Biomedical Engineering Reference
In-Depth Information
2. Calculate the objective function
I
1
(C, K)
and the constraint function
I
2
(C, K)
using Eqs. (3.119) and (3.121).
3. Solve the constrained minimization problem
I
1
(C
0
,K
0
)
=
min
C,K
{
I
1
(C, K)
|
I
2
(C, K)
≤
1
}
.
(3.122)
The solution yields
1
.
(3.123)
The details of the solution are given in Balandin, Bolotnik, and Pilkey
(2001).
To represent the solution of Problem 3.3 as a function of the parameters
V
and
U
, use Eqs. (3.116) to convert the relations of Eq. (3.123) to the
dimensional variables, giving
C
0
=
0
.
931
,K
0
=
1
.
330
,
1
(C
0
,K
0
)
=
0
.
521
,
2
(C
0
,K
0
)
=
1
.
330
U
2
0
.
521
V
2
U
0
.
931
U
U.
(3.124)
A comparison of the expressions of Eq. (3.124) for the minimum of the
peak magnitude of the relative displacement of the object provided by the
linear isolator with the respective expression of Eq. (3.39) corresponding
to the limiting performance indicates that the linear isolator is only 4%
inferior to the hypothetically perfect isolator and, hence, provides highly
effective protection for objects from disturbances that can be modeled as
an instantaneous shock pulse.
c
0
=
V
,k
0
=
V
2
,J
1
(c
0
,k
0
)
=
,J
2
(c
0
,k
0
)
=
3.5
PRE-ACTING CONTROL FOR SHOCK ISOLATORS
3.5.1
Basic Concept: Statements of the Problems
So far, only cases in which the isolator starts responding to a disturbance
only after the disturbance has been applied to the base have been discissed.
In fact, it is the disturbance that triggers the isolator to act. Accordingly,
in the statements of Problems 3.1 - 3.4, the initial time instant after which
the controller is allowed to act was fixed. However, in a number of cases,
it is possible to predict the action of the disturbance and to actuate the
controller in advance, which can substantially improve the isolation qual-
ity. A control engaged before the disturbance will be called a
pre-acting
control
. The pre-acting control can be utilized in seismic protection and
injury prevention systems. Consider, for example, a helicopter performing
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