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

Abstract

This paper proposes a novel torque measurement and control technique for cycling-assisted electric bikes (E-bikes) considering various external load conditions. For assisted E-bikes, the electromagnetic torque from the permanent magnet (PM) motor can be controlled to reduce the pedaling torque generated by the human rider. However, the overall cycling torque is affected by external loads, including the cyclist's weight, wind resistance, rolling resistance, and the road slope. With knowledge of these external loads, the motor torque can be adaptively controlled for these riding conditions. In this paper, key E-bike riding parameters are analyzed to find a suitable assisted motor torque. Four different motor torque control methods are proposed to improve the E-bike's dynamic response with minimal variation in acceleration. It is concluded that the wheel acceleration is important to determine the E-bike's synergetic torque performance. A comprehensive E-bike simulation environment is developed with MATLAB/Simulink to evaluate these adaptive torque control methods. In this paper, an integrated E-bike sensor hardware system is built to verify the proposed adaptive torque control.

Keywords: E-bike cycling quality; E-bike pedaling power; electric-assisted bicycle; permanent magnet motor; two-wheeler simulation.

Figure 1

Relationship between crank position and pedaling torque: (a) pedaling torque component ${\mathrm{F}}_{\mathrm{p}\mathrm{y}}$/${\mathrm{F}}_{\mathrm{p}\mathrm{x}}$ and crank position; (b) pedaling torque with respect to the crank position (no horizontal pedal force is assumed for simplicity).

Figure 2

Block diagram of E-bike torque management signal process.

Figure 3

Free-body diagram of E-bike system with external loads.

Figure 4

Analysis of wheel friction torque in E-bike.

Figure 5

Analysis of windage torque in E-bike.

Figure 6

Analysis of climbing-reflected torque.

Figure 7

Block diagram of E-bike model control process.

Figure 8

Simulation of pedaling torque versus time under 30 cpm cadence.

Figure 9

Bike dynamics based on NMT: (a) wheel angular acceleration; (b) wheel angular speed.

Figure 10

Torque comparison under the CT method.

Figure 11

Bike dynamics based on CT: (a) wheel angular acceleration; (b) wheel angular speed.

Figure 12

Torque comparison under the SPPT method.

Figure 13

Bike dynamics based on SPPT: (a) wheel angular acceleration; (b) wheel angular speed.

Figure 14

Torque comparison under the DPPT method.

Figure 15

Bike dynamics based on DPPT: (a) wheel angular acceleration; (b) wheel angular speed.

Figure 16

Torque comparison under the CGPT method.

Figure 17

Bike dynamics based on CGPT: (a) wheel angular acceleration; (b) wheel angular speed.

Figure 18

E-bike experimental test setup and sensor hardware installation.

Figure 19

Hardware setup and signal process for E-bike torque control experiment.

Figure 20

Electrical circuit of six-switch motor drive inverter.

Figure 21

Photograph of motor drive inverter.

Figure 22

Torque comparison under the NMT.

Figure 23

NMT-reflected E-bike response: (a) wheel angular acceleration and (b) wheel angular speed.

Figure 24

Torque comparison under CT control.

Figure 25

CT-reflected E-bike response: (a) wheel angular acceleration and (b) wheel angular speed.

Figure 26

Torque comparison under SPPT control method.

Figure 27

SPPT-reflected E-bike response: (a) wheel angular acceleration and (b) wheel angular speed.

Figure 28

Torque comparison under DPPT control method.

Figure 29

DPPT-reflected E-bike response: (a) wheel angular acceleration and (b) wheel angular speed.

Figure 30

Torque comparison under CGPT control method.

Figure 31

CGPT-reflected E-bike response: (a) wheel angular acceleration and (b) wheel angular speed.

Figure 32

Graphical conclusion of proposed E-bike torque control.