THORACIC INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 206

index. The other criteria are biomechanical characteristics that measure the
severity of the injuries. These criteria should lie below threshold limits.
The limiting performance analysis yields the absolute minimum of the per-
formance index and the corresponding open-loop optimal control, which
subsequently can be utilized as the reference control to be sustained by a
feedback.
The difference between the performance index value provided by a spe-
cific shock isolation system and the absolute minimum indicates the success
or failure of the design of this system. The limiting performance philoso-
phy and techniques were outlined in Chapter 3 for single-degree-of-freedom
systems. For more detail, read Sevin and Pilkey (1971) and Balandin, Bolot-
nik, and Pilkey (2001). The limiting performance analysis for the human
thorax injury model developed by Lobdell et al. (1973) will be a basis
for this chapter. This model has been utilized often for the analysis of the
response of the thorax of a car occupant to a frontal crash deceleration
pulse. A simplified single-degree-of-freedom model will be used initially.
The impact isolation limiting performance can be provided by standard
seat belts, the tension of which is controlled by moving the point of attach-
ment of a seat belt to the vehicle or by retracting and releasing the belt.
The law of motion of the attachment point is determined so as to fit the
force transmitted to the occupant by the seat belt to the optimal control
force. The control of motion of the attachment point can be designed as
a feedback relating the velocity of the attachment point to the difference
between the current value of the control force and the reference optimal
value. This approach is close to the indirect optimization proposed by
Sevin and Pilkey (1971). Indirect optimization involves the identification
of parameters of a feedback control law defined as a prescribed function
of the phase coordinates of the system. The time histories of the phase
coordinates corresponding to the optimal motion are substituted into the
feedback law and then the unknown parameters are identified to approxi-
mate the optimal control force time history by the function of time resulting
from this substitution. In general, the indirect optimization method does
not enable one to achieve complete agreement of the motion of the system
controlled by the feedback with the optimal motion characteristics of the
limiting performance. This follows because the number of parameters to
be identified is finite, whereas the number of points at which the refer-
ence control law should coincide with the control law to be synthesized is
infinite. In the approach proposed in the present chapter, the parameter to
be identified is chosen to be the coordinate of the point of attachment of
the restraint system to the vehicle. This coordinate changes continuously
over time, which enables one to provide complete agreement of the system
motion corresponding to the synthesized control law with that of the limiting