Optimal control of drop-induced shock mitigation using magnetorheological energy absorbers considering quadratic damping

The optimal control of a magnetorheological energy absorber (MREA) shock mitigation system is investigated considering quadratic damping in the MREA. To this end, the equation of motion of a single-degree-of-freedom (SDOF) shock suspension system using an MREA with quadratic damping is analyzed. To achieve a soft landing and to maintain stroking load below a maximum allowable value, it is required that the payload comes to rest after fully utilizing the available stroke. For low sink rates, a generalized Bingham number (quadratic) or GBN-Q control algorithm is developed that achieves a soft landing by selecting an initial magnetorheological (MR) force level or generalized Bingham number (GBN) for the quadratic damping at the initial sink rate. To cope with the cases above a critical sink rate, where the deceleration exceeds a maximum allowable threshold when using the GBN-Q control only, a minimum duration deceleration exposure-quadratic (MDDE-Q) controller is developed. This controller seeks to maintain the stroking load at its maximum allowable threshold until the payload slows such that the GBN-Q controller can be used to achieve the soft landing condition. The switching methodology between the GBN-Q controller and the MDDE-Q controller is discussed. Each control method relies on an optimal GBN that is computed to ensure a soft landing. Results show that the MDDE-Q controller can successfully minimize the exposure of the payload to the maximum allowable stroking load.