Mechatronics 24 (2014) 1214–1222

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Mechatronics

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Gearshift control system development for direct-drive automatedmanual transmission based on a novel electromagnetic actuator

http://dx.doi.org/10.1016/j.mechatronics.2014.09.0080957-4158/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: changsiqin@hotmail.com (S. Chang).

Shusen Lin a,b, Siqin Chang a,⇑, Bo Li a

a School of Mechanical Engineering, Nanjing University of Science and Technology, PR Chinab College of Engineering, Zhejiang Normal University, PR China

a r t i c l e i n f o

Article history:Received 16 August 2013Accepted 22 September 2014Available online 12 October 2014

Keywords:Gearshift systemAutomated manual transmissionControl strategyElectromagnetic actuator

a b s t r a c t

A novel gearshift system which comprises a 2 degree-of-freedom electromagnetic actuator is introducedto simplify the structure of gearshift system of automated manual transmission (AMT), increase trans-mission efficiency and improve shift quality. The working principle and characteristics of the actuatorare analyzed. The gearshift process is divided into the non-synchronization and the synchronizationphase. Extended state observer (ESO) based inverse system method (ISM) and active disturbance rejec-tion controller (ADRC) are designed for the two processes respectively. ISM can eliminate the nonlinearityof the actuator and ESO can estimate and compensate the uncertainties, parameter variations andexternal disturbances. ADRC is adopted to improve the tracking accuracy of the synchronization process.Comparative simulations and experimental results demonstrate the effectiveness of the proposed controlmethod, and good gearshift performance has been achieved. Combined with the new designed controlstrategy, the novel gearshift system provides a new solution for AMT applications.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Nowadays, vehicle manufactures put more attention onreducing vehicle fuel consumption due to high fuel price and con-cerns on global warming. Transmission system is one of the crucialsystems which affect the vehicle fuel economy. Currently, twomain types of transmission used in passenger cars are manualtransmission (MT) and automatic transmission (AT). MT has a highmechanical efficiency and the driver can select gears autono-mously. AT is convenient to operate but has relatively higher fuelconsumption. Therefore, a new type of transmission namedautomated manual transmission (AMT), which combines theadvantages of AT and MT, represents a promising solution and isspreading in the recent years [1].

AMT shares a similar mechanical structure with MT, but it isequipped with electro-mechanical or electro-hydraulic actuatorswhich are controlled by a transmission control unit (TCU). The fueleconomy of vehicles equipped with AMT is supposed to beimproved compared with vehicles with AT. However, a poorlydesigned or controlled AMT system may not achieve desiredresults. Torque interruption which leads to driving comfort reduc-tion is the bottleneck of the AMT for its wide application. However,the driving comfort can be improved by proper gearshift control

strategy. An integral control strategy aiming to improve gearshiftquality should take into account the reduction of gearshift time,driveline oscillations, friction work of clutch and synchronizer ring.

Currently, hydraulic and electrohydraulic actuation technolo-gies are preferred for the control of AMT due to its higher densityand the readily available source of hydraulic power [2]. However,hydraulic systems may represent up to 50% of the total transmis-sion loss. Electrohydraulic actuation provides an alternative solu-tion and it is widely employed in AMT vehicles though the lossassociated with leakage and flow is still present. Besides, electro-hydraulic systems are complex, having many solenoids valvesand hydraulic lines, which occupy a large volume and are relativelyexpensive. Presently, electromechanical actuation system is con-sidered as an alternative to electrohydraulic system, since it offersthe potential for improving the efficiency, dynamic response androbustness. Recent investigations to adopt electromechanical actu-ation for AMT control generally utilize DC motors in conjunctionwith reduction gear or motion conversion device to achieve thedesired force and motion. Although this solution offers greatpotential for efficiency improvement, the large gear reduction ratioand low efficiency of the gearbox compromise the performance.Turner et al. present a direct-drive electromechanical actuationsystem for gearshift control of AMT [2,3]. The actuation systemcomprises a high-force moving magnet linear actuator and a rotaryactuator. As the actuation system employs the direct-drivetechnology, it does not suffer from significant hysteresis,

Nomenclature

U voltageI currentR resistanceL inductancem moving mass of the linear partE back electromotive forceT electromagnetic torqueF electromagnetic forcex displacement of the linear partFc friction forceJt rotary inertia of the actuatorx rotary speedTd resistance torquev velocity of the sleevec viscous friction damping coefficientS displacement of the sleevexi element of the state variable xx state variabley output variableA state matrixB input matrixC output matrixw state variables of the pseudo-linear systemwi element of the state variable wr desired valueyf feedback valuen damping ratioxn natural frequencyts transition timeu input variable of the pseudo-linear systems laplace variableK state variable feedback matrixai element of Ku control input

b, b0 system parametere estimate errorsz1 estimates of the output yz2 estimates of the derivative of yz3 estimates of total disturbanceh sampling periodb01, b02, b03 observer gainsfal(e, a, d)

