An Improved Torque Sensorless Speed Control Method for Electric Assisted BicycleW ith Consideration of Coordinate Conversion

Tinghua Li,Qinghua Yang,Xiaowei Tu,and Bin Ren

Abstract—In this paper, we propose an improved torque sensorless speed control method for electric assisted bicycle, this method considers the coordinate conversion. A low-pass filter is designed in disturbance observer to estimate and compensate the variable disturbance during cycling. A DC motor provides assisted power driving, theassistancemethod is based on the realtime wheel angular velocity and coordinate system transformation. The effect of observer is proved, and the proposed method guarantees stability under disturbances. It is also compared to the existing methods and their performances are illustrated through simulations.The proposed method improves the performance both in rapidity and stability.

I.In t roduction

W ITH the improvementof modern life, people paymore and more attention to health and personal safety.Almost every country has been calling for green traveland the shared bicycles are very popular in all big cities around the world,likeofo bicycleand mobike[1].So the development of intelligent bicycles must be an important trend in the future [2].

Traditional bicycles are w idely used in our daily life as an individual transportation tool,which hasamerit to relieve the traffic pressure.Although bicycle travel is very environmental friendly,there are still some lim itations.Since traditional bicycle is completely driven by cyclist,if the road is in a poor condition w ith various geometric complexity,the torque output by the cyclistmay decrease as well as the speed of bicycle.Besides,it w illbe very laborious for people to rideon an uphill road.

Once lacking of the power of human input,the bicyclew ill not maintain running. As far as this major drawback is concerned, man-powered bicycles are not as good as electric bicycles.

Electric bicycle equipped w ith motor can solve this problem.The energy expenditure of riding an electric bicycle was 31%lower than the conventional bicycle on the uphill[3].It has greatly extended the scope of application for traditional bicycle by providing assisted power w ith amotor[4]?[6]. Nowadays,electric bicycle has become one of the main vehicles in theworld.Compared w ith the other vehicles powered by gasoline,electric bicycle can reduce the energy consumption,the air pollution and noise[7].As we can see from Liet al.[8],the emissions of pollutants by electric bicycles per person per kilometer are several times smaller than those by motorcycles and cars,more or less equivalent to thoseby buses,and higher than thoseby bicycles.

For electric bicycles,cyclist can control the outputof motor by adjusting the power controller to adapt different road conditions or individual preferences.However,electric bicycle also has its limitations.Since the cyclist can control themotor freely,the speed of electric bicycles may be too fast to be safe.Itnotonly affects the service life of themotor, but also increasespollution.

Moreover,electric bicycles are heavy,when the motor runs out of electricity,itw ill be very hard for people to ride w ith hisown human power.

In order to protect the environment aswellas to achieve the assisted riding,the electric bicycle equipped w ith torque sensorhasbeen produced.The sensor detects the pedal torque and converts it into an electrical signal,which is the input for themotor controller[9].However,the torque sensor may be easily damaged since it contactsw ith the cyclist’s feet directly and the damage costsarenot negligible[10].

Besides,the emerging development of connected and automated vehicles imposesa significant challenge on current vehicle control systems[11].

To solve the problemsmentioned above,the bestway is to design a torque estimation method to measure the pedaling torque in real time and provide assistance[12],[13].

Nikiet al.[14] proposed a torque separation method based on high pass filter,they used high pass filter (HPF)to separate the human torque input from running friction.In 2015,Sankaranarayanan and Ravichandran[15]designed a torque sensorless controller for bicycles, but they did not take the disturbance force during cycling into account.The Fourier filtering was also applied to decouple the load torque and pedaling torque[16].

In 2017,Fukushimaland Fujimoto[17] presented amethod for pedaling torque estimation using the recursive leastsquare algorithm w ithmultiple forgetting factors and they considered the condition for travelling on upward aswell.In 2018,Ralloet al.[18]measured the wheel speed w ith a magnetic wheel encoder and showed that the pedaling cadence is correlated w ith the speed oscillation.

In addition,Bertucciet al.[19]analyzed the crank torque in road cycling on level and uphill, and the results show that when the pedaling cadences are the same, the crank torque profile differencesareminimal between levelground and uphill road.In thisway,we can see that themain factor affecting pedaling torque is cadences.The inertialmeasurementunit isalso used to detect the angular velocity [20],[21].

Nevertheless, none of them focused on the speed control.The purposeof electric assistance is to keep the speed w ithin a certain range in all circumstances.And it is worthwhile to note that although the inertial measurement unit was used,none of the above papers considered the coordinate conversion of angular velocity.

Sim ilarly to the inertial navigation,in order to obtain the accurate positions,angular velocity based on the inertial coordinate system needs to be converted to another coordinate,which is consistent w ith the movement of the bicycle.For instance, Nilssonet al.[22] presented an opensourcew ireless foot-mounted inertial navigation modulew ith an intuitive and significantly simplified dead reckoning interface,which can display the data after coordinate conversion.

Disturbance observer is often used to elim inate the effects of interference on system control,considering that there are many kindsof disturbancesduring cycling [23].

Therefore,in order to achieve a safe and convenient riding,it is very important to design an improved highly accurate speed control method for electric bicycles.

This paper proposes an improved speed control method for the electric assisted bicycle. A second-order low-pass filter is designed in disturbance observer to estimate and compensate disturbances during cycling.The quaternionmethod isused to convert the coordinateand users can set a motor auxiliary ratio which is variable w ith the real-time speed of bicycle.The result finally comes out that the speed can be self-adaptively stabilized in a set safety range despite of the disturbances during cycling.

