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This paper proposes an optimization-based transmission gear shifting strategy for electrified powertrains with a transmission. With the demand for reduced vehicle emissions, electrified propulsion systems have garnered significant attention due to their potential to improve vehicle efficiency and performance. An electrified propulsion system architecture of significance includes multiple electric motors and a transmission where some driveline actuators can transmit torque through changing gear ratios. If there is at least one electric motor arranged before the input of the transmission and at least one after the transmission output, a unique design opportunity arises to shift gears in the most energy efficient manner.

This paper delves into the investigation of flatness-based active damping control for hybrid vehicle transmissions. The main objective is to improve the current in-production controller performances without the need for additional sensors or observers. The primary goals include improving torque setpoint tracking, enhancing robustness margins, and ensuring zero steady-state torque correction. The investigation proceeds in several steps: Initially, both the general differential flatness property and the identification of flat outputs in linear dynamical systems are revisited. Subsequently, the bond graph formalism is employed to deduce straightforwardly the dynamical equations of the system. Next, a new flat output of the vehicle transmission is identified and utilized to formulate the trajectory tracking controller to align with the required control objectives and to fulfill the system constraints.

Through real-time online optimization, the full potential of the performance and energy efficiency of multi-gear, multi-mode, series–parallel hybrid powertrains can be realized. The framework allows for the powertrain to be in its most efficient configuration amidst the constantly changing hardware constraints and performance objectives. Typically, the different gears and hybrid/electric modes are defined as discrete states, and for a given vehicle speed and driver power demand, a formulation of optimization costs, usually in terms of power, are assigned to each discrete states and the state which has the lowest cost is naturally selected as the desired of optimum state. However, the optimization results would be sensitive to numerical exactitude and would typically lead to a very noisy raw optimum state. The generic approach to stabilization includes adding hysteresis costs to state-transitions and time-debouncing.