Hybrid optimal control of an electric vehicle with a dual-planetary transmission

Abstract A hybrid systems framework is presented for the analysis and optimal control of an electric vehicle equipped with a seamless dual stage planetary transmission. A feature of special interest is that, due to the perpetual connectedness of the motor to the wheels via the seamless transmission, the mechanical degree of freedom changes during the transition period. These circumstances where autonomous and controlled state jumps at the switching instants are accompanied by changes in the dimension of the state space are reflected in the definition of hybrid systems and the corresponding statement of the Hybrid Minimum Principle (HMP). Furthermore, the state-dependent motor torque constraints which impose mixed input-state constraints are converted to state-independent input constraints via a change of variables and the introduction of auxiliary discrete states. Optimal control problems for the minimization of acceleration duration and the minimization of energy consumption for the acceleration task are formulated within the presented framework and simulation results are presented for the optimal control inputs and the optimal gear changing instants for reaching the speed of 100 k m / h r from the stationary initial condition. A phenomenon of note that appears in the dynamical evolution of the vehicle is the presence of power regeneration as a part of the acceleration task for the minimization of the energy consumption.

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