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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
Solving for t
1
gives
t
1
¼ t ln
(T
0
þ RQ) T(0)
(
T
0
þ RQ) (T
d
þ D)

¼ 0:24 ln
(50 þ 28:8) 50
(50 þ 28:8) (75 þ3)

¼ 0:86 h (2:155)
From Equation 2.153 with T(0) ¼508F, the temperature response is
T(t) ¼ 50e
t=0:24
þ 78:8(1 e
t=0:24
), 0 t 0:86 (2:156)
(d) The furnace shuts off when the temperature reaches T
d
þD ¼788F and the subsequent cooling
from 788FtoT
d
D ¼728F follows the step response in Equation 2.153 with Q ¼0 and T(0) ¼
T
d
þD ¼788F. Thus,
T(t) ¼ (T
d
þ D)e
(tt
1
)=t
þ T
0
[1 e
(tt
1
)=t
], t
1
t t
2
(2:157)
¼ 78e
(t0:86)=0:24
þ 50[1 e
(t0:86)=0:24
], 0:86 t t
2
(2:158)
where t
2
is the time when the building temperature is T
d
D 728F. Note the (
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Publisher Resources

ISBN: 9781439836736