Sergey V. Purtsezov

Optimal Control of Restraint Forces in an Automobile Impact

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. DOI: 10.1115/1.2718240

Test system, vehicle and occupant response repeatability evaluation in rollover crash tests: the deceleration rollover sled test

The goal of this study was to evaluate the repeatability afforded by a rollover test system in terms of the test conditions, vehicle and occupant response, and vehicle deformations. Eight full-scale rollover tests were performed using three 2002 Ford Explorer vehicles, instrumented with anthropomorphic test devices and arrays of accelerometers and angular velocity sensors, to examine both intra- and inter-vehicle repeatability in five non-destructive low-speed (LS) and three full-thrown high-speed (HS) rollover crash tests using the deceleration rollover sled method. The cart was accelerated to the target velocity (LS: 19.3 km/h, n = 5; HS: 48.3 km/h, n = 3) and then decelerated (soil trip simulation) to initiate vehicle roll. All five LS and the first two HS tests showed a high degree of repeatability (peak lateral acceleration: 5.3 ± 0.2 g LS and 5.5–6.5 g HS; peak roll rate: 134 ± 12 deg/s LS and 237.3–237.4 deg/s HS; peak curb force: 92.4 ± 2.0 kN LS and 92.6–92.9 kN HS; peak dummy head resultant acceleration: 6 ± 0.2 g LS and 45–56 g HS; peak dummy upper neck axial load: 162 ± 35 N LS and 10.7–13.6 kN HS). However, despite nearly identical deceleration pulses, the third test exhibited significantly different kinematics (237 vs. 250 deg/s, four quarter turns vs. two). These results demonstrate that the test system can generate repeatable test conditions, which result in repeatable vehicle and dummy responses, but that these responses are highly sensitive to variations in the test conditions.

External biofidelity in lateral impact measurement of global and local forces

A study was conducted to develop high-resolution external biofidelity data for the response of post-mortem human surrogates (PMHS) in side-impact loading. This study implemented stationary PMHS (N = 3) impacted by a wall moving at a constant velocity. The wall was subdivided into 15 impact plates, each instrumented to record the normal and shear forces as well as reaction moments about the shear axes. A method to determine the time-history of the centre of pressure (COP) of each load plate was developed and validated in both quasi-static and dynamic loading conditions. A validation test demonstrated that the COP can be predicted to within 1 cm for loads generally achieved by the shoulder and pelvis. The repeatability of COP was very good for the pelvis, where maximum variation was 1.44 cm, but higher for the thorax (3.4 cm) and shoulder (4.1 cm). Patterns of COP motion on the pelvis plate were consistent for all subjects.

Extremal disturbance analysis for dynamical systems with uncertain input

The philosophy of the extremal disturbance analysis for dynamical systems with uncertain inputs is described. This analysis involves solving optimal control problems in which the time histories of the inputs (external disturbances) are regarded as the control functions and a response measure of the system serves as the performance index. The performance index should be maximized or minimized over the disturbances within a prescribed class. Often this class is specified by lower and upper bounds (a corridor) between which the values of the disturbance must lie. The maximization and minimization problems are referred to as the worst disturbance and best disturbance problems, respectively. The solutions of these problems provide the extreme values between which the response measure lies for any disturbance from the specified class. The extremal disturbance analysis is important, in particular, when designing standards for testing devices for the protection of fragile objects from impact loads. This approach is illustrated for a single-degree-of-freedom system that can be regarded as a simplified model of the equipment for sled tests of automobile restraint systems.

Optimal control problem for head injury criterion

The optimal control of the deceleration of a particle moving along a straight line after an impact against a surface covered with an impact isolation coating is considered. The force applied to the particle by the surface is treated as the control variable, that is, the control force replaces the coating. The deceleration distance is minimized under the constrained value of the HIC functional - an integral criterion that is utilized in engineering biomechanics to evaluate the expected severity of impact-induced head injury of a human being. The solution indicates the limiting capabilities of the prevention from the head injuries in the case of traffic accidents, falling, or other occurrences by means of an appropriate coating of the surface against which impacts can occur.

Impact isolation limiting performance analysis for three-component models

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.