Biomedical Engineering Reference
In-Depth Information
the platform are determined after solving optimal control problems for a
simplified model with one degree of freedom. The system with the moving
platform will be compared with the system in which the platform is rigidly
fixed to the vehicle.
8.2 OPTIMAL SHOCK ISOLATION OF
SINGLE-DEGREE-OF-FREEDOM SYSTEM
8.2.1
Mathematical Model
A simple single-degree-of-freedom model that involves a base with an
object to be protected moving along the same straight line can be used to
illustrate the optimization of the control of shock isolators and the pre-action
effect. The base and the object are regarded as rigid bodies. The object is
attached to the base by a shock isolator that acts on the object with a force
that provides the absolute acceleration
u
for the object. The motion of the
object relative to the base is governed by the equation
x
=
u
−
z,
(8.1)
where
z
is the displacement of the base relative to a fixed frame and
x
is
the displacement of the object relative to the base.
This system can be regarded as a simplified model of a crashworthy
vehicle. The base can be identified with the vehicle body, the object with
an occupant to be protected from high loads in a crash, and the shock
isolator with the occupant's restraints (seat belts). With reference to the
platform-based isolation system for a wheelchair-seated occupant, the
object can be identified with the platform, the wheelchair, and the occupant
regarded as a single rigid body, and the isolator acts between the platform
and the vehicle body. The function
¨
z(t)
represents the crash deceleration
pulse applied to the vehicle, which can be modeled by the half-sine wave
−
a
sin
π
≤
≤
T
t,
0
t
T,
z
¨
=
(8.2)
0
,
t <
0
,t> T,
where
a
and
T
are the amplitude and the duration of the pulse. This is a
typical model of crash pulses utilized in theoretical studies. The absolute
value of the integral of the function of Eq. (8.2) with respect to
t
from 0
to
T
measures a decrease in the vehicle velocity due to the crash pulse:
2
aT
π
v
0
=
.
(8.3)
Search WWH ::
Custom Search