Sergey V. Purtsezov

This study concerns a concept for an optimal control of the force developed in an automotive restraint system during a frontal impact. The concept is close to that of “smart” restraint systems and involves continuous control of the restraint force by moving the point of attachment of the restraint system to the vehicle or retracting and releasing the seat belts. The analytical foundation for the control of the restraining force does not appear to have been formulated prior to this study. The control design involves the limiting performance analysis of the isolation of an occupant from the crash impact and the formation of a feedback to sustain the open-loop control law that provides the limiting performance. Initially, the problem is outlined using a single-degree-of-freedom system and solved for optimal isolator characteristics. This exercise shows that the optimal force is constant and that the performance of a restraint system behaving as a linear spring is half as effective as the optimal. The methodology is then applied to a published thoracic model having multiple degrees of freedom. A set of functionals is defined as constraints corresponding to injury criteria and the displacement of the occupant relative to the vehicle. The characteristics of the optimal isolator force are then determined. It is shown that this force has a short-duration period of high magnitude early in the profile, followed by an interval of nearly constant force. Next it is shown that a restraint behaving as a linear spring can generate the optimal control force if its attachment point in the vehicle is allowed to move. The design of the control law for this motion involves the determination of an optimal open-loop control and the formation of a feedback to sustain this control. Forms for both of these are presented. A substantial improvement in the behavior of an automobile occupant’s restraint systems can be anticipated from an active control of the seat belt retraction.

For the crashworthiness analysis of transport vehicles a three-component system that consists of a base, a container, and an object to be protected, connected by shock isolators, can be utilized as a model. An approach for a limiting performance analysis of shock isolation for such a model is proposed. This approach involves the reduction of the optimal control problem for the three-component system to an auxiliary optimal control problem for a two-component system. A detailed description of the technique for the determination of the absolute minimum of the performance index and construction of the optimal control is presented. A proposition that provides a mathematical substantiation for this technique is stated and proven. Example problems included in the paper demonstrate the effectiveness of the proposed technique.