Gear-shifting in a novel modular multi-speed transmission for electric vehicles using linear quadratic integral control

The efficiency of electric vehicles (EVs) can be improved by applying multi-speed transmissions (MSTs), while ensuring that gear-shifting is swift and smooth. This paper establishes a gear-shifting control algorithm for a novel MST, with the advantages of simplicity and modularity, designed for EVs. Firstly, the mathematical model of the proposed MST is derived. Next, the control algorithm developed for gear-shifting is clarified, which guarantees seamlessness and swiftness. The system under study is over-actuated, with end constraints on some control inputs. Therefore, for acceleration and jerk continuity, while satisfying the input terminal constraints, one input is suggested to be changed independently, based on a 2-3 blending polynomial. Then, the new fully-actuated system is controlled using a linear quadratic integral (LQI) controller, which is an extension of the linear quadratic regulator (LQR) for tracking problems. Simulation results indicate the effectiveness of the proposed control algorithm in the presence of unknown external disturbances.