INTRODUCTION - Injury Biomechanics and Control: Optimal Protection from Impact - page 2

do not involve sensors, controllers, or actuators, while active isolators may
integrate these components.
When properly designed and controlled, isolators can substantially reduce
the risk of severe injuries.
For injury prevention applications, injury criteria serve the role of per-
formance criteria. The injury criteria are quantitative response measures
indicating the severity of injury in terms of mechanical quantities such
as displacements, velocities, accelerations, energy, and power. In addition,
performance criteria may include geometric characteristics such as the max-
imum excursion of an occupant of a vehicle relative to the vehicle's interior
in response to a crash impact load. The objective of designing injury coun-
termeasures is to minimize the injury potential as interpreted by the injury
criteria. When optimizing the design of shock isolators, it is desirable to
reduce the values of all performance criteria to the greatest extent possible.
However, the performance criteria are often competing and simultaneous
minimization of them is impossible. There are a number of approaches to
solving multicriteria optimization problems. For example, a single objective
function to be minimized can be formed as a weighted sum of the perfor-
mance criteria. A success or failure of this approach depends on the choice
of the weighting coefficients. Another approach, which will be used in this
topic, involves minimizing one of the performance criteria while the other
criteria are constrained.
An important stage of the optimal design of shock isolators is the evalu-
ation of the absolute minimum of the performance index (the performance
criterion to be minimized) that characterizes a hypothetically perfect (ideal)
isolator that cannot be surpassed by any real isolator irrespective of its
design and engineering configuration. This evaluation involves replacing
the particular isolator configuration with a generic control force and solv-
ing an optimal control problem for this force. The absolute minimum of the
performance index that results from the solution of this problem character-
izes the limiting performance of the system in terms of the performance
index. The evaluation of the absolute minimum of the performance index
and the investigation of the behavior of this performance index relative to
constraints is often called limiting performance analysis . By comparing the
performance characteristics of a proposed design or prototype with those of
the ideal isolator, an engineer can see how close his or her design comes
to the ideal.
To characterize the limiting potentials for improving shock isolators,
trade-off curves that plot the performance index against the criteria sub-
jected to constraints can be used. A typical trade-off curve is shown in
Fig. 1.1, for two performance criteria J 1 and J 2 . Any design correspond-
ing to points above this curve is feasible but is not optimal, because both