Simultaneous observation of hybrid states for cyber-physical systems: a case study of electric vehicle powertrain

As a typical cyber-physical system (CPS), electrified vehicle becomes a hot research topic due to its high efficiency and low emissions. In order to develop advanced electric powertrains, accurate estimations of the unmeasurable hybrid states, including discrete backlash nonlinearity and continuous half-shaft torque, are of great importance. In this paper, a novel estimation algorithm for simultaneously identifying the backlash position and half-shaft torque of an electric powertrain is proposed using a hybrid system approach. System models, including the electric powertrain and vehicle dynamics models, are established considering the drivetrain backlash and flexibility, and also calibrated and validated using vehicle road testing data. Based on the developed system models, the powertrain behavior is represented using hybrid automata according to the piecewise affine property of the backlash dynamics. A hybrid-state observer, which is comprised of a discrete-state observer and a continuous-state observer, is designed for the simultaneous estimation of the backlash position and half-shaft torque. In order to guarantee the stability and reachability, the convergence property of the proposed observer is investigated. The proposed observer are validated under highly dynamical transitions of vehicle states. The validation results demonstrates the feasibility and effectiveness of the proposed hybrid-state observer.