Virtual-bike control for a series human-powered electric bike via internal model control

Electric bikes (e-bikes) play an important role in the transition toward more sustainable mobility. Among the various powertrain architectures, series e-bikes – where human power is converted into electrical energy via a generator and then used to propel the vehicle – offer unique control challenges and opportunities due to the absence of a mechanical chain. A prior control strategy is the virtual-chain control, aimed to emulate the behavior of a mechanical chain through a bilateral control of the motor and the generator. Thanks to its extension to the virtual-bike framework, it is possible to mimic the entire longitudinal dynamics of a traditional bike, tuning the virtual chain ratio, the virtual mass and the virtual friction. Due to the limitations of both the first version of the virtual-bike and the self-tuned one, in this work, we reinterpret the virtual-bike within the framework of internal model control (IMC), using a linearized parameter-varying model. In the experimental validation, we showed that, although all approaches track the virtual-bike reference with a root mean square error (RMSE) below 1 km/h, the best performance is achieved by the proposed IMC-based approach, reaching an RMSE below 0.3 km/h, but IMC is the only one providing robustness in all tested conditions.