Optimal assistive control of a pedal-electric drive unit

Highlights

• Travel Range of Pedelecs depends on elevation, motor support, and cyclist’s fitness.

• Nonlinear model predictive controller chooses an optimal level of assistance.

• Elevation profile and cyclist’s fatigue are taken into account.

• The proposed Battery management guarantees a user-defined state of charge.

Abstract

The distance that an electrically powered bicycle can cover depends on factors such as the route’s elevation profile, the motor support selected, and the fitness of the cyclist. This fact requires the cyclist to estimate which motor support may be chosen to reach the goal with the battery’s current state of charge. For this reason, we propose a battery management control system based on a nonlinear model predictive controller (NMPC) for pedal-electric drive units (Pedelecs) that takes into account route information and cyclist fatigue. The goal is to guarantee a user-defined state of charge (SoC) at the end of the route while minimizing cyclist fatigue. The degree of support of the Pedelec is considered as the manipulated variable. In order to find an optimal level of assistance, the NMPC minimizes a quadratic cost function that is subject to three nonlinear distance-dependent models. The first two models describe the bicycle dynamics and the discharge behavior of the battery. To obtain an estimate of the maximum voluntary force that the cyclist can apply, the third model describes the cyclist’s fatigue. The identified models and the control strategy are validated with a trekking Pedelec on a 33 km test track. The proposed NMPC is able to guarantee a predefined target SoC at the end of the track while keeping the estimated cyclist’s fatigue low.

Introduction

Traffic congestion, high particulate emissions, and noise pollution in urban areas are challenges that are becoming increasingly important worldwide. For example, between 1999 and 2019 the annual vehicle miles driven in the USA increased by 22% (Administration, 2019). To meet the challenges of increasing urban traffic such as air pollution, fossil fuel scarcity, and noise pollution, electric mobility concepts have recently been introduced. Electrically assisted bicycles play an important role in modern urban mobility concepts, especially for short to medium distances. The fact that these bicycles are powered by electrical energy in combination with human power leads to a vehicle concept that, on the one hand, does not cause noise and air pollution during the ride and, on the other hand, offers a health and fitness component for the cyclist.

A challenge with e-bikes is the estimation of the range, as this depends not only on the size of the battery and the motor’s efficiency but also on the altitude profile of the track, the level of motor assistance and the fitness of the cyclist. In today’s e-bikes, range estimation is usually done by assuming an average power consumption for the route ahead without including track information or the cyclist’s fatigue. Thus, the cyclist needs to choose the level of motor support himself by estimating the elevation profile of the route ahead and his fitness capacity in order to arrive at his destination with the remaining battery charge.

Battery management control strategies for electric and hybrid-electric cars, in general, have been investigated in many studies (e.g. Kim et al., 2011, Park and Lee, 2019, Schwickart et al., 2014, Yu et al., 2016, Yu et al., 2014), but only a few have examined the battery management in electric-assisted bicycles. Those studies that do consider electric-assisted bicycles, however, almost exclusively examine bicycles with energy recuperation (e.g. Corno et al., 2016, Guanetti et al., 2017, Wan et al., 2014). Guanetti et al. for example, present an optimal control approach for a series Hybrid Electrical Bicycle which has no mechanical link between the pedals and the wheel (Guanetti et al., 2017). They aim to minimize physical exertion while simultaneously guaranteeing a predetermined electric range. Nevertheless, most electric-assisted bicycles on the roads today do not support recuperation and provide motor assistance only when the cyclist is pedaling. For that reason, the main subject of interest in this study are pedal-electric drive units (Pedelecs) which are characterized by a maximum continuous rated power of 250 W and motor assistance up to a velocity of 25 $\frac{\text{km}}{\text{h}}$. To the best of the author’s knowledge, there is no study that provides a control strategy for the level of support for Pedelecs that considers the remaining battery or the cyclist’s fatigue. Most studies control strategies consider only the load torque and the current road slope to select the level of support (Deyi et al., 2017, Gromba, 2018).

There are a few studies (e.g. Fayazi et al., 2013, Wan et al., 2014) addressing optimal pacing problems with dynamic programming (DP). However, a well-known problem with DP is the curse of dimensionality (Powell, 2007). For example, in Fayazi et al. (2013), a 168 km test track requires 34 GB of random-access memory (RAM) and 11.75 h of simulation time. In this paper, we propose a novel battery management control strategy based on a nonlinear Model Predictive Controller (NMPC), which enables a new intelligent driving mode for Pedelecs. MPCs are not affected by the curse of dimensionality and they can be calculated in real-time. This fact allows it to take model uncertainties into account such as different ground, driver and wind conditions and spontaneously changing routes. Finally, the MPC approach allows a combination of the newly developed driving mode with real-time navigation. The goal of the suggested NMPC is to reach a selected destination with a predefined remaining State of Charge (SoC) by setting optimal motor assistance during the ride with regard to the altitude profile and the cyclist’s fatigue. The optimal motor assistance is calculated by taking three different models into account, which are derived in Section 2. Section 3 follows with the implementation of the NMPC. In Section 4, simulation and experimental results are shown and discussed. Finally, a conclusion and outlook is given in Section 5.