Synthesis and verification of motor-transmission shift controller for electric vehicles

Motor transmission-based drive systems are attractive for electric vehicles but, as the motor is directly connected to the transmission shaft which meshes with the gears, controlling gear shifts is challenging. In this paper, we present a methodology for synthesis and verification of open-loop optimal control of the electric motor in a motor-transmission drive system. The key steps in this methodology are (a) developing a continuous-time model of the trajectory of the sleeve during the meshing process based on appropriate coefficients of restitution, (b) discrete-time controller synthesis for finitely many initial states using model predictive control (MPC) and (c) verification of the synthesized controller for a higher-fidelity continuous time hybrid automaton model. First, we develop a model of the motor-transmission drive system as a continuous-time hybrid automaton (CHA) with uncertain initial states. Next, this model is transformed to a piece-wise affine (PWA) form for solving an optimal control problem using the multi-parametric toolbox (MPT). Finally, the delay bound for the synthesized controller is verified by computing a bounded time over-approximation of the reach set using an existing algorithm for deterministic linear hybrid automata. Our results show that on the average our synthesized controller can shorten the meshing duration by 71.05% and reduce impacts impulse by 85.72% compared to an existing controller and the sleeve can mesh with the gear within a desired time from every initial state.