Self-Equilibrium Control on a Dynamic Bicycle Ride · analyzing the stability characteristic of a bicycle when it was driven on each sloping road, the position of the center of gravity

Self-Equilibrium Control on a Dynamic Bicycle Ride

Chieh-Tsung ChiDepartment of Electrical Engineering, Chienkuo Technology University

No. 1, Chieh Shou N. Rd., Changhua City, Taiwan, R.O.C.E-mail: [email protected]

Abstract: - It is very important for a biker to ride comfortably and safely around everywhere. Throughanalyzing the stability characteristic of a bicycle when it was driven on each sloping road, the position of thecenter of gravity (COG) was commonly one of the key influencing factors. Therefore, this study presented asimple approach to measure the inclination degree of sloping road and fed to the system controller for changingthe COG position. Moreover, the front-to-back adaptive equilibrium control of a bicycle ride was controlled bymeans of a hysteresis algorithm, and built in a control unit. The COG position of a whole bicycle systemallowed to be changed by either manual or automatic mode which was completely dependent upon bikerdecision. For convenience, an experimental prototype had first been established in the laboratory. Later, severalexperiments, such as the feasibility and flexibility concerning system control structure were related to a bicyclewere performed on the prototype. Simulation and experimental results showed that the dynamic equilibrium ofa bicycle when it was driven on each sloping road could be controlled by using the posture control approachproposed in this paper. In addition, the increasing cost concerning additional facilities was cheap and easilyretrofitted into the existing bicycles.

Key-Words: - Bicycle, Center of gravity, Hysteresis controller, Sloping road, Equilibrium control, Cost.

1 IntroductionIn recent years, there is growing concerns withbicycles in our daily life as a result of theiroutstanding advantages, such as energy saving, highenergy efficiency, and facility of maintenance.Bicycles have also been attracting more and moreattention result from transportation without anyenvironmental burden. Especially, it is the bestcharming thing for many peoples that a bicycle ridewould increase their health. However, bicycle isunstable when it not controlled and it will fall downwithout human assistance like steering handle ormoving upper body. It requires in general manytrials and much time to learn.

Research studies were carried out a bicycle andits performance characteristic analysis of a dynamicmotion have been performed for many years [1]-[6].According to the characteristics of these studieswhich could be commonly divided into two mainaspects: the first aspect was concerning theoreticalstudies that were started as early as ten years ago bylots of scientists. In the early’s of 1970, Sharp [7]developed a bicycle dynamic model, named asSharp model, it was complicated and not easy to beapplied to design bicycle posture controller. Afeedback control law and bicycle model werederived by Getz [4], which caused a nonlinear,nonholonomic, non-minimum phase model of aunmanned powered two-wheel bicycle obtained a

stably tracking on a arbitrary smooth trajectories ofroll-angle non-zero velocity. Getz and his coworkerpresented a first controller, which allowed trackingof arbitrary trajectories while maintaining balance.Under rider control conditions, Later Getz furtherapplied the internal equilibrium control of theproblem of path-track with balance for the bicycleby using steering and rear-wheel torque as inputs,and also proposed a bicycle model [8]. In 2002, Leeand Ham [9] presented a control algorithm for theself-stabilization of the unmanned bicycle by usingnonlinear control. The second aspect wasconcerning practical studies had been relativelyscarce with regard to another aspect, for exampleMiyamoto [10] implemented the trial of autonomousbicycle robot for a short time period. In addition,there are several researchers begun to study theexpert control of a bicycle, Chen who used the fuzzyintelligence to a electric-power bicycle [2][3],named as Elebike, which was designed and then abicycle could be automatically controlled by theswivel handle.