The rest of the paper is organized as follows.Section II describes the dynam ic model of the electric assisted bicycle system.In Section III, the quaternion method is used to recoordinate the angular velocity which ismeasured by inertial measurement units(IMU).Besides,we simplify the calculation of pedaling torque.Section IV presents the design of low-pass filter(LPF)in disturbance observer to estimate and compensate the disturbances during riding.Section V is the introduction of motor assisted control.The stability of the proposed method is analyzed in Section VI.Simulation and results comparison are presented in Section VII.Finally,some conclusionsare drawn and summarized in Section VIII.

Table Ilists the acronymsand symbolsexplanations used in this paper.

TABLE I List of Pa rameter

II.System M odel ing

Assuming that an electric assisted bicycle is running on an uphill road,the longitudinal dynam ic model of the electric bicycle is shown in Fig.1 and the forces during riding are indicated.We consider a rear-wheel-assisted electric bicycle,themotor is installed on the rear wheel,so as to collect the angular velocity and provideassisted power directly.

Fig.1.Electric assisted bicyclemodel.

Fig.2.Uphill road riding.

Fig.3.Block diagram of a transfer function.

III.Coor dina te Conversion

Fig.4.Chain transmission model of theelectric bicycle.

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IV.Obser ver Design

As wementioned in Section II,the electric bicycle w ill be disturbed by many kindsof frictions during riding.This paper mainly considers three kinds of frictions,namely the friction between tires and road,thew ind resistance and the impedance force due to thegravitational potentialenergy.

On the basis of kinematic model,Huanget al.[26]used a sensor fusion algorithm as an observer.In this paper,in order to compensate the disturbances of frictions during riding,a disturbance observer is used to estimate the interference,as shown in Fig.5[27].Considering the variability of frictions,we seta special cut-off frequency in LPF so that themajority of disturbances can beobserved and compensated.

Fig.5.Block diagram of the proposed method.

Fig.6.The second-order low-pass filter (LPF).

Fig.7.Theamplitude-frequency characteristic of LPF.

Fig.8.Disturbanceand observation.

Fig.9 captures and amplifies the waveforms from 0.6 s to 2 s.The two dashed lines indicate the amplitude values of the waveform vertexes respectively.It is clear that the difference in amplitude is 0.4,which proves that the observer can estimate themajority of disturbance.

Fig.9.Difference between disturbance and observation.

V.M otor-Assisted Con t rol

To achieve the purpose of the assisted riding,a permanent magnet brushless DC motor isused in this paper and installed in the rear wheel.

When the riding speed decreases and riding becomesmore laborious,themotor can provide assistance based on the realtime angular velocity of wheel.As shown in Fig.5,is fed

Fig.10. Auxiliary coefficient.

Because of the gear transmission between motor and the rear wheel, the formula of speed transm ission can be expressed as

VII.Simu lation

Fig.11. Angular velocity before transformation.

Besides,the dynam ic parameters used in simulation are shown in Table II.

TABLE II Simu la tion Parameter Va lues

Fig.12.Angular velocity after transformation.

Fig.13.Pedaling torque.

Accordingly,them inimum limited angular velocity for the wheel can be set to 10 rad/sand the maximum limit is13 rad/s.If the wheelangular velocity is lower than 10 rad/s,the motor and manpower w ill provide power together by the ratio of 1:1.If the wheel angular velocity is higher than 13 rad/s, motor w ill be reversed,so as to avoid danger.

The angular velocity variation curves of the rearwheel are shown in Figs.14 and 15.

Fig.14. Angular velocity of the wheel in previousmethods.

Fig.15. Angular velocity of wheel in previousand new proposed methods.

Three kinds of methodsare simulated in our system,two of which are the previousmethod.A low pass filter is used in method 1.In method 2,low pass filterand band pass filterare used in combination to estimate disturbance and human pedaling torque.

In Fig.14,the dotted line indicates the result of previous method 1,and the solid line represents the previousmethod 2.After setting the same safety angular velocity range for both of methods, the rapidity of method 2 is faster but fluctuation is more turbulent.

Fig.15 shows the contrast curve between the results of this paper and the previous method 1.It can be seen that they can both well control the angular velocity but the rapidity and stability are not the same.Obviously,themethod proposed in this paper ismuch faster and more stable,it takes reaction in the first 5 seconds.

As the cyclist begins to step on,theangular velocity value is the largest at the beginning in Fig.15.When the value exceeds 13 rad/s, motor w ill turn to the reverse direction to decrease the value and the curvew illshow a downward trend.Later,when the value is between 10 rad/s and 13 rad/s,the curve rises up due to themotor’sassistance.

W ith the control and assistance,we can see clearly that the wheel angular velocity can still be effectively stabilized in a safe range,even though there are disturbances such as frictions and slopes during riding,so the same as the velocity of an electric bicycle.

VIII.Conc lusion

The contribution of this paper lies in the presenting of an improved speed control method for the electric assisted bicycle w ithout torque sensor installed.

On the basis of dynam ic model system,we combine the disturbance observer,coordinate transformation and motor assistance to realize the speed control.

Based on the simulation resultsabove,the proposedmethod can wellestimate and compensate themajority of disturbances during cycling,and improve the measurement and control accuracy by means of coordinate system conversion.Finally,the bicycle speed can be intelligently stabilized w ithin a safe range w ith the motor assistance.

Compared w ith the previous methods,this new proposed method has a higher rapidity and stability than that of the previous methods.Meanwhile,the stability of themethod is also analyzed.It further validates that the speed control method can not only assist the cycling under different road conditions,but also improve the accuracy.