Control Strategy Development of Driveline Vibration Reduction for Power-Split Hybrid Vehicles

applied sciences

Article Control Strategy Development of Driveline Vibration Reduction for Power-Split Hybrid Vehicles

Hsiu-Ying Hwang 1, Tian-Syung Lan 2,* and Jia-Shiun Chen 1

1 Department of Vehicle Engineering, National Taipei University of Technology, Taipei 10608, Taiwan; [email protected] (H.-Y.H.); [email protected] (J.-S.C.) 2 College of Mechatronic Engineering, Guangdong University of Petrochemical Technology, Maoming 525000, Guangdong, China * Correspondence: [email protected]

Received: 16 January 2020; Accepted: 25 February 2020; Published: 2 March 2020

Abstract: In order to achieve better performance of fuel consumption in hybrid vehicles, the internal combustion engine is controlled to operate under a better efficient zone and often turned off and on during driving. However, while starting or shifting the driving mode, the instantaneous large torque from the engine or electric motor may occur, which can easily lead to a high vibration of the elastomer on the driveline. This results in decreased comfort. A two-mode power-split hybrid system model with elastomers was established with MATLAB/Simulink. Vibration reduction control strategies, Pause Cancelation strategy (PC), and PID control were developed in this research. When the system detected a large instantaneous torque output on the internal combustion engine or driveline, the electric motor provided corresponding torque to adjust the torque transmitted to the shaft mitigating the vibration. To the research results, in the two-mode power-split hybrid system, PC was able to mitigate the vibration of the engine damper by about 60%. However, the mitigation effect of PID and PC-PID was better than PC, and the vibration was able to converge faster when the instantaneous large torque input was made. In the frequency response, the effect of the PID blocking vibration source came from the elastomer was about 75%, while PC-PID additionally reduced 8% by combining the characteristics of the two control methods.

Keywords: power-split hybrid system; two-mode hybrid system; driveline vibration; motor feedback control; vibration reduction

1. Introduction With the advantages of low fuel consumption and low exhaust emissions, hybrid electric vehicles strike a balance between gasoline vehicles with high fuel consumption, exhaust emissions and electric vehicles with limited travel range. In the hybrid system, the internal combustion engine (ICE) is set to operate under the efficiency range, and the motor/generator (M/G) is operated at a low vehicle speed or when the power source and output need to be adjusted. The energy management of electric and ICE power systems, and the emission control have been studied and developed in different types of hybrid systems [1–4]. However, the power source setting causes the internal combustion engine to start and shut down frequently and unpredictably, and the mode shifting changes the torque of the power source greatly. Both situations may result in more obvious vibration of the driveline, which brings out the problem of comfort and decreases power transmission efficiency [5,6]. Numerous hybrid systems have been proposed recently, with commercially available vehicles mainly using the Toyota Hybrid System (THS) or Two-Mode power-split Hybrid (TMH) [7,8]. Hendrickson et al. [9] and Meisel [10] explained the mechanical structure and advantages of the transmission for the TMH system. For various driving needs, two Electric Variable Transmission (EVT)