On the basis of the nonlinear characteristics in abicycle robot dynamic system, thus make thebicycle robot control much more difficult. Severalresearcher were carried out using each intelligentcontrol approach such as fuzzy sliding-mode control,adaptive neuro-Fuzzy control to stabilizeautonomous bicycle [11][12]. Additionally, Ham

WSEAS TRANSACTIONS on SYSTEMS and CONTROLManuscript received Aug. 1, 2007; revised Nov. 30, 2007

Chieh-Tsung Chi

ISSN: 1991-8763 527 Issue 11, Volume 2, November 2007

and Cho who utilized the lateral motion of mass andsuggest a control algorithm for steering angle anddriving wheel speed for a given desired path. Theyalso suggested a new algorithm for nonlinearinverse kinematic problem which was similar toPiccard's iterative method in basic concept tostabilize bicycle. In practical aspect, Yamakita, et al.proposed a trajectory tracking and balancing controlfor autonomous bicycles with a balancer, an input-output linearization is applied for trajectory trackingcontrol and a nonlinear stabilizing control is usedfor the balancing control [13]. As mentioned abovestudies, even though the control results forstabilizing an autonomous bicycle might be better,but these controlling approaches are generally toocomplex and expensive to be implemented.

To protect bicycle falling down when it wasongoing, environmental information should bespecially considered. This paper focuses theattention on a posture control approach for a bikerunder various environments. The control strategy isdivided into two aspects; the first aspect is to designa scheme for measuring the gradient of the sloping.The second aspect deals with the gait for a bicycleto be safely driven on a sloping. To maintain abicycle static stability, it requires that the center ofgravity (COG) should be always controlled withinthe supporting area of bicycle. For the purpose ofthis study, a riding posture for a biker in the sagittalplane can be controlled by an innovative systemcontroller configuration.

2 The Mechanism of CTUbike BicycleIn order to carry out concerning experiments whichwere mentioned in this paper, the CTUbike bicyclewas first constructed at Chienkuo TechnologyUniversity. Its fa1cilities were installed as shown inFig. 1(b). A pair of potentiometer was used tomeasure the inclination angle of the road; one wasattached on the head tube, while the other one wasinstalled beneath the saddle. The latter one was alsomechanically linked with the shaft of a dc motor.For convenience, there is no difference exists forbicycle driven on a ground level or on a slopingroad in the frontal plane. Consequently, this studywill be concentrated on the sagittal plane.

2.1 The Structure of CTUbike BicycleFig. 1 shows the photograph of a completedprototype and the illustration of CTUbike bicycle.The facilities are related to the CTUbike bicycle isrespectively introduced in Fig. 1(b).

Most of the CTUbike mechanism is similar to atraditional popular bicycle. In theory, the supportingarea of a bicycle system is formed by the points ofcontact between front and rear wheels and ground.However, in case of the position of the center ofgravity of a whole bicycle system was alwayscontrolled in this supporting area, a safe andcomfortable ride would be achieved for bikers. Forthe purpose of obtaining a safe and comfortabledynamic riding, the traditional bicycle systemshould be modified in mechanism and added severalfacilities for implementing the adaptive controlmission. There is a dc motor installed beneath thesaddle, and the shaft of dc motor is directly couplewith the supporting frame of saddle. The rotationdirection and angle of dc motor varies with the typeof sloping roads and their inclination angle. Using apotentiometer to dynamically measure theinclination angle of bicycle, and then fed to thesystem controller for adjusting the rotation directionand angle of dc motor. The position of center ofgravity of a whole bicycle system was controlled bythe rotation direction and angle of saddle or dcmotor. In other words, in order to achieve acomfortable ride and fail to upside down duringbicycle riding, the biker posture was generally oneof the key influencing factors. Taken themanufacturing cost into consideration, the systemdynamic equilibrium control of a bicycle is made bya control unit which is composed of some hardwareelectronic circuits.

(a)

DC motor(Gear train is included)

Crank arm

Pedal

Rear wheel

Pendulum

Fear wheel

Potentiometer

Roller chain

Handlebar

Seat

Control boxRack

Front tube

(b)Fig. 1. (a) showing completed photograph ofCTUbike bicycle (b) and facility designation.

