Biomedical Engineering Reference
In-Depth Information
k
h
2
2
(u
i
+
v
i
)
[2
(k
−
i)
+
1]
≤
D
2
,
(3.71)
i
=
1
D
2
−
D
1
≤
D,
u
i
≥−
U
0
,
u
i
≤
U
0
,
i
=
1
...,N,
k
=
1
...,N,
and minimize
U
0
.
3.4
PARAMETRIC OPTIMIZATION
3.4.1
Basic Concepts: Problem Definitions
Parametric optimization is a design technique that involves the identification
of the design variables of an isolation system with a given configuration by
solving a mathematical programming problem. This technique requires the
control force to be represented as a parametric family of functions
u
=
u(x,
x,t,α),
˙
(3.72)
where
x
and
x
are the coordinate and the velocity of the object relative to
the base,
t
is time, and
α
is a finite set (vector) of design variables to be
identified. The function
u(x,
˙
x,t,α)
reflects specific features of the design
configuration of the isolation system. Consider a few simple examples.
˙
Example 3.1 Linear Spring-and-Dashpot Isolator
An object attached to the base by a spring-and-dashpot isolator is shown
in Fig. 3.5. The linear isolator generates the control force proportional
to
the
displacement
and
the
velocity
of
the
object
relative
to
the
base,
u
=−
c
x
˙
−
kx,
(1)
where
c
is the damping coefficient of the dashpot and
k
is the stiffness of
the spring. The coefficients
c
and
k
are the design variables. The function
u
of (1) is a particular case of Eq. (3.72) for
α
[
c, k
]. Here the design
variable set
α
consists of two components,
c
and
k
.
=
(continued)
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