Appl. Sci. 2020, 10, 1712; doi:10.3390/app10051712 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1712 2 of 13 modes were provided to accommodate power requirements under low-speed/high-speed, and were paired with four sets of fixed gear ratios to overcome the operating limitations between power sources during mode conversion. These ensured that the internal combustion engine remains stable in the efficiency range at all speeds. This transmission consisted of two sets of planetary gears that connected power sources such as an internal combustion engine, two motors/generators, and amplified its output power to the wheels. However, relying solely on the TMH system was not able to express the vibrate situation of the driveline. Ito et al. [11] explained that adding elastomers to the system could simulate the operation of the overall driveline accurately, and present the phenomenon caused by torque transfer. In addition to the half-shaft, this research added elastomer modules such as an internal combustion engine damper and tires to indicate the source of the low-frequency vibration on the driveline, and half shaft speed was fed back to control strategy for vibration reduction of the driveline system. In addition, in terms of vibration reduction, the motor could be quickly fed back when vibration occurred due to the faster dynamic response and the speed-shifting function within the system, without changing the structure of the system. Canova et al. [5] introduced a belted starter/alternator (BSA) mild hybrid system with control of the electric motor to start and stop the engine smoothly. This paper focused on the control of the start and stop dynamics of a Hybrid Electric Vehicle (HEV) with a belted starter/alternator. Davis et al. [12] and Fesefeldt et al. [13] presented an integrated starter alternator model which generated a disturbance input decoupling torque command for the electric motor to cancel the engine torque ripples. Yang et al. [14] developed a control optimization strategy to lower the driveline fluctuation of an axially paralleled hybrid system. Wang et al. [15] studied the single-shaft parallel hybrid powertrain, and proposed a transition control method based on predictive control algorithm. He et al. [16] developed a three-stage control strategy to smooth the transition from electric mode to hybrid mode. Ito et al. [11] proposed a control strategy that within the signal planetary gear hybrid system, while the internal combustion engine was having a large torque output to cause vibration, the signal was sent to control logic to calculate torque feedback by the gear ratio relationship. The torque feedback would be sent back to the controller changing the motor torque output signal to an equal but reverse torque to cause vibration neutralization. Guo et al. [17] focused on the driveline vibration caused by the traction motor in the launch situation, and proposed a superposition control strategy to suppress the driveline vibration. Wang et al. [18] provided an improved genetic algorithm method to reduce the speed-up transient vibration of planetary power-split driveline system. For PID control, Herbst [19] introduced the active disturbance rejection control (ADRC) as an alternative for PID control. This research used a discrete-time case to speed up real time implementation in dynamic system. Liao [20] compared the current rotation speed with the expected rotation speed of the counter shaft when the internal combustion engine ran, and sent the difference to the PID controller. The torque feedback could neutralize the remaining vibration. However, the above two control methods were only for the internal combustion engine when starting. Thus, this research further explored the vibration reduction effect such as adding feedback control when a greater change in power source torque existed. This research focused on improving the elastomer vibration in the TMH driveline caused by the instantaneous large torque from each power source. Two control methods were implemented to neutralize the vibration. One was using the motor output torque feedback generated by predicting the torque when the internal combustion engine started and shut down. The other one was adjusting the motor speed by comparing the monitored rotation speed of the output axis and the estimated rotation speed based on the stable vehicle speed. Finally, the characteristics of two control methods were combined to reduce vibration. The remaining sections are as follows: the theoretical background and modeling of two-mode power-split hybrid system, the control strategies of vibration reduction, the results and comparison of vibration reduction, and the conclusions. Appl. Sci. 2020, 10, 1712 3 of 13

2.Appl. Two-Mode Sci. 2020, 10 Power-Split, x FOR PEER REVIEW Hybrid System Model 3 of 13

2.1.2.1. Two-Mode Two-Mode Power-split Power-split Hybrid Hybrid SystemSystem TransmissionTransmission TheThe General General Motors Motors (GM) (GM) Two-Mode Two-Mode hybrid hybrid transmission transmission systemsystem waswas appliedapplied in the research, as shownas shown in Figure in Figure1. This 1. This transmission transmission system system includes includes two two sets sets of planetaryof planetary gear gear mechanisms mechanisms (P1, (P1, P2), twoP2), sets two of sets brake of brake clutch clutch (CB4, (CB4, CB12R), CB12R), and twoand setstwo ofsets power of power transfer transfer clutch clutch (C13, (C13, C234), C234), as wellas well as an internalas an internal combustion combustion engine engine and two and motors two motors/generators/generators (MG1, (MG1, MG2) MG2) connected connected to to the the ring ring gear, gear, the sunthe gear, sun andgear, the and planet the planet carrier carrier on P1, on respectively. P1, respectively This. systemThis system transferred transferr theedpower the power from from the powerthe sourcepower to source the output to the driving output driving shafts. shafts.