WSEAS TRANSACTIONS on SYSTEMS and CONTROL Chieh-Tsung Chi


2.2 Reasons of Positioning the ComponentsIn order to complete the dynamic posture control ofbiker during bicycle riding, some additionalcomponents was necessary, such as a sensing unitwas used to dynamic sensing the inclination angle ofsloping road, a dc motor was used to adjust theinclined angle of saddle, a battery was applied to allcontrol units and a control unit which was used todrive and control the rotation angle and direction ofdc motor. The designing objective and operatingprinciple of these additional facilities would bedescribed respectively in the following:Potentiometer: A potentiometer was attached to thetop stainless steel pipe of front wheel (head tube)and its shaft also suspending a pendulum todynamically sense the inclination angle of the sloesurface. Initially, pendulum would lie in a position,where was called start point, due to the gravity forceeffect. In case of the bicycle was driven on a slopingroad, the inclination angle of the sloping road wouldbe immediately sensed by the potentiometer. Byusing a special pendulum mechanism, theinclination angle of sloping road was sensed bypotentiometer and output a corresponding directvoltage. At the same time, this real-time senseddirect voltage would feed to the system controller.According the default setting, the rotation angle anddirection of dc motor or saddle would be controlledby system controller.DC motor: Either the bicycle system was safe orupside down, it depended on the position of centerof gravity of a whole bicycle system. In this paper,in order to compensate for the position of center ofgravity center out of supporting area (safe area), thebiker posture would be adjusted according to thetype of sloping roads and inclination angle. A dc-motor was installed beneath the saddle and linkedwith the saddle. Once the inclination angle and thetype of sloping roads were determined, the systemcontroller then commanded the dc motor to rotate inthe opposite direction with the same angle as thepotentiometer had sensed. The rated output torqueof dc motor should be designed enough to drivebiker’s body forward or backward inclination whena bicycle was driven on a sloping road. Since it isimportant for the total volume and weight of the dcmotor to be controlled as low as possible; therefore,a gear train was coupled with the rotor shaft of dcmotor for reducing speed.Battery: In general, there are two types of bicycle,with and without power assisted bicycle. Since theNickel-hydrogen (Ni-H) battery essentiallypossessed high energy density characteristics; arated voltage is 12V Ni-H battery is adopted in our

experimental bicycle.Control unit: The dc-motor torque wascontrolled by hysteresis controller. A sufficientpower was supplied through a dc-poweramplifier. Because of the resonance mode of thedc motor control and acoustic noise might beexcited result from the frequency change. Theamplifier was designed to have a constantswitching frequency, such a switching amplifierwas called PWM (Pulse Width Modulation)amplifier, and here only the width of the pulseswould vary with the load.

3 Equilibrium Analysis on DifferentSloping roads

As mentioned in the preceding section, since in thefrontal plane almost no difference exists for bicycledynamic driven on a level or sloping road, so thatwe will concentrate our attentions on the bicycledriven gait in the sagittal plane. Fig. 2 shows theangle definition of the inclination of the slopingroad. In general case, the sloping road may have anunpredictable gradient in the direction of driving.But both the level and slope do not have inclinationin the frontal plane of the bicycle. Here we definethat the frontal plane is perpendicular to thedirection of motion.

Bicycle driven direction

: the inclination angle of the sloping road

Fig. 2. Illustrating the sloping road andinclination angle definition

Because of the lack of an available mechanismfor a bicycle driven on a sloping road, our study hadto start from an investigation of a bicycle driven ona level ground, on an ascending slope surface, anddescending slope surface. From the analysis, weobtained a generally stably and efficient driven gaitfor a bicycle. This will be the main topic of the nextsection.

In order to create an algorithm for controlling abicycle in a sloping driving gait, we must firstanalyze the bicycle driven pattern. Firstly, someassumptions are made and described as follows:

(1) The diameter of the bicycle’s front wheel andrear wheels are equal.



(2) The form of the front wheel and rear wheel iscircle.

(3) The projecting distances from the COG toeither the front or rear wheel on the x axis isequal.

(4) The center of rider’s body can be representedby a particle.

(5) The front and rear wheels of the bicycle areconstrained to roll without slipping.

(6) There is no difference exists in the frontalplane. Consequently, sagittal plane motions areof most importance to this study.

(7) Strictly speaking, when a bicycle is driven on asloping road is a static motion, not dynamicmotion. Because of that the ZMP of the bicyclealways is located on the contact line.

(8) In the analyzing the motion of bicycle period,the environmental parameters and rider’smotivation are not considered.

(9) The weight of supporting tubes, which aredistributed in the bicycle, can be neglected forsimply analyzing bicycle motion behaviors.

3.1 Bicycles Driven on a Flat Ground Level

1w2w

3w Front wheelRear wheel

1m

2m

3m

Ground G.Cx 1

x2x

y

x

1

3x

Contact line

Fig. 3. A bicycle was driven on flat ground level.

