INTRODUCTION - Injury Biomechanics and Control: Optimal Protection from Impact - page 4

Since many of the constitutive laws for multibody or finite-element mod-
els of the body are not currently available, much of the model development
is empirical; the parameters are found by comparing the response character-
istics of the model with appropriate experimental data. Since these models
may be sensitive to the type of loading, the reliability of the optimization
results obtained by using these complicated models is unknown for loading
regimes beyond those used in the development process. In the optimization
process for isolator development, a number of control laws are tested until
the solution converges to an optimum. Since each trial control changes the
load of the object to be protected, a more detailed and complicated model
does not necessarily give more reliable optimization results. On the other
hand, reasonably simple models enable the basic qualitative features of
the optimal control law to be observed. These features may be taken into
account when constructing a realistic impact isolator.

1.1 STRUCTURE OF THE TOPIC

The topic consists of two parts, one of which (Chapters 2 - 4) provides
background information on shock isolation, control, and optimization, while
the remaining part (Chapters 5 - 8) presents solutions of a number of topi-
cal problems related to the optimal control of shock isolation systems for
protection from the injuries caused by impacts.
Chapter 2 presents the fundamentals of impact and shock isolation. In
this chapter, basic concepts of the theory of shock isolation are introduced,
the physical principles of shock isolation are explained, and the effective-
ness of the isolation is discussed. For those with a mechanical engineering
background, this chapter may be a quick review.
Chapter 3 provides a basic knowledge of the optimization of shock iso-
lators for single-degree-of-freedom systems. The general statement of the
optimal shock isolation problem is given as a problem of constrained mini-
mization of an objective function (performance index) or an optimal control
problem. The concept of the limiting performance analysis is introduced and
developed in detail. A number of simple but important control problems for
shock isolators are solved.
Chapter 4 presents a rigorous mathematical consideration of an optimal
control problem for a shock isolation system for a two-degree-of-freedom
model shown in Fig. 1.2. The object to be protected in this model consists
of two bodies m 1 and m 2 connected by a spring-and-dashpot element with
linear properties. This model can be used, for example, to evaluate the
response of a seated person to a vertical impact load. Bodies m 1 and m 2
take into account the inertial properties of the upper and lower torso, while