nonlinear functionu control inputu0 intermediate control inputJc equivalent inertia of the input shaft of the AMTTs friction torqueJs equivalent inertia of the output shaftTL load torqueig gear ratioid differential ratio respectivelyxc clutch speedxs out put shaft speedFs gearshift forcefs friction coefficientRc effective radius of the friction conea half cone angled, d0 parameters of function f(v1 � v, v2, r, h)v desired signaly0 parameter of function f(v1 � v, v2, r, h)v1 transitional trajectory of vv2 differential signal of v1

rg parameter determining the dynamic characteristics ofv1

a, a4 parameter of function f(v1 � v, v2, r, h)b11, b12 controller parametersa1, a2 controller parameters

S. Lin et al. / Mechatronics 24 (2014) 1214–1222 1215

compliance and backlash. Only part of the published researchfocuses on the structure innovation of AMT. Galvagno presents akind of AMT equipped with an additional flywheel to reduce thetorque gap during the gearshift [4]. R.P.G. Heath proposed the zero-shift hub which is housed within an existing synchronizer to pro-vide an uninterrupted path to deliver torque from the engine towheels [5]. Sandooja [6] developed a double indexing synchronizeris developed to amplify the synchronizer capacity so that smoothgearshift and good shift feeling are achieved.

Current research on AMT is focused on the control of clutch,gearshift, engine speed and torque [7,8], and many kinds ofintelligent control algorithms such as fuzzy control, optimal con-trol, sliding mode control, are adopted to solve the nonlinearity ofan AMT system and achieve better gearshift performance [9–11].However, in spite of the extensive literature on AMT control, thecontrol methodology is still not mature enough for the wideapplication of the AMT system. Few papers about the gearshiftsynchronization process when the clutch is disengaged have beenpublished. Eventhough poorly controlled gearshift synchroniza-tion process will cause vibration of the driveline and abrasionof the synchronizer ring. Literature [12] presents the detailedanalysis of the synchronization process, but control method isnot involved.

In this research, a novel gearshift system based on direct-drivetechnology is proposed. A totally improved direct-drive electromag-netic rotary-linear actuator (EMRLA) is developed and adopted as agearshift actuator. The gearshift synchronization process is dividedinto two main phases, the non-synchronization phase and the

synchronization phase. Speed difference is synchronized duringthe synchronization phase and gaps are eliminated during non-syn-chronization phase. Obviously, the task and the drag force are differ-ent in each phase. As a result, it is necessary to adopt differentcontrol algorithm to achieve the desired performance. Direct-drivetechnology eliminates transmission mechanisms such as reductiongear and lead screws, which lead to a lower component counts,improved robustness and dynamic response of the gearshift system.However, this structural simplification makes the EMRLA easilyaffected by model uncertainties and disturbances. As a result, therequirements for the control method are relatively high. PID controlalgorithm is applied in previous work [13]. However, the algorithmis insensitive to the variation of target displacement but sensitiveenough to the nonlinearity and disturbances, therefore the controlis not precise enough since the gearshift process is nonlinear andsuffers from disturbances. Inverse system method (ISM) isintroduced to eliminate the nonlinearity of the actuator and gear-shift process [14]. Additionally, extended state observer (ESO) isused to estimate the uncertainties and disturbances, and compen-sates these unfavorable factors. The active disturbance rejectioncontroller (ADRC) is employed during the synchronization phase[15]. The ADRC is not predicated on precise plant model and isextremely tolerant of uncertainties and nonlinearity. Knownand unknown disturbances occurring during synchronizationprocess are lumped together as total disturbance, which isestimated and compensated by ADRC in real time. Simulation andexperimental results indicate the effectiveness of the proposedcontrol strategy.

Fig. 1. The novel gearshift system.

1216 S. Lin et al. / Mechatronics 24 (2014) 1214–1222

2. The novel gearshift system

Fig. 1 shows the novel gearshift system which employs theEMRLA as the AMT gearshift actuator. It consists of EMRLA, trans-mission, shift block, shift lever and displacement sensor. Differen-tiating from existing AMT gearshift systems, direct-drivetechnology is adopted so that the EMRLA acts directly on the shiftrail of AMT. The large reduction gear and motion conversion deviceare eliminated, which simplifies the structure of the system andimproves the mechanical efficiency.

The novel gearshift system based on an EMRLA offers a numberof advantages,

(1) Simplified construction and lower component count whichresult in improved robustness.

(2) Elimination of reduction gear and motion conversion linkagewhich improves efficiency and reduces mechanical hystere-sis, compliance and backlash.

(3) Adoption of the EMRLA which has high driving ability andfast dynamic response is beneficial to the reduction of gear-shift time and the improvement of shift quality.

3. The EMRLA

A prototype of the EMRLA has been developed for gearshift con-trol. The EMRLA is illustrated schematically in Fig. 2. The actuatorincludes a high-force linear part which controls the engagement ofgears and a high-torque rotary part which is coupled to the shaft ofthe linear part directly. The rotary part is in charge of gearselection. The linear part comprises the output shaft, coil, perma-nent magnets, outer core and inner core. The rotary part comprisesarmature, permanent magnets, coils, outer core and inner core.

Fig. 2. Structure of the EMRLA.

Both the linear part and the rotary part act on the same outputshaft which is connected with a shift lever as shown in Fig. 1.The motion of the linear part and the rotary part do not interferewith each other so that the output shaft can rotate and movelinearly at the same time. In order to achieve high driving ability,a high energy sintered NdFeB magnet, with a maximum operatingtemperature of 180 �C, is selected for the permanent magnetdesign.

Fig. 3 presents the working principle of the EMRLA. The direc-tion of the electromagnetic field and magnetic-curve of the rotarypart are shown in Fig. 3(a). There is a small gap between the arma-ture and the inner core so that the armature can rotate freely. Themagnetic-curve produced by symmetrical coils overlap on thearmature and drives it to rotate to the right. The armature willrotate to the left when the coils are energized reversely.

Halbach magnetized topology is utilized to maximize the actu-ating force of the linear part [16]. The air gap is full of radial mag-netic field. According to the Fleming’s left-hand rule, the directionof the electromagnetic force acting on part 1 is towards right. Boththe direction of magnetic field and of current are reverse from part1 which means the direction of the electromagnetic force is exactlythe same as the part 1. As a result, the output shaft moves towardsright. The motion could be bidirectional since the direction of thecurrent is alterable. The produced force is nearly proportional tothe current so that accurate motion control is achievable.

The electromagnetic actuator is a coupling system with stronglyinteractive subsystems, including electrical, magnetic and mechan-ical subsystems. The mathematical model can be described as

UðtÞ ¼ Eþ RIðtÞ þ L dIðtÞdt Electrical subsystem

FðtÞ ¼ kmIðtÞTðtÞ ¼ ktIðtÞ

�Magnetic subsystem

m d2xðtÞdt2 ¼ FðtÞ � Fc

Jt _xðtÞ ¼ TðtÞ � Td

(Mechanical subsystem

8>>>>>>><>>>>>>>:

ð1Þ

where U is the voltage applied to the actuator, E is the back electro-motive force (EMF), I is the current through the coil, R and L repre-sent the resistance and inductance of the coil respectively, F and Trepresent the produced force and torque respectively, km is the forcecoefficient and kt is the torque coefficient, m is the moving mass ofthe linear part, x denotes the displacement, Fc is the friction force, Jt

is the rotary inertia of the actuator, x is the rotary speed, Td is theresistance torque. Note that the electrical subsystem for linear partis the same as the rotary part.

The specifications of the EMRLA are shown in Table 1 [13].The electrical time constant and the electromechanical time

constant of the electromagnetic actuator are relatively small dueto the low moving mass and rotary inertia, and as a result thedynamic response of the actuator is definitely fast. Additionally,the driving ability of the actuator is large enough to realize gear-shift. The quick response of the EMRLA is conducive to increasingthe controllability of the actuator.

4. Gearshift controller design

This research focuses on the gearshift process after the disen-gagement of the clutch. The gearshift process can be divided intoseveral phases according to different research purposes [12,17].Before the synchronization process, the sleeve moves forward toeliminate the gap between the synchronizer ring and friction cone.The synchronization process starts when the friction torqueemerges, and the rotary speed difference decreases. When therotary speed difference disappears, the sleeve moves forward againand finally finishes meshing with target gear. The gearshift processis divided into two main phases as synchronization phase and

Fig. 3. Working principle of the actuator.

Table 1Specifications of the actuator.

Parameter Linear Rotary

Moving mass and rotary inertia 0.671 kg 7.04 � 10�6 kg m2

Resistance 1.6 X 0.56 XInductance 1.1 mH 0.29 mHElectrical time constant 0.69 ms 0.51 msElectromechanical time constant 0.97 ms 0.68 msMaximum driving ability 1300 N 2.5 Nm

S. Lin et al. / Mechatronics 24 (2014) 1214–1222 1217

non-synchronization phase. The inverse system method (ISM) [18]is easy to realize in engineering applications. During the non-syn-chronization process, inverse system method is employed toachieve linearization of the gearshift system. The ISM of the gear-shift system can be established by using feedback method. Besides,an extended state observer (ESO) is introduced to replace the stateobserver of the ISM. Model uncertainties and disturbance are esti-mated and compensated by ESO so that fast and precise gearshiftcontrol is achievable. The active disturbance rejection controller(ADRC) [19] is a new way of control design, which is independentof an accurate model and is highly tolerant of uncertainties anddisturbance. Since the disturbance and vibration are immeasur-able, ADRC is adopted to consider all of these as total disturbanceand compensated by an ESO. It will reduce force ripple whichcontributes to the improvement of the shift quality. The schemeof the controller is shown in Fig. 4.

Fig. 4. Scheme of the controller.

4.1. ISM-ESO controller design for non-synchronization phase

For a given system, the inverse system of the original systemcan be developed by using feedback method. A pseudo-linear sys-tem is obtained when the inverse system and the original systemare combined. As a result, linear system theory is appropriate tobe applied to achieve high performance. Combined with Eq. (1),the mathematical model of the gearshift system can be describedas

_I ¼ � RL I � km

m v þ uL

_v ¼ kmm I � c

m v_S ¼ v

8>><>>: ð2Þ

where v is the velocity of the sleeve, c is the viscous frictiondamping coefficient, S is the displacement of the sleeve. As shownin the Eq. (1), the input variable of the gearshift system is voltageu, and the output variable is S. Therefore, the gearshift system is asingle-input single output (SISO) system. The state variables aregiven as

x ¼ x1 x2 x3½ �T ¼ I v S½ �T ð3Þ

According to the mathematical model of the gearshift systemdescribed in Eq. (2), the state equation can be depicted as

_x1

_x2

_x3

264

375 ¼

� RL km 0

kmL � c

m 00 1 0

264

375

x1

x2

x3

264

375þ

1L

00

264

375u ð4Þ

The system output equation is expressed as

y ¼ 0 0 1½ �x1

x2

x3

264

375 ð5Þ

The necessary and sufficient condition for the reversibility ofthe gearshift system is the existence of the relative order of thestate equation a in a given neighborhood. The step of reversibilityanalysis can be described as [18]:

(1) Computing the derivatives of the output equation y = h(x, u)until the input variable u appears in equation y(a) = ha(x, u).

(2) If the partial derivative of the equation y(a) = ha(x, u) is notequal to zero in the neighborhood of (x0, u0), there is a rela-tive order a of the gearshift system, and if the relative orderis less than or equal to the dimension of the state vector x, itis reasonable to conclude that the gearshift system isreversible.

Fig. 6. State feedback controller.

1218 S. Lin et al. / Mechatronics 24 (2014) 1214–1222

According to the above theory, the equations

y ¼ x3

_y ¼ _x3 ¼ x2

€y ¼ _x2 ¼ kmm I � c

m_y

yv¼ €x2 ¼ � c

m€yþ km

m � RL x1 � km

L_yþ u

L

� �

8>>>><>>>>:

ð6Þ

are obtained.It is obvious that there is not input variable u in expression y; _y

and €y, but the expression yv

includes the input variable u. Hence, therelative order of the system a is 3. The relative order is equal to thedimension of the state vector so that the gearshift system isreversible. From the expression y

v, the expression of the inverse

system can be solved as

u ¼ mLkm

yvþ cL

km€yþ km _yþ Rx1 ð7Þ

By connecting the inverse system with the original system, thepseudo-linear system is obtained as shown in Fig. 5.

The state variables of the pseudo-linear system is given as

w ¼ w1 w2 w3½ �T ¼ y _y €y½ �T ð8Þ

The state space equation of the pseudo-linear system can bedescribed as

_w1

_w2

_w3

264

375 ¼

0 1 00 0 10 0 0

264

375

w1

w2

w3

264

375þ

001

264

375u ¼ Awþ Bu

y ¼ 1 0 0½ �w1

w2

w3

264

375 ¼ Cw

8>>>>>>>><>>>>>>>>:

ð9Þ

As a result, the pseudo-linear system has been developed andlinear system theory can be applied.

The pseudo-linear system has a ath-order integral attribute,thus linearization of the nonlinear system has been achieved. Inthis section, state feedback control is used to design a controllerfor the pseudo-linear system according to the system control target(see Fig. 6).

If the state variable feedback matrix is K ¼ a0 a1 a2½ �, thenthe state feedback controller can be described as

u ¼ r � yf

yf ¼ a0yþ a1 _yþ a2€y

(ð10Þ

where r is the desired value and yf is the feedback value.To seek a rapid response with a low overshoot, a desired system

characteristic equation can be chosen such as

s2 þ 2nxn þx2n

� �ðsþ nxnÞ ¼ 0 ð11Þ

where n is the damping ratio, xn is the natural frequency.The dynamic response is decided by the variables n and xn. The

transition time can be calculated by equation ts � 4/(nxn). Accord-ing to the transient response of the system, the transition time isthe smallest when the value of the damping ration is 0.707. The

Fig. 5. Pseudo-linear system.

transition time is decided as 20 ms on the basis of experiments.Therefore, the natural frequency is figured out as 283. The desiredsystem characteristic equation is

s3 þ a2s2 þ a1sþ a0 ¼ 0 ð12Þ

By applying Ackermann’s formula, a2 = 600, a1 = 160,021,a0 = 16,004,218 is obtained.

Consider the following nonlinear second-order equation

_x1 ¼ x2

_x2 ¼ f ðx1; x2Þ þ buy ¼ x1

8><>: ð13Þ

where y is the output to control, x1, x2 are state variables, u is thecontrol input, b is the system parameter, and f(x1,x2) denotes thetotal disturbance which is nonlinear. The objective is to synthesizea control input u so that the output y gets to the desired point yd asquickly and accurately as possible in spite of the total disturbance.Consider the function f(x1,x2) as a new variable x3, and expressed as_x3 ¼ wðtÞ. The Eq. (13) is converted to

_x1 ¼ x2

_x2 ¼ f ðx1; x2Þ þ bu_x3 ¼ wðtÞy ¼ x1

8>>><>>>:

ð14Þ

The discrete-time form of the ESO for Eq. (14) can be written as

e ¼ z1ðkÞ � yðkÞz1ðkþ 1Þ ¼ z1ðkÞ þ h � ðz2ðkÞ � b01 � eÞz2ðkþ 1Þ ¼ z2ðkÞ þ h � ðz3ðkÞ � b02 � falðe;0:5; dÞ þ b � uðkÞÞz3ðkþ 1Þ ¼ z3ðkÞ � h � b03 � falðe;0:5; dÞ

8>>><>>>:

ð15Þ

where z1, z2, and z3 are estimates of x1, x2 and f(x1,x2) respectively, his the sampling period. b01, b02, and b03 are observer gains whichcan be selected as b01 � 1/h, b02 � 1/1.6h1.5, b03 � 1/8.6h2.2.

Non-linear function fal(e,a,d) is defined as

falðe;a; dÞ ¼ e � da�1; jej 6 d

jeja � sgnðeÞ; jej > d

(ð16Þ

Parameters a and d satisfy conditions of a < 1 and d = k � h,where k is a positive integer.

Since z3 tracks f(x1,x2) well, the control input u can be designedas

u ¼ ðu0 � z3Þ=b ð17Þ

to compensate the total disturbance. Therefore, the original nonlin-ear system Eq. (13) is linearized as

_x1 ¼ x2

_x2 ¼ u0

y ¼ x1

8><>: ð18Þ

Fig. 7. ISM-ESO controller.

S. Lin et al. / Mechatronics 24 (2014) 1214–1222 1219

Finally, the designed ISM-ESO control method for non-synchroniza-tion phase is illustrated in Fig. 7. The parameters are: h = 0.0001,b01 � 10,000, b02 � 625,000, b03 � 73,400,000, b � 23.87.

Stability is the most important characteristics of the controlsystem. The stability of Eq. (13) under the ISM-ESO controller hasbeen proved in reference [20,21] by using Lyapunov stabilityprinciple, and Additionally, Lyapunov’s second method for stabilityis adopted to prove the stability of the ESO controller in reference[15].

The designed controller for the non-synchronization phase hasbeen compared with a tuned PID controller by simulation. In ourprevious work, an incremental PID controller was adopted to real-ize displacement control during the gearshift process [13], and thecontroller is

eðkÞ¼ ydðkÞ�xðkÞDuðkÞ¼KpðeðkÞ�eðk�1ÞÞþKieðkÞþKdðeðkÞ�2eðk�1Þþeðk�2ÞÞ

�ð19Þ

where yd is the desired displacement, x is the actual displacement, eis the error between desired and actual values, Kp, Ki and Kd are con-troller parameters, Du is the increment of the control variable. Thegearshift process was divided into four phases and three of themexcept synchronization phase were controlled by PID method.According to the tuning method described in reference [23], thecontroller parameters were determined by trial and error, and thePID gains for the corresponding phase when the targetdisplacement is 4 mm are Kp = 13,500, Ki = 0.5, Kd = 10.

Fig. 8 shows the system response with respect to various targetdisplacement. The target displacements are set to 4 mm and2.5 mm. Obviously, it is demonstrated that the ISM-ESO controlconverges more quickly than PID control does, which ensures ashorter shift time. When the target displacement is 4 mm, thetransition time of ISM-ESO control and PID control are 17.7 msand 24.4 ms respectively. When the target displacement is2.5 mm, the transition time of ISM-ESO control is 4.9 ms and lessthan that of PID control. Besides, since the PID parameters are

Fig. 8. Response curve for different desired displacement.

tuned when the target displacement is 4 mm, there is an overshootwhile the target displacement changes to 2.5 mm, and theovershoot is nearly 1.1%. An overshoot may be result in crash ofsynchronizer ring and cone which is not allowed. For ISM-ESOcontrol, no overshoot occurs at either target displacement.

The system parameters such as the coil resistance R may varybecause of some factors. Fig. 9 shows the simulation results whenthe value of R increased by 20%. No matter how the R varies, thesimulation results of ISM-ESO control is the same with the originalR. The simulation results of PID control are relatively bad comparedwith ISM-ESO control. The variation of R causes steady-state errorwith PID control, and the range is 1.7%.

The gearshift system suffers from various disturbances duringgearshift. To test the robustness performance of the ISM-ESO con-trol, a large step external disturbance F = �100 N is added between0.01 s and 0.015 s. It can be seen in Fig. 10 that the displacementtrajectory of ISM-ESO control is not influenced to a great extent.Inconclusion, the ISM-ESO control has excellent performance and itis conducive to improving the shift quality.

4.2. ADRC controller design for synchronization phase

The mathematical model of the synchronization phase can bedescribed as

Jc _xc ¼ � Tsig

Js _xs ¼ Ts � TLid

Ts ¼ Fs �f s �Rcsin a

8>><>>: ð20Þ

where Jc is the equivalent inertia of the input shaft of the AMT, Ts isthe friction torque Js is the equivalent inertia of the output shaft, TL

is the load torque, ig and id is the gear ratio and the differential ratiorespectively, xc and xs represent the clutch speed and the outputshaft speed respectively. Fs is the gearshift force, fs is the frictioncoefficient, Rc is the effective radius of the friction cone, a is the halfcone angle.

As it is known, the shift force is the critical factor which affectsthe gearshift time, and the degree of impact is mostly influenced bythe change rate of the shift force. As a result, it is necessary todesign shift force control strategy to achieve good shift quality.

Optimal control based on Pontryagin’s minimum principle isadopted to optimize the change rule of the shift force during thesynchronization phase so that a compromise between synchroni-zation time and shift quality is obtained, and the result is shownin Fig. 11. The target of the shift force control is to track the optimaltrajectory precisely. The controller should be reliable whendisturbance and uncertainty occur. Besides, considering that theoptimal trajectory varies according to the different work conditionof the transmission, the controller should adjust itself to trackdifferent trajectories well. The active disturbance rejectioncontroller (ADRC) is exactly the appropriate control method.

Fig. 9. Response curves with parameter variation.

Fig. 10. Response curve with 100 N disturbance.

Fig. 11. Optimal trajectory of synchronization process.

1220 S. Lin et al. / Mechatronics 24 (2014) 1214–1222

The shift force can be described as

Fs ¼ kmI ð21Þ

Hence, the shift force control is converted into the closed-loopcontrol of current. The back electromotive force is zero duringthe synchronization since there is no displacement process. As aresult, the electrical equation in Eq. (1) can be rewritten as

_I ¼ �RL

I þ uL

ð22Þ

The basic topology of the ADRC is given in Fig. 12, which is com-prised of a tracking differentiator (TD), an extended state observer(ESO), and a nonlinear state error feedback (NLSEF) controller.

The TD is used for generating a transitional trajectory v1 of thedesired signal v to improve transition performance especially whenv is a constant. Differential signal of v1 is given as v2 simulta-neously. The discrete-time form of TD is written as

g ¼ f ðv1 � v; v2; rg ; hÞ_v1 ¼ v1 þ hv2

_v2 ¼ v2 þ hg

8><>: ð23Þ

where h is the sampling period, f(v1 � v, v2, rg, h) is a kind oftime-optimal control function, and the function is given as

Fig. 12. Basic topology of the ADRC.

f ðv1 � v ;v2; rg ;hÞ ¼

d ¼ rg � hd0 ¼ h � dy0 ¼ v1 � v þ h � v2

a4 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid2 þ 8rg � jy0j

qa ¼

v2 þ ða4 � dÞ � sgnðy0Þ=2; jy0j > d0

v2ðkÞ þ y0=h; jy0j 6 d0

�

f ¼�rgsgnðaÞ; jy0j > d0

�rga=d; jy0j 6 d0

�

8>>>>>>>>>>>>>><>>>>>>>>>>>>>>:

ð24Þ

where rg is a parameter of the function f(v1 � v, v2, rg, h) whichdetermines the dynamic characteristics of v1, and the larger thevalue of rg, the shorter the time taken by the transitional trajectoryv1 of a specific v.

The main role of the ESO is to estimate the total disturbance,and its discrete-time form with the sampling period h is

e ¼ z1 � y

z1 ¼ z1 þ hðz2 � b11 � eþ b0 � uÞz2 ¼ z2 � h � b12 � falðe;a; dÞ

8><>: ð25Þ

where z1, and z2 are estimates of the output y and the totaldisturbance respectively. b11 and b12 are observer gains which canbe selected as b11 � 1/h, b12 � 1/1.6h1.5 [19].

Non-linear function fal(e, a, d) is defined as the same in Eq. (16).The control input u can be designed as

u ¼ u0 �z3

b0ð26Þ

The NLSEF is designed to produce the intermediate variable u0,and it can be described as

e1 ¼ y1 � z1

e2 ¼ y2 � z2

u0 ¼ b11 � falðe1;a1; dÞ þ b12 � falðe2;a2; dÞ

8><>: ð27Þ

where b11 and b12 are controller parameters, a1 and a2 satisfy thecondition 0 < a1 < 1 < a2. The main parameters are: b11 = 10,000,b12 = 625,000, b0 = 909.

Though the ADRC theory can guarantee the stability of theADRC according to the reference [19], switched systems basedmultiple Lyapunov function method which was proposed in refer-ence [22] was adopted to prove the stability of the ADRC controller.Besides, reference [24] also demonstrated the stability of the ADRC.

The desired trajectory is shown in Fig. 12, and the trackingerrors of the ADRC and PID are compared in Fig. 13. Both the twocontrollers achieve good tracking performance, but the error ofADRC is smaller. In addition, a tiny steady-state error about 0.6%is seen in the error profile of PID control.

Fig. 13. Tracking error of the two controls.

S. Lin et al. / Mechatronics 24 (2014) 1214–1222 1221

5. Experimental validation

In order to verify the designed gearshift system and assess theperformance of the control strategy, a gearshift test bench is devel-oped. Fig. 14 shows the arrangement and the main components ofthe test bench. It is mainly made up of six parts: actuator, trans-mission, sensors, variable-frequency motor, control system andother assistant mechanisms. The engine input is represented by avariable-frequency motor. The actuator mounted on the transmis-sion connects with the shift rail through a lever. The test bench ismounted on a big plate to avoid vibration.

The structure of the controller is shown in Fig. 15. LPC2294microcontroller is used as main controller since it has many

Fig. 14. Test bench.

Fig. 15. Hardware schematic of the controller.

Fig. 16. Comparasion of the experimental results of the two controllers.

available on-chip resources. Sensor signals are transmitted to A/Dports after filtered and amplified by peripheral circuits. The con-troller deals with the signals and transmits them to PC throughCAN-BUS. The pulse signal produced by speed sensor is capturedby capture module. Modularization method is adopted duringsoftware design.

Fig. 16 shows the displacement response and shift force whenthe target displacement is 4 mm. Additionally, a large step distur-bance F = �50 N is added at t = 0.008 s and removed at t = 0.01 ms.The response of ISM-ESO control is quicker than that of PID control.The influence of added disturbance to displacement profile is moreapparent with PID control and the overdamping lasts a long timecompared with ISM-ESO control.

(a) Displacement

(b) Shift force

Fig. 17. Gearshift results with the two controllers.

Fig. 18. Degree of impact curve of the two controllers during synchronizationprocess.

Fig. 19. Tracking errors of synchronization process with the two controller.

Table 2Comparison of indexes with two control methods.

Method Maximum degree ofimpact j/(m/s3)

Friction work perunit WA/(J/mm2)

Synchronizationtime t/ms

ADRC 2.95 0.077 90PID 4.12 0.065 98

1222 S. Lin et al. / Mechatronics 24 (2014) 1214–1222

Fig. 17 shows the displacement and shift force variations of theentire gearshift process. The ripple of displacement and shift forcewith PID control is more apparent than those with ISM-ESO–ADRCcontrol. Force ripple will result in vibrations, reduction of the gear-shift comfort and should be avoided. Fig. 18 shows the degree ofimpact of the synchronization process with ADRC control and PIDcontrol. The degree of impact is lower with ADRC control. Besides,PID control tracks the desired trajectory worse than ADRC controlduring the synchronization process. The error curves of synchroni-zation process in Fig. 19 prove it. Table 2 compares the mainindexes of shift quality with two control methods. Both the maxi-mum degree of impact and the synchronization time are smallerwith ADRC control. Although the friction work per unit grows a lit-tle, they are under the permission value 1.2 J/mm2 [25]. It is veri-fied that the ADRC control track the desired trajectory better andhas decent robustness.

6. Conclusions

A novel gearshift system based on a 2-DOF electromagneticactuator is introduced. The novel system eliminates reductiongears and drives the shift lever directly which improves thedynamic response and efficiency of the gearshift system. It has alower component count which simplifies the system and improvesthe robustness. The characteristics of the actuator indicate that the2-DOF electromagnetic actuator has powerful driving force andtorque. Besides, the dynamic response is fast which is in favor ofimproving shift quality.

Since the gearshift process is nonlinear and suffers from uncer-tainties and external disturbances, robust controller is necessary toguarantee good gearshift performance. The gearshift process isdivided into synchronization phase and non-synchronizationphase so that more suitable and effective control strategy can bedesigned according to the different purpose of each process.Inverse system method (ISM) is introduced to eliminate the non-linearity of the actuator. Extended state observer (ESO) is used toestimate the uncertainties and disturbances, and compensatesthese unfavorable factors. The simulation and experiments resultsprove that the designed ISM-ESO controller can achieve quick

response, good precision and robustness with respect to varioustarget displacement during non-synchronization process. TheADRC is not predicated on precise plant model and is extremelytolerant of uncertainties and nonlinearity. Compared with PIDcontrol, it tracks desired trajectory better and the tracking erroris relatively small which results in low degree of impact andsynchronization time. Consequently, this novel gearshift systemalong with ISM-ESO–ADRC controller provides a new solution forwide applications of AMT.

Acknowledgements

This work was supported by the National Natural Science Foun-dation of China (Grant No. 51306090).

References

[1] Chang S. Automotive powertrain. Beijing: China Machine Press; 2006.[2] Turner AJ, Ramsay K, Clark RE, Howe D. Development of high force

electromechanical linear actuator for shift-by-wire automated manualtransmissions. SAE 2006 World Congress, Warrendale PA, SAE 2006-01-0360;2006.

[3] Turner AJ, Ramsay K, Clark RE, Howe D. Direct-drive rotary-linearelectromechanical actuation system for control of gearshifts in automatedtransmissions. In: Proceedings of the 2007 IEEE vehicle power and propulsionconference, Arlinton, USA; 2007. p. 267–72.

[4] Galvagno E, Velardocchia M, Vigliani A. A model for a flywheel automaticassisted manual transmission. Mech Mach Theory 2008;07:1–12.

[5] Heath R, Child A. A seamless automated manual transmission (AMT) with notorque interrupt. SAE 2007 World Congress, Warrendale (PA), SAE 2007-01-1307; 2007.

[6] Amit Sandooja. Double indexing synchronizer – to amplify the synchronizercapacity. SAE 2012 World Congress, Warrendale (PA), SAE 2012-01-2003;2012.

[7] Glielmo L, Iannelli L, Vacca V, Vasca F. Gearshift control for automated manualtransmission. IEEE/ASME Trans Mech 2006;11:17–26.

[8] Dolcini P, Carlos CW, Hubert B. Lurch avoidance strategy and itsimplementation in AMT vehicles. Mechatronics 2008;18:289–300.

[9] Lu T, Dai F, Zhang J. Optimal control of dry clutch engagement based on thedriver’s starting intentions. Proc IMechE, J Automob Eng 2012;226:1048–57.

[10] Yasui Y, Shimojo K, Saito M. Rapid engine speed control for AMT using two-degree-of-freedom sliding mode algorithm. SAE 2005 World Congress,Warrendale PA, SAE 2005-01-1592; 2005.

[11] Horn J, Bamverger J, Michau P, et al. Flatness-based clutch control forautomated manual transmission. Control Eng Pract 2003;11:1353–9.

[12] Lovas L, Play D, Marialigeti J, et al. Mechanical behaviour simulation forsynchromesh mechanism improvement. Proc IMechE, J Automob Eng2006;220:919–45.

[13] Lin S, Chang S, Li B. Research on gearshift piecewise control for AMT based on a2-DOF electromagnetic actuator. China Mech Eng 2013;24(15):2076–80.

[14] Liu L, Chang S. Improvement of valve seating performance of engine’selectromagnetic valvetrain. Mechatronics 2011;21:1234–8.

[15] Shi Xinxin, Chang Siqin. Extended state observer-based time-optimal controlfor fast and precise point-to-point motions driven by a novel electromagneticlinear actuator. Mechatronics 2013;23:445–51.

[16] Chang S, Liu L. A moving coil permanent magnet linear actuator with highpower density. China patent, CN101127474B; 2010.

[17] Liu Y, Tseng C. Simulation and analysis of synchronization and engagement onmanual transmission gearbox. Int J Vehicle Des 2007;43:200–20.

[18] Li C, Miao Y, Feng Y, Du J. Inverse system method for nonlinear systems control(1) – single variable control theory. Control Decis 1997;12:529–35.

[19] Han J. Active disturbance rejection control technique. 1st ed. Beijing: NationalDefense Industry Press; 2008.

[20] Xu Q, Dai X. Improved ANN-inversion control scheme of excitation and valvesystem for turbogenerator. J Southeast Univ 2010;40(6):1196–202.

[21] Xu Q, Huang J, Li H. An online learning and active disturbance rejectioncontrol-based ANN-inversion robust control scheme of excitation and valvesystem for turbogenerator. J Univ Sci Technol China 2012;42(7):590–6.

[22] Pan Y, Xu J, Chen H, Gao R. Stability analysis and application of ESO in directtorque control of matrix converter. Control Decis 2013;28(4):585–9.

[23] Cominos P, Munro N. PID controllers: recent tuning methods and design tospecification. IEE Proc Control Theory Appl 2002;149:46–53.

[24] Zheng Q, Chen Z, Gao Z. A practical approach to disturbance decouplingcontrol. Control Eng Pract 2009;17(9):1016–25.

[25] Naunheimer H, Bertsche B, Ryborz J, et al. Automotive transmissions—fundamentals, selection, design and application. 2nd ed. Germany: Springer;2011.