The symbols were labelled on Fig. 3 arerespectively defined as follows:

1m : is the mass of front wheel;

2m : is mass of rear wheel;

3m : is the equivalent mass of a biker;: is the distance on the x axis between the

projection point of COG of a whole bicyclesystem and the COG projection points of thefront wheel or the rear wheel;

1w : is the weight of front wheel;

2w : is the weight of rear wheel;

3w : is the weight of a biker;

: is the distance between the center of mass ofthe biker and saddle;

1: is the distance on the x coordination betweenthe projections of the front wheel and the rearwheel;G.Cx : is the projection location of COG of a whole

bicycle system on the x axis;1x : is the projection location of front wheel on x

coordination;2x : is the projection location of rear wheel on x

coordination;3x : is the projection location of the rider’s saddle

on x coordination;For convenient analysis, the static motion for a

bicycle driven on an even terrain can be divided intofollowing phases;

Phase 1: As shown in Fig. 3, the bicycle was drivenon an even terrain, the center of gravity of frontwheel, rear wheel, and biker’s body are projectedinto the x coordination, 1x , 2x , and 3x ,respectively.We could find the location of the center of gravity(i.e. COG) of bicycle G.Cx is almost overlapped withthe projected point of the center of gravity ofrider 3x . If the bicycle wanted to be stably driven onlevel ground, the resultant moments should have anequilibrium relation. The COG of the bicycle

G.Cx could be expressed as follows:

3

1iiiG.C xmMx (1)

where M is the total weight of the bicycle; ix is thedistance between the rear-wheel, front-wheel andthe COG of the bicycle, respectively; im is thecenter of mass of the rear-wheel, front-wheel, andrider.

Rearranging (1) to form a more simplerepresentation, it was given by

M

xmx i

ii

G.C

3

1 (2)

Phase 2: Under the constant environmentalconditions, the bicycle could always obtain asufficient driven efficiency and stability. It isunnecessary to change the COG of the biker forimproving the bicycle’s stability here.



Phase 3: The COG of the bicycle was located in thecenter position of the contact line. As shown in Fig.4, a pseudo circle was formed and where theradius r was the length from the COG to front hub.According to the conservation of angularmomentum, if there is a rigid rotating around a fixedshaft and the net external torque was zero, then theamount of the angular momentum reacted on therigid was given by

0dtdL

(3)

and

ImrL 2

(4)

where L is the angular momentum, which wasalways kept constant here, it also could berepresented in (4); I is the momentum of a wholebicycle; is the angular velocity of pseudo circle.Equation (4) showed that the stability of a bicycledepended on the number of radius r . That means thebicycle driven on a flat ground level was not easy tofall down in the front plane.

r

G.Cx

Front wheel

Pseudo circle

Fig. 4. Angular momentum analysis for abicycle driven on a ground level

3.2 Bicycles Driven on an Ascending SlopeFig. 5 showed that a bicycle was driven on anascending slope. The definition of symbols whichwere labeled on the Fig. 5 was similar to that of Fig.4.

When a bicycle was driven on a sloping road,there is an inclination angle existed betweencontact-line and ground level. The forces owing tothe gravitational effect on the components wereperpendicular to the ground level; it was dividedinto two x

and y

parts, respectively. The COG

projection of a whole bicycle on x axis then was

obtained from that of x

parts of each componentand given by

321

332211

mmmcos)xmxmxm(

x G.C

(5)

As seen in (5), the more the inclination angle, theless value did cos . The COG position of a wholebicycle system G.Cx was shifted to the origin of thereference coordination. The equivalent inertiamoment of a whole bicycle system became less withrespect to the center of rear wheel. This means thatbicycle was easy to fall down.

y

x

1w

2w

3w1

m

2m

G.Cx

1x

2x

1

3x

3m

Contact line

Front wheel

Rear wheel

Ground level

Fig. 5. A bicycle was driven on an ascendingslope.

