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Research Papers

Determination of Motor Torque for Power-Assist Electric Bicycles Using Observer-Based Sensor Fusion

[+] Author and Article Information
Chun-Feng Huang

Department of Power Mechanical Engineering,
National Tsing Hua University,
Hsinchu 30013, Taiwan
e-mail: benson516@hotmail.com

Bang-Hao Dai

Department of Power Mechanical Engineering,
National Tsing Hua University,
Hsinchu 30013, Taiwan
e-mail: spring9527@gmail.com

T.-J. Yeh

Professor
Department of Power Mechanical Engineering,
National Tsing Hua University,
Hsinchu 30013, Taiwan
e-mail: tyeh@pme.nthu.edu.tw

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 18, 2017; final manuscript received December 22, 2017; published online March 28, 2018. Assoc. Editor: Ardalan Vahidi.

J. Dyn. Sys., Meas., Control 140(7), 071019 (Mar 28, 2018) (11 pages) Paper No: DS-17-1035; doi: 10.1115/1.4039280 History: Received January 18, 2017; Revised December 22, 2017

This paper proposes a sensor fusion algorithm to determine the motor torque for power-assist electric bicycles. Instead of using torque sensors to directly measure the pedaling torque, outputs from a wheel encoder and a six-axis inertial measurement unit (IMU) are processed by the fusion algorithm to estimate the slope angle of the road and the longitudinal acceleration of the bicycle for conducting mass compensation, gravity compensation, and friction compensation. The compensations allow the ride of the electric bicycle on hills to be as effortless as the ride of a plain bicycle on the level ground regardless of the weight increase by the battery and the motor. The sensor fusion algorithm is basically an observer constructed on the kinematic model which describes the time-varying characteristics of the gravity vector observed from a frame moving with the bicycle. By exploiting the structure of the observer model, convergence of the estimation errors can be easily achieved by selecting two constant, subgain matrices in spite of the time-varying characteristics of the model. The validity of the sensor fusion is verified by both numerical simulations and experiments on a prototype bicycle.

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References

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Figures

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Fig. 2

Coordinate definitions of Euler angles

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Fig. 1

Schematic of an E-bike in the sagittal plane

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Fig. 4

An iterative scheme for estimating centrifugal acceleration

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Fig. 15

Comparisons between the power-assist bike and non-power-assist bike in a road-riding test. Time zone 1: the bike is accelerating; time zone 2: the bike is climbing a hill; time zone 3: the bike is turning left.

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Fig. 16

Schematic of the modified bicycle model with two lumped masses and spring-damper connection

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Fig. 3

Simplified two-dimensional bicycle model

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Fig. 5

Estimation of longitudinal acceleration and pitch angle when the linear acceleration is a mixture of two sinusoids with DC bias

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Fig. 6

Estimation of longitudinal acceleration and pitch angle when the linear acceleration is a pulse train

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Fig. 7

Estimation of longitudinal acceleration and pitch angle when the linear acceleration is a sawtooth waveform

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Fig. 12

Yaw rate and velocity responses for centrifugal acceleration compensation

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Fig. 13

Y and Z components of the estimated centrifugal acceleration

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Fig. 8

Actual and approximated values of the yaw rate and components of centrifugal acceleration

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Fig. 9

Estimated pitch angle and roll angle with the centrifugal acceleration compensation

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Fig. 10

Estimated pitch angle and roll angle without centrifugal acceleration compensation

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Fig. 11

Photo of the power-assist electric bicycle

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Fig. 14

Pitch and roll angles for centrifugal acceleration compensation

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