Biomedical Engineering Reference
In-Depth Information
J
s
Criteria that characterize the relative
motion of the housing and the
components of the object,
s
=
4
, ..., p
Constraints
D
2
Maximum allowable value for the
criterion
J
2
D
s
Maximum allowable value for the
criterion
J
s
,
s
=
4
, ..., p
J
min
1
Optimal solution
Optimal value of the performance
index
J
1
u
2
Optimal control
u
2
x
2
Optimal time history of displacement
x
2
For the system
i
=
1
¯
n
x
0
¨
=
σ(t),
x
2
¨
+
μ
i
(
x
2
¨
+¨
y
i
)
=
u
2
,
(4.165)
y
i
+
x
2
=
f
i
(
y
,
˙
y
),
i
=
1
, ..., n,
subjected to the initial conditions
x
0
(
0
)
=
x
2
(
0
)
=
0
,
y
i
(
0
)
=
0
,
i
=
1
, ..., n,
(4.166)
x
0
(
0
)
˙
=˙
x
2
(
0
)
=
V,
y
i
(
0
)
˙
=
0
,
i
=
1
, ..., n,
find an optimal open-loop control
u
2
(t)
which minimizes the peak mag-
nitude of the displacement of body 2 relative to the base,
J
1
(u
2
)
=
max
t
∈
[0
,
∞
)
|
x
2
(t)
−
x
0
(t)
|
,
(4.167)
provided that the peak magnitude of the control
u
2
applied to body 2,
J
2
(u
2
)
=
t
∈
[0
,
∞
)
|
u
2
(t)
|
,
max
(4.168)
and the criteria
J
s
(u
2
)
,
s
4
,...,p
, that characterize the relative motion
of the components of body 2 (i.e., the housing and the internal masses)
are constrained by
=
J
2
(u
2
)
≤
D
2
,
J
s
(u
2
)
≤
D
s
,
s
=
4
,...,p.
(4.169)
Search WWH ::
Custom Search