According to the physics principle, in order toimprove the stability of a bicycle ride, the COGposition of a whole bicycle system would be simplymoved forward in the driving direction by incliningbiker body forward, as shown in Fig. 6. In otherword, if the projection location of biker on the xaxis moved away the center of rear wheel aspossible as, the dynamic stability of a bicycle ridewas achieved due to the equivalent inertia momentwith respect to the center of rear wheel increased,and the final COG position of a whole bicycle couldbe represented as follows:

321

332211

mmmsinxcosmcosxmxm

x G.C

(6)where the anglerepresented the inclined forwardangle of biker.



y

x

1w

2w

3w Front wheel

Rear wheel

1m

2m

Ground level

G.Cx

1x

2x

1

3x

3m

Fig. 6. The COG position of a whole bicycle systemwas modified by moving biker body forward in the

driving direction.

3.3 Bicycles Driven on a Descending SlopeFig. 7 showed that a bicycle was driven on adescending slope. The definition of symbols whichwere labeled on the Fig. 7 was similar to that of Fig.4.

y

xGround

G.Cx

1w

2w

3w

Front wheel

Rear wheel

1m

2m

1x

2x

1

3x

3m

Contact line

Fig. 7. A bicycle was driven on a descending slope.

To observe the Fig. 7, it is easy to upside downdue to the COG position of a whole bicycle systemis too near the contact point of front wheel.Resulting in the inertia moment of the pseudo circledecreased significantly. In this case, the biker bodyshould be moved backward, as shown in Fig. 8, toimprove the bicycle ride.

When a bicycle was driven on a descending slope,and assumed that there is an inclination angle between contact-line and ground level. The COGprojection of a bicycle on x axis also can beobtained from that of x

parts of each component

and given by

321

332211

mmmcos)xmxmxm(

x G.C

(7)

The COG position of a whole bicycle system G.Cxwas dependent on the inclination angle. It showedthat would shift away the origin of the referencecoordination. The equivalent inertia moment withrespect to the center of front wheel became less.This means that bicycle was situated at an unstablestatus, and it was easy to fall down.

As mentioned above case, the stability of abicycle ride was improved by changing the bikerposture. The COG position of a whole bicyclesystem should be moved backward in the drivingdirection by inclining biker body backward, asshown in Fig. 8. After compensation had beencompleted, the equivalent inertia moment withrespect to the center of front wheel was increasedsince the final COG position of a whole bicyclesystem was moved away the contact point of frontwheel. The expression of the COG position on xaxis could be expressed by

321

332211

mmmsinxcosmcosxmxm

x'

G.C

(8)where the angle ' represented the inclinedbackward angle of biker.

y

x

G.Cx

1w

2w

3w

1m

2m

1x

2x

1

3x

3m

Front wheel

Rear wheel

Fig. 8. The COG position of a whole bicycle systemwas modified by inclining biker body backward in

the driving direction.

4 Controller DesignIf there was a larger inclination angle betweensloping road and ground level, thus it is difficult for



a biker to apply force to pedal. Not only biker easilyfelt fatigue, but also he/she would consume muchmore energy during a bicycle ride on sloping road.In this paper, a simple and low cost control strategywas proposed based on a sensory subsystemdynamically measured the inclination angle of thesloping road as well as fed back to the control unit.By regulating biker upper body posture inclinedforward or backward in the sagittal plane, thestability of a whole bicycle system would beimproved significantly [10]. Due to the projectedposition of the bicycle’s COG on the x-axismoved toward to the center of the contact line,thus the inertia moment increased with respectto the center of lower wheel of the bicycle.Regardless of the inclination angle value of thesloping road, no matter when only the normal line ofthe saddle was controlled by control unit alwaysparallel to that of the ground level. Thereafter, thesaddle and chain wheel of the bicycle was seemedas to form a rigid body, the biker would feelcomfortable when he/she ride a bicycle on a slopingroad was similar to ride on a horizontal road.

4.1 Sensory CircuitThe measuring structure of the inclination angle of aroad was shown in Fig. 9. A linear potentiometerwas acted as the inclination angle measuringcomponent for a road here and installed beside headtube. As seen in Fig. 9, it showed that the shaftdisplacement of the potentiometer had differentrotation direction when the bicycle was on theascending slope or descending slope, respectively.Notice the point which was labelled, o , also calledas balance point, it represented that bicycle wassituated at flat ground level (horizontal road), andoutputted a reference voltage value.

