Biomedical Engineering Reference
In-Depth Information
T
p
Duration of the shock acceleration
pulse
v
0
Initial velocity of the vehicle and
masses
m
1
,
m
2
,and
m
3
Performance index
J
1
Maximum excursion of the
occupant in the vehicle evaluated by
the maximum magnitude of the
displacement of mass
m
1
relative to
the vehicle
Performance criteria
subjected to a constraint
J
2
Maximum chest compression
evaluated by the maximum
magnitude of the relative
displacement of masses
m
1
and
m
2
J
3
Maximum chest acceleration
evaluated by the maximum
magnitude of the acceleration of
mass
m
2
J
4
Maximum rate of chest compression
evaluated by the maximum
magnitude of the difference between
the velocities of masses
m
1
and
m
2
J
5
Maximum chest viscous response
evaluated by the maximum
magnitude of the product of the
chest compression and by the chest
compression rate
Constraint
D
i
Maximum allowable value for the
criterion
J
i
,
i
=
2
,...,
5
Optimal solution
J
1
(u
0
)
Optimal value of the performance
index
J
1
u
0
Optimal control
u
For the system of Eq. (6.26) subjected to the conditions of Eq. (6.27),
find an optimal control force
u
0
(t)
such that
J
1
(u
0
)
=
min
u
J
1
(u)
(6.33)
subject to
J
i
(u)
≤
D
i
,
i
=
2
,
3
,
4
,
5
,
(6.34)
(continued)
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