonable approximations provided Dt is small. Substituting Equations
1.8 and 1.9 into Equation 1.7 yields
DV F
1
(t)Dt F
0
(t)Dt (1:10)
Substituting Equations 1.5, 1.6, and 1.10 into Equation 1.4 gives
AH( t þ Dt) AH(t) þ[F
1
(t) F
0
(t)]Dt (1:11)
) A[H(t þ Dt) H(t)] [F
1
(t) F
0
(t)]Dt (1:12)
) A
DH
Dt

F
1
(t) F
0
(t)(1:13)
where DH is the change in liquid level over the interval (t, t þDt). Note that DH=Dt is the average ...
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Publisher Resources

ISBN: 9781439836736