Descending road

o 1

Pendulum

o2

Pendulum

Ascending road

Enlarge

Enlarge

Potentiometer

Pendulum

Shaft

Potentiometer housing

Front wheel Front hub

Fork

Head tube

Handlebar

Fig. 9. Sketch of a linear potentiometer was used tomeasure the type of terrain and its inclination angle.

Since the effects of the gravitational force on thependulum, the pendulum always moves toward theground. The rotating angle of the shaft of linearpotentiometer depended on the number ofinclination angle of a sloping road. On thedescending road, the inclination angle was a positiveangle. On the ascending road, the inclination anglewas then a negative angle.

4.2 Controller for Adjusting COG PositionAccording to working necessities of the system, thesystem configuration of the controller wasillustrated in the Fig. 10. The hysteresis controlleroutput signal was modulated by using PWM (PulseWidth Modulation) technology due to the energy-saving factor was taken into account. For thepurpose of increasing the output torque and compactthe total volume of dc servo motor used as possibleas. In addition, the control unit was composed ofsimple and cheap analogue hardware circuit.Therefore, the manufacturing cost of control unitwould be cost down greatly, and the system waseasily implemented.

PWMGen.

ref

ref

cV

DriverHTypeBridgeM

Ke

Gear Box

e

Counterclockwise

Clockwise

Fig. 10. System configuration of the controller.The input variable of the hysteresis controller was

the amplified voltage error value between referencevoltage and feedback voltage )t(e was obtainedand represented by

))t()t((K)t(e fr (9)

where the parameters in (9) were defined as follows,respectively.

)t(e : is the error voltage [V]K : is proportional constant [V/rad.]

r: is the reference angle [rad.]

f : is the actual angle [rad.]

The dynamics and circuit dynamics were expressedas follows [6]:

)t(T)t(Tdt

)t(dD

dt)t(d

J mLm

2

2

(10)



u)t(iRdt

)t(diL

dt)t(d

K aa

ae

(11)

)t(iK)t(T aim (12)

where the parameters in (10), (11) and (12) weredefined as follows:

)t(TL : is load torque [N-m])t(Tm : is generated by dc motor [N-m]

)t(ia : is armature current [A]u : is the control input voltage [V]

)t( : is the rotor placement [rad.]J : is the inertia moment [N-m-sec. 2 ]D : is the friction coefficient

eK : is the back emf. constant [V/rad./sec.]

iK : is the torque constant [N-m/A]Because of the electrical time constant was in

general much smaller than the mechanical one, thedelay of electrical response could be neglected herefor convenience. Where the parameter mB was theviscous-coefficient, and due to the frictioncoefficient was small so that it was neglected here,the viscous-coefficient could simply be representedas

a

iem R

KKB (13)

Generally speaking, the mechanism of thetorsional spring constant value between the gear boxand the load (namely saddle) was very large, thusassumed that it was approaches to infinity.Therefore, a simplification transfer function form ofthe dc motor position control system could beexpressed as follows [14]:

ECsBsAsE

)s()s(

r

o

23(14)

where the abbreviate transfer function form in (14)the parameters respectively defined as follows,

aJLA (15)

ama LBJRB (16)

eima KKBRC (17)

nKKKE is (18)

A constant voltage source was applied on the twofixed terminals of linear potentiometer. Fig. 11(b)showed the sketch of saddle response when thebicycle was driven on an ascending slope (uphill)road. Fig. 11(c) showed the sketch of saddleresponse when the bicycle was driven on adescending slope (downhill) road condition.

DC motor

Flexible shaft

Saddle

Shaft

Front view

DC motor

DC motor

Saddle

Shaft

Saddle post(movable)

Sadlle lug(fixed)

Side view Side view

(a) (b) (c)Fig. 11 Saddle and potentiometer response (a) frontview (b) side view, on the uphill road (c) side view,

on the downhill.

5 Laboratory Tests and ResultsThe CTUbike bicycle was constructed at ChienkuoTechnology University, and it would be used as theexperimental rig in this study. In order to enhancethe system’s adaptive capability, a linearpotentiometer was mounted the head tube. Almostthere is no any variation if a bike motion viewedfrom the frontal plane; therefore, the biker posturecontrol would be especially concentrated on thesagittal plane here. Fig. 12(a) showed the practicalmeasuring mechanism of the inclination angle ofroad and Fig. 12(b) showed that saddle drivingmechanism based on dc servo motor for regulatingthe biker posture.

