Real-time estimation of rollover index for tripped rollovers with a novel unknown inputs nonlinear observer

In rollover prevention systems, a traditional rollover index can detect only un-tripped rollovers that happen due to high lateral acceleration from sharp turns. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. In order to develop a new rollover index that can detect both tripped and un-tripped rollovers, state estimation in the presence of unknown disturbance inputs is required. Therefore, this paper develops a methodology for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of bounded Jacobian nonlinear systems with unknown inputs. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8^th scaled vehicle. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both un-tripped and tripped rollovers.