The need for reducing the cost of and space in Electrically Assisted Bicycles (EABs) has led the research to the development of solutions able to sense the applied pedalling torque and to provide a suitable electrical assistance avoiding the installation of torque sensors. Among these approaches, this paper proposes a novel method for the estimation of the pedalling torque starting from an estimation of the motor load torque given by a Load Torque Observer (LTO) and evaluating the environmental disturbances that act on the vehicle longitudinal dynamics. Moreover, this work shows the robustness of this approach to rotor position estimation errors introduced when sensorless techniques are used to control the motor. Therefore, this method allows removing also position sensors leading to an additional cost and space reduction. After a mathematical description of the vehicle longitudinal dynamics, this work proposes a state observer capable of estimating the applied pedalling torque. The theory is validated by means of experimental results performed on a bicycle under different conditions and exploiting the Direct Flux Control (DFC) sensorless technique to obtain the rotor position information. Afterwards, the identification of the system parameters together with the tuning of the control system and of the LTO required for the validation of the proposed theory are thoroughly described. Finally, the capabilities of the state observer of estimating an applied pedalling torque and of recognizing the application of external disturbance torques to the motor is verified.

This paper presents an improvement of sensorless techniques based on anisotropy for the estimation of the electrical angular position of synchronous machines by means of an iterative algorithm. The presented method reduces the effect of the fourth saliency harmonics on the measured signals avoiding the use of an observer or filter, thus, no additional dynamics are introduced on the system. Instead, a static algorithm based on iterative steps is proposed, minimizing the angular position error. The algorithm is presented and applied using the DFC (Direct Flux Control) technique but it is not limited to this choice. The advantages and limitations of this method are presented within this paper. The proof of the algorithm convergence is given. Simulations and experimental tests are performed in order to prove the effectiveness of the proposed algorithm.