(a) (b)Fig. 12. Illustration of (a) linear potentiometer and

(b) the diving mechanism of dc motor.

5.1 Simulation ResultsThe dc-motor dynamic motion model was expressedin (14). Related parameters for a dc motor electricaland mechanical model as listed in Table 1. If thebicycles ride on a sloping road condition occurred,especially like mountain ride, the bicycle might falldown due to the COG position of the whole bicycle



system was out of its safe area. Since the inertiamoment for the lower wheel of the bicycle was less,thus the bicycle was easy to fall down. To make useof dynamically changing the biker upper bodyposture or rotating the inclined angle of saddle, theCOG position of the bicycle system was shifted andthe system stability was improved greatly.

Table 1. DC motor electrical specifications.

Start

Automatic?

Operating modeselection?

Calculatevoltage error

Clockwiserotation

Counter-clockwiserotation

Inclinedforward?

Inclinedbackward?

Y

N

Y Y

N N

N

NY

YRead inclinedangle of slope road

Setting referencevoltage

fV

rV

fr VVV

H_refVV L_refVV

Fig. 13. Sketch of a calculation flow chart of thehysteresis controller.

The feasibility and performance of the proposedcontrol unit was verified by observing the stepresponse. By using the proposed control strategythat was described in section 4, a hysteresiscontroller was used and assumed that upper andlower limit voltage error was 1 V and 0 V,respectively. A detailed calculation flow chart of thecontroller was diagrammed in Fig. 13. The stepresponse of dc motor used in this study wasobtained by means of Matlab/Simulink simulationsoftware and displayed in Fig. 14.

r

f

Fig. 14. In case of only the saddle acted as load, thestep response of dc motor control.

5.2 Experimental ResultsIn the experiments, a biker rode the bicycle on anascending road and on a descending road associatedwith an inclination angle. The experimental bicyclewhen it was driven on these special terrainconditions were successfully recorded on film. Fig.15 displayed a sequence of three pictures of theexperimental bicycle when it was driven on anascending road, and with a negative inclinationangle 30 . Fig. 16 showed a sequence of threepictures of the experimental bicycle when it wasdriven on a descending road, and with a positiveinclination angle 30 .

(a) (b) (c)

Fig. 15. Photographs, on an ascending road.

Parameters Symbol Unit DataDc-motorinertia

mJ 2mKg 0.00025

Dc-motorviscous frictioncoefficient

mB secmKg 0.00638

Torsional springconstant

LK rad/mKg 2232.

Load inertiaLJ 2mKg 0.00192

DC-motortorque constant

tK A/mKg 020.

Back-emfconstant

eK sec/.rad/V 0.15

DC-motorresistance aR 1.42

DC-motorinductance

aL mH 1.17

Gear ratio n 1:100



(a) (b) (c)Fig. 16. Photographs, on a descending road.

6 ConclusionWhen a bicycle was driven on a sloping road, notonly the biker was easily felt fatigue and fall downsince the COG position out of safe area, but alsoresulted in wasting much more power energy. Theeffects of the COG position moved away the centerof contact line was unstable for a bicycle ride,especially mountain ride. Because of the equivalentinertia moment with respect to the lower wheel ofthe bicycle was decreased when driven on a slopingroad. In this paper, a novel simple control systemwas proposed based on a sensory system forattempting to overcome those issues. By changingbiker posture through driving the saddle forward orbackward, the stability of the bicycle could beimproved greatly. The results caused by thesimulation and experiments could validate theproposed control strategy was feasible and useful.The proposed control approach not only isinexpensive but also easily retrofitted into existingbicycles. The technique presented in this papershould be helpful in designing the new mechanismand analyzing the dynamic behavior of an electricbicycle. Additionally, if the intelligent controlapproaches, such as fuzzy logic control or geneticalgorithm are used, hence the system performance,in general, may further be improved.

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Documents

Self-Equilibrium Control on a Dynamic Bicycle Ride · analyzing the stability characteristic of a bicycle when it was driven on each sloping road, the position of the center of gravity