THORACIC INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 229

The behavior of the system under the control of Eq. (6.50) with α =
1s / kg was simulated. The optimal control u 0 (t) corresponding to T p =
80 ms was chosen as the nominal (reference) control. The simulation demon-
strates that the behavior of the system controlled by such a feedback cor-
responds to the limiting performance with a high degree of accuracy.

6.4.4 Constant-Force Control

It is apparent from Fig. 6.2 that the optimal control force u 0 (t) is constant
over a substantial portion of the occupant's deceleration. In view of this,
it is of interest to investigate the behavior of the system subjected to the
constant-force control u(t)

U ,where U coincides with the magnitude
of the optimal control force when it is constant. For the numerical values
of the parameters of the injury model and the impact deceleration pulse
adopted for the simulation, we have U

≡−

1500 N. The simulation shows
that the replacement of the optimal control by the constant control force
leads to an 11, 22, and 30% increase in the occupant's peak excursion
for T p

≈

0 . 08 , 0 . 1 , 0 . 12 s, respectively. The chest compression reaches its
upper bound, and the other injury criteria remain below the upper limits
prescribed by the constraints. Taking into account the fact that when the
force in the optimal control law is constant, the chest compression is con-
stant and reaches its upper bound, one can calculate the value of U without
solving an optimization problem. The constant value of the control force is
defined by U = f(D 2 ) ,where f is the elastic characteristic of the thorax
[Eq. (6.30)] and D 2 is the maximum value allowed for the chest com-
pression. If an increase in the occupant excursion due to the replacement
of the optimal control by the constant-force control law is acceptable, the
constant-force control can be recommended for practical applications. To
sustain the constant tension of the restraint system by controlling the point
of attachment of the restraint system to the vehicle, use the feedback of
Eq. (6.50), with u 0 (t) replaced by

=

− U .

6.5 CONCLUSIONS

The control concept for elastic restraint systems can be used for the design
of active controllers for automobile seat belts to improve their efficiency
in crash situations. For example, belt systems can be equipped with con-
trollers that can regulate the seat belt retraction process so as to provide
the optimal (or near-optimal) time history of the decelerating force exerted
on the occupant. The reference optimal control law should be calculated
in advance as the solution of the limiting performance problem for the