Biomedical Engineering Reference
In-Depth Information
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 by the chest
compression rate
Constraint
D
i
Maximum allowable value for the
criterion
J
i
,
i
=
2
,...,
5
Optimal solution
J
1
(w
0
)
Optimal value of the performance
index
J
1
w
0
Optimal control
w
For the system of Eq. (6.42) subjected to the conditions of Eq. (6.43),
find an optimal control
w
0
(t)
to provide a minimum
J
1
(w
0
)
=
min
w
J
1
(w)
(6.45)
under the constraints
J
i
(w)
≤
D
i
,
i
=
2
,
3
,
4
,
5
.
(6.46)
The total order of the system of governing differential equations in Prob-
lem 6.2 is reduced by 2 as compared with that of Problem 6.1. In addition,
the control variable
w
in Problem 6.2 is constrained, since the criterion
J
3
of Eq. (6.44) is constrained, while the control variable
u
in Problem 6.1 is
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