Sensorless Pedalling Torque Estimation Based on Motor Load Torque Observation for Electrically Assisted Bicycles

Abstract

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.

Torque Measurement and Control for Electric-Assisted Bike Considering Different External Load Conditions

“…References Torque control for assisted E-bike [1,2,24,38,39] Instantaneous pedaling torque waveform [4][5][6][7] Pedaling torque component analysis [8][9][10][11][12][13][14] Factors affecting riding [15][16][17][18][19][20][21][22][23][25][26][27][28][29][30][31][32][33][34][35]] Recharge control for assisted E-bike [36,37] To overcome these limitations on existing E-bike assisted torque control, this paper's motivation is to find the best-suited assisted torque considering external loads. It is shown that the overall cycling torque is affected by external loads, including the cyclist's weight, wind resistance, rolling resistance, and the road slope.…”

“…In addition, Figures 26 and 28 compare the waveforms of the pedaling T pdl , motor T M , and total T total under the dynamic SPPT and DPPT control methods, respectively. Since the motor torque T M is dynamically controlled under the SPPT and DPPT methods, T M is calculated proportionally to the measured pedaling torque T pdl for the SPPT method in (14) and the DPPT method in (15).…”

“…The pedaling torque might not fully contribute to the E-bike's wheel torque. As reported in [8][9][10][11][12][13][14], an effective pedaling torque can be different depending on different crank positions.…”

“…The sources in [ 1 , 2 , 24 , 38 , 39 ] aim to design suitable torque controllers for assisted E-bikes; however, no further analysis of the influence of the cyclist’s pedaling torque was addressed. By contrast, [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ] investigate the cyclist’s pedaling dynamic with no motor-assisted torque assumed. Moreover, [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ] focus on E-bike cycling performance with respect to human behaviors, including heartbeat, gender, and weight.…”

“…Similarly, Figures 28 and 29 illustrate the corresponding measurements of torque and bike dynamics collected under the DPPT condition.In addition, Figures26 and 28compare the waveforms of the pedaling T , motor T , and total T under the dynamic SPPT and DPPT control methods, respectively. Since the motor torque T is dynamically controlled under the SPPT and DPPT methods, T is calculated proportionally to the measured pedaling torque T for the SPPT method in(14) and the DPPT method in(15).It is noted that for the DPPT method, the time-domain waveform of the motor torque T is delayed by 90° with respect to the measured pedaling T . Considering the same…”