Non-Uniform Velocity Profile Compensation for an Electric Bicycle Based on Repetitive Control With Sinusoidal and Non-Sinusoidal Internal Models

This paper considers the application of repetitive control in improving the comfort of electric bicycle riders under uphill riding condition. A particular problem addressed is the nonuniform torque input from the rider. The human torque input can be decomposed into two parts: the DC or near-DC local average torque and the fluctuating torque. The latter is due to nonuniform pedal torque production by the rider and is near periodic. It makes the acceleration and the velocity of the bicycle non-uniform, which is pronounced at low speeds. This makes uphill climbing a difficult task for the rider. Repetitive control will be used in this paper to compensate for this component during low speed uphill riding. We will consider both sinusoidal and non-sinusoidal periodic models for the non-uniform torque generated by the rider. The time-varying characteristic of the rider input will be dealt with by both time domain and pedal-angle domain methods. Simulation results for both cases will be shown and compared.