FigureFigure 1. 1.Schematic Schematic diagram of of a a two two-mode-mode power power-split-split hybrid hybrid system. system.

ThisThis transmission transmission system system consistedconsisted of two continuous continuous variable variable speed speed modes modes (EVT) (EVT) to tocover cover the the needsneeds for for low low speed, speed, high-speed high-speed cruise, cruise and, and rapid rapid acceleration acceleration whichwhich alsoalso cooperatedcooperated with four sets sets of ﬁxedof fixed gear gear ratio ratio to smoothen to smoothen the the mode mode shift. shift. When When thethe CB12R clutch clutch was was engaged, engaged, the the torque torque was was outputoutput by by MG2 MG2 with with the the driving driving forceforce need.need. When a a certain certain speed speed was was reached reached or orthe the state state of charge of charge (SOC)(SOC) was was low, low, the the engine engine would would turnturn onon to provide power, power, which which was was called called EVT EVT-1-1 mode, mode, mainly mainly usedused at at low low speed. speed. When When enteringentering thethe high-speedhigh-speed segment, segment, the the CB12R CB12R would would be be loosened loosened and and the the C234C234 clutch clutch was was engaged, engaged, so so that that the the sun sun gear gear (S1) (S1) of of P1 P1 was was connected connected to to the the ring ring gear gear (R2) (R2) of of P2. P2. This allowedThis allowed the internal the internal combustion combustion engine engine to provide to provide more more power power to the to output, the output, which which was was called called EVT-2 mode.EVT-2 This mode. research This research was aimed was at aimed the vibration at the vibration of the driveline, of the driveline, and the situationand the situation of the remaining of the clutchremaining would clutch not be would included. not be included. InIn addition, addition, in in order order to toaccurately accurately grasp the the situation situation of of overall overall torque torque transmission, transmission, and and present present thethe speed speed adjusting adjusting function function of of MM/G/G inin the power system system and and the the accelerating accelerating function function of ofthe the internal internal combustioncombustion engine, engine, the the considerations considerations of the of moment the moment of inertia of ofinertia each componentof each component in the transmission in the systemtransmission and the system internal and force the betweeninternal force gears between were added gears to w furtherere added estimate to further the estimate speed of the each speed power of each power source and output axis [21]. source and output axis [21]. The torque angular acceleration relationship of the EVT-1 mode was exemplified in the The torque angular acceleration relationship of the EVT-1 mode was exempliﬁed in the following. following. In mode one, the clutch CB12R was locked, the internal combustion engine power was In mode one, the clutch CB12R was locked, the internal combustion engine power was input to P1 and input to P1 and split, and P2 was operated with the reduction gear. At this time, the rotation speed relationship of each gear on P1 and P2 were as shown in Equations (1) and (2). Appl. Sci. 2020, 10, 1712 4 of 13 split, and P2 was operated with the reduction gear. At this time, the rotation speed relationship of each gear on P1 and P2 were as shown in Equations (1) and (2).

(R R )ω• + R ω• R ω• = 0 (1) R1 − S1 C1 S1 S1 − R1 E

R ω• (RR + R )ω• = 0 (2) S2 S2 − 2 S2 trans After the internal combustion engine was connected to the damper, it was connected with the ring gear (R1) of P1. MG1 was connected with the sun gear (S1), and MG2 was connected with the planet carrier (C1) to transmit the torque into the transmission system. According to the connection relationship between each power source and the transmission in Figure1, the torque calculation formula Equations (3)–(5) were listed. Among them, TMG1, IMG1, and ωMG1 were the torque, moment of inertia, and rotation speed, respectively. The rest, ICE Damper end (coded as ED in below) and MG2 end, are presented in the following. Sun gear end—MG1:

TMG1 = (IMG1 + IS1)ωMG• 1 + F1RS1 (3) Ring gear end—ICE Damper: TED = I ω• F R (4) R1 ED − 1 R1 Planet carrier end—MG2:

T = (I + I + I )ω• F (R R ) + F R (5) MG2 MG2 C1 S2 MG2 − 1 R1 − S1 2 S2 At the output of the transmission, due to the connection with the ﬂexible shaft, a reaction force (Treact.) was fed back to here when the power output to the shaft. Therefore, the transmission output axis angular acceleration calculation is shown in Equation (6). Wherein, the Itrans is the sum of the moment of inertia from the transmission output to the half-shaft.

Treact = (Itrans)ω• F (R + RR ) (6) − trans − 2 S2 2 Next, the above-mentioned formula was organized into a matrix form as the transmission torque calculation, as shown in Equation (7). Among them, ωE_damper, ωMG1, ωMG2, ωtrans were the rotational speed of the internal combustion engine, the MG1, MG2, and the output axis of the transmission, respectively. The J6 6 matrix was shown in Equation (8). ×    .   TED   ωED     .   T   ω   react   trans     .   TMG1   ωMG1    = [ J6 6] .  (7)  T  ×  ω   MG2   MG2       0   F1      0 F2    IR1 0 0 0 RR1 0   −   0 I 0 0 0 (R + S )   trans R2 2   −   0 0 IMG1 + IS1 0 RS1 0    (8)  0 0 0 I + I + I R R R   MG2 C1 S2 R1 S1 S2   −   RR1 0 RS1 RR1 RS1 0 0   − −  0 (RR + S ) 0 R 0 0 − 2 2 S2 Finally, the formulas were rearranged, and the rotation speed was set as demand. Through the information of the three power sources and reaction force from the shaft, the changes of the rotation speed of each power source were obtained. Appl. Sci. 2020, 10, 1712 5 of 13

Appl. Sci. 2020, 10,2.2. x FOR Internal PEER Combustion REVIEW Engine Model 5 of 13 The internal combustion engine is the main power output source of the hybrid system, providing reason a great poweramount under of high vibration torque demand occurs and, but providing also sutheﬃcient main power source for a vehicle of the to low meet- thefrequency driver’s vibration of driving requirement. The engine power changes with the cylinder pressure, which is not only the the driveline. Inreason order a great to amountpresent of vibrationthe vibrat occurs,ion but situation also the main of sourcetorque of the while low-frequency outputting vibration power, of the torque caused by enginethe driveline. cylinder In order pressure to present was the vibrationused as situation the engine of torque output. while outputting The single power, the-cylinder torque mechanism caused by engine cylinder pressure was used as the engine output. The single-cylinder mechanism is is shown in Figureshown 2. in Figure2.

Figure 2. FigureSchematic 2. Schematic diagram diagram of of a a single-cylindersingle-cylinder mechanism mechanism [21]. [21]. The calculation formula of single-cylinder engine torque is as shown in Equation (9) [22]. Among The calculationthem, Te ,formulaAP, P, Pamb ,ofr, Lsingle, and θe-arecylinder respectively engine the engine torque torque is provided as shown by the in cylinder Equation pressure (9) [22]. Among (N-m), piston top area (m2), the cylinder pressure (psi), the atmospheric pressure (psi), the crankshaft them, 푇푒 , 퐴푃 , radiusP, 푃 (m),푎푚푏 the, r connecting, L, and rodθ푒 length are (m), respectively and the crank angle the (deg).engine torque provided by the cylinder 2 pressure (N-m), piston top area (푚 ), the cylinder pressure (psi), the atmospheric pressure (psi), the  r sin θE  TE = AP(P Pamb)r sin θE1 +  (9) crankshaft radius (m), the connecting rod length (m), andp 2the crank2  angle (deg). − L r sin θE) − A six-cylinder 3.6 L internal combustion engine was applied in this research. The torque values at r sin  the respective crank anglesT  ofA each(P cylinder P ) werer sin listed 1 and used to calculateE the overall torque output of the engine. A torqueE curveP with relativeamb proportionE  was drawn according to the diﬀerent throttle (9) L2  r sin )2 angles, as shown in Figure3.  E 

A six-cylinder 3.6 L internal combustion engine was applied in this research. The torque values at the respective crank angles of each cylinder were listed and used to calculate the overall torque output of the engine. A torque curve with relative proportion was drawn according to the different throttle angles, as shown in Figure 3.

Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13

reason a great amount of vibration occurs, but also the main source of the low-frequency vibration of the driveline. In order to present the vibration situation of torque while outputting power, the torque caused by engine cylinder pressure was used as the engine output. The single-cylinder mechanism is shown in Figure 2.

Figure 2. Schematic diagram of a single-cylinder mechanism [21].

The calculation formula of single-cylinder engine torque is as shown in Equation (9) [22]. Among

them, 푇푒 , 퐴푃 , P, 푃푎푚푏 , r, L, and θ푒 are respectively the engine torque provided by the cylinder pressure (N-m), piston top area (푚2), the cylinder pressure (psi), the atmospheric pressure (psi), the crankshaft radius (m), the connecting rod length (m), and the crank angle (deg).   r sin  T  A (P  P )r sin 1 E  E P amb E   (9) L2  r sin )2  E 

Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13 Figure 3. Output torque of internal combustion engine with ignition. Figure 3. Output torque of internal combustion engine with ignition. However, in an actual hybrid system, the internal combustion engine acts on the eﬃcient zone, that is, it doesHowever, not start in an the actual ignition hybrid in system, the general the internal idle speed combustion range, butengine only acts when on the the efficient motor zone, drives the internalthat combustionis, it does not enginestart the to ignition a certain in the speed general or above.idle speed This range, driving but only process when also the makesmotor drives the piston movethe in internal the cylinder, combustion but the engine power to a stroke certain is speed excluded or above. due This to no driving ignition. process Since also the makes compressibility the piston of move in the cylinder, but the power stroke is excluded due to no ignition. Since the compressibility the air, when the piston nears the top dead center (TDC), the air pushes the piston down. This process of the air, when the piston nears the top dead center (TDC), the air pushes the piston down. This can createprocess torque can creat vibration,e torque whichvibration is, relativewhich is smallrelative compared small compar withed engine with engine torque torque pause pause with with ignition. The mechanismignition. The of mechanism no ignition of of no the ignition internal of combustion the internal combustionengine before engine 1200 before rpm was 1200 included rpm was in the researchincluded model, in and the researchthe torque model, corresponding and the torque to di ﬀ corerentresponding crank angles to different was established crank angles according was to the throttleestablished angle, according as shown to the in throttle Figure4 angle,. as shown in Figure 4.

FigureFigure 4. Output4. Output torque torqueInternal Internal combustion engine engine without without ignition. ignition.

2.3. Flexible2.3. Flexible Shaft Shaft Module Module Ideally,Ideally, the componentsthe components of of a drivelinea driveline connect connect to to each each other other with with rigid rigid connection, connection, which which means means the drivethe drive shaft shaft is sti isﬀ ,stiff, does does not not absorb absorb energy, energy, and and is ableis able to to fully fully transmit transmit the the torque torque toto thethe wheelwheel after after receiving external torque, and the vehicle produces the corresponding speed for driving requirement. However, the real-life drive shafts and even tires are elastomers, each with rotational stiffness and damping. After the force taken, a certain amount of energy will be absorbed. In addition, elastomers generate corresponding, oscillating torque feedback to the front and rear components when they are subjected to a large external torque in an instant. Flexible shaft modules such as half shafts, tires and engine damper were established in this research. In order to perform the elastomers torsional vibration caused by an external torque, the elastic coefficient and damping were added. Taking the drive shaft as an example, after the drive

shaft rotational speed received from the output of the transmission system (ωt) and shaft speed according to the vehicle speed (휔푎푥푙푒), the torque fed back to the transmission system was calculated according to Equations (10) and (11), which was also the output torque that the shaft transmitted to the differential. Finally, this torque information was transmitted to the final drive mechanism to calculate the driving force. The flexible shaft module was shown in Figure 5.  gap  t  axle (10) Appl. Sci. 2020, 10, 1712 7 of 13 receiving external torque, and the vehicle produces the corresponding speed for driving requirement. However, the real-life drive shafts and even tires are elastomers, each with rotational stiffness and damping. After the force taken, a certain amount of energy will be absorbed. In addition, elastomers generate corresponding, oscillating torque feedback to the front and rear components when they are subjected to a large external torque in an instant. Flexible shaft modules such as half shafts, tires and engine damper were established in this research. In order to perform the elastomers torsional vibration caused by an external torque, the elastic coefficient and damping were added. Taking the drive shaft as an example, after the drive shaft rotational speed received from the output of the transmission system (ωt) and shaft speed according to the vehicle speed (ωaxle), the torque fed back to the transmission system was calculated according to Equations (10) and (11), which was also the output torque that the shaft transmitted to the differential. Finally, this torque information was transmitted to the final drive mechanism to calculate the driving force. The flexible shaft module was shown in Figure5. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13 ωgap = ωt ω (10) − axle t Zt T  C   K  dt (11) Treactionreaction= Cshashaft f t ωgapgap+ Kshashaft f t  ωgapgap dt (11) 0 · 0

Figure 5. Flexible shaft module. Figure 5. Flexible shaft module. 3. Vibration Reduction Control Methods 3. Vibration Reduction Control Methods 3.1. Pulse Cancellation (PC) 3.1. Pulse Cancellation (PC) During engine start, the internal combustion engine was set to operate within the eﬃcient range in theDuring hybrid engine system, start, and the the internal rotational combustion speed can engine be increased was set sharplyto operate to within reach the the desiredefficient speed. range Thisin the process hybrid is system, coupled and with the the rotational vibrating torquespeed can from be the increased internal combustionsharply to reach engine. the A desired large amount speed. ofThis vibration process happens is coupled and iswith transmitted the vibrati tong the torque output from axis while the internal starting-up combustion the engine, engine. resulted A large in a lossamount of comfort. of vibration happens and is transmitted to the output axis while starting-up the engine, resultedThe systemin a loss was of comfort. able to prejudge the information about the operation of the internal combustion engine.The Torque system feedback was able ofto theprejudge faster the transient information response about M /theGs operation was designed of the to internal reduce combustion the output vibrationengine. Torque caused feedback by the start-upof the faster of the transient internal response combustion M/Gs engine. was designed The vibration to reduce torque the output of the internalvibration combustion caused by engine the start to- theup transmission of the internal system combustion was neutralized engine. The by M vibration/Gs, and torqueM/Gs, which of the alsointernal provided combustion suﬃcient engine power to to the drive transmiss the vehicle,ion system and the was output neutralized axis torque by M/Gs, could driveand M/Gs the wheel, which at aalso smoother provided curve sufficient (mean value).power to The drive torque the designvehicle, for and both the M output/Gs was axis required torque to could maintain drive the the torque wheel balanceat a smoother of the planetarycurve (mean gears. value). The torque design for both M/Gs was required to maintain the torqueThe balance corresponding of the planetary torque gears. required for the output when the internal combustion engine was startedThe was corresponding calculated, as torque shown required in Equations for the (12) output and (13).when Amongthe internal them, combustionTmg1_ f and engineTmg2_ f wasare thestarted torque was feedback calculated, MG1 as andshown MG2, in Equations which should (12) neutralizeand (13). Among the vibration them, while푇푚푔1_푓 maintaining and 푇푚푔2_푓 theare balancethe torque of the feedback system force.MG1 andRS1 andMG2R,R 1whichare respectively should neutralize the radius the of vibration sun gear andwhile the maintaining ring gear of thethe compoundbalance of the planetary system gear force. set. 푅푆1 and 푅푅1 are respectively the radius of sun gear and the ring gear of the compound planetary gear set. RS1 Tmg1_ f = ∆TE (12) −RR1 RS1 Tmg1_ f   TE (12) (RR1 R RS1) Tmg2_ f = −R1 ∆TE (13) − RR1

(RR1  RS1) Tmg 2 _ f   TE (13) R R1

3.2. Proportional-Integral-Derivative Control (PID) PID control was applied in this research as another control method in addition to PC. When the vibration was sensed, the vibration was neutralized by corresponding torque feedback provided by the motors, which was also able to meet the power demand. The vehicle speed of the previous time step was recorded, and the corresponding transmission rotation speed was calculated as the reference.

The calculation is shown in Equation (14). Among them, 푁푡 is the base speed of the transmission, 푉푣푒ℎ𝑖푐푙푒 is the vehicle speed, and r is the effective radius of the tire.

Nt Vvehicle /r *(30/) (14) The previous time step actual rotation speed of the transmission was compared with reference speed, and the difference was sent into the PID controller to obtain the required vibration reduction torque feedback. The feedback started when a large change in speed occurred. The calculation is

shown in Equations (15) and (16). Among them, 푁푡_푒푥푎푐푡 is the actual rotational speed of the Appl. Sci. 2020, 10, 1712 8 of 13

Nt = V /r (30/π) (14) vehicle ∗ The previous time step actual rotation speed of the transmission was compared with reference speed,Appl. Sci. and2020, the 10, x di FORfference PEER REVIEW was sent into the PID controller to obtain the required vibration reduction8 of 13 torque feedback. The feedback started when a large change in speed occurred. The calculation is shown intransmission, Equations (15)∆푁푡 and is the (16). difference Among value them, ofN thet_exact rotationalis the actual speed, rotational Kp, KI, and speed KD are of the the gain transmission, values of ∆theN tPIDis the control, difference and valueu is the of control the rotational effort needed speed, K forp, K vibrationI, and KD reduction.are the gain values of the PID control, and u is the control effort needed for vibration reduction. Nt  Nt  Nt _ exact (15)

∆Nt = Nt Nt_exact (15) −푡 ∆푁푡 푢 = 퐾 ∆푁 + 퐾Z∫t ∆푁 푑푡 + 퐾 (16) 푝 푡 퐼 푡 퐷 ∆푑푡Nt u = Kp∆Nt + KI 0 ∆Ntdt + KD (16) 0 dt Finally, the control effort needed for vibration reduction was sent to the M/G instruction controllerFinally, to theadjust control the torque eﬀort needed for vibration for vibration reduction. reduction was sent to the M/G instruction controller to adjust the torque for vibration reduction. 4. Simulation Results 4. Simulation Results

Driving Cycle For a clearerclearer representationrepresentation ofof showing showing the the elastomer elastomer vibration vibration derived derived from from the the great great change change of Mof /M/GG torque torque while while the the internal internal combustion combustion engine engine was was running running and and shifting shifting modes modes during during driving, driving, the drivingthe driving cycle cycle applied applied in this in researchthis research is shown is shown in Figure in Figure6. The 6. vehicle The vehicle initially initially accelerated accelerated to 32 miles to 32 permiles hour per in hour 10 s, in held 10 s in, held the ﬁx-speedin the fix for-spe 5ed s andfor 5 then s and dropped then dropped at rest in at 10 rest s. Inin addition,10 s. In addition, this research this setresearch the mode set the shift mode at the shift time at when the time the speed when reached the speed 30 miles reached per hour.30 miles It has per shown hour. aIt greater has shown torque a ingