Reducing rider effort for electric bicycles by environment disturbance compensation

Mammar, Said; Oufroukh, Naima Ait; Glaser, Sebastien · 2011 · Crossref

DOI: 10.1109/cca.2011.6044379

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Summary

This paper addresses the limitation of current electric bicycle (EB) power assistance systems, which typically provide support proportional only to rider effort while ignoring environmental disturbances such as road slope and friction. The authors argue that this approach is unsuitable for varied terrains, particularly in European cities with significant relief, as it fails to compensate for gravitational and frictional forces, potentially affecting stability and rider comfort. To solve this, the study proposes a robust estimation method to reconstruct these environmental disturbances, allowing the electric motor to actively compensate for them rather than merely reacting to rider input. The methodology involves designing a Proportional Two Integrals (P2I) observer to estimate the unknown environmental disturbance, defined as the sum of gravitational drag and static rolling resistance. The authors model the longitudinal dynamics of the electric bicycle, coupling mechanical equations with electric DC motor dynamics. The observer is synthesized using Linear Matrix Inequality (LMI) conditions to ensure robustness against parameter variations, including changes in rider mass and motor characteristics, while attenuating the effect of the disturbance’s second derivative on estimation error. The design assumes that the second derivative of the disturbance is bounded and that the human thrust force is measurable. The proposed observer was validated through simulations under three conditions: nominal conditions with a reference disturbance profile, a real-world 3 km itinerary near Versailles, France, and scenarios with significant parameter variations. In nominal tests, the observer accurately reconstructed the disturbance with an estimation error of less than 0.05 N. When tested on the real road slope profile, the estimated disturbance closely matched the actual environmental force, with a mean estimation error of $4 \times 10^{-3}$ N and a relative error consistently below 1%. Under parameter variations, where the total mass increased to 130 kg and motor parameters varied by up to 20%, the observer maintained performance, keeping the estimation error mostly under 4 N, with a maximum peak error of 6 N. The significance of this work lies in demonstrating that environmental disturbances can be robustly estimated and compensated for in real-time, even with parameter uncertainties. By using the estimated force to actuate the electric motor, the system can provide more adaptive and stable assistance, overcoming the limitations of basic proportional assistance strategies. This approach enhances the usability of electric bicycles in urban environments with variable terrain, ensuring consistent performance regardless of rider weight or road grade.

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