Passive in-vehicle safety systems such as the air bag and the belt restrain the occupant during a crash. However, often their behavior is not optimal in terms of occupant injuries. This paper discusses an approach to design an ideal restraint system. The problem is formulated as a feedback tracking problem with the objective to force the controlled variables, i.e., the acceleration of the head and the chest of the occupant, to follow a priori defined reference signals by simultaneous manipulation of the belt and the air bag. The reference signals have to reflect minimal injuries to the head, the chest, and the neck. More or less realistic numerical models of a crash test are far too complex to be used in control design processes. Therefore, a strategy is presented to derive simple, linear MIMO models. These models approximate the local dynamic behavior of the complex model and are suitable for control design. Analysis of the interactions in these simple models makes it plausible that the control design problem can be split into two separate tracking problems. Next, stabilizing low order controllers are designed using these models, and implemented in the closed loop system with the realistic numerical model. Results are presented, suggesting that feedback control with low order controllers is extremely effective as a basis for ideal restraint systems. Reductions of the adopted injury measures of at least 40% in comparison with the uncontrolled restraint system are achieved. (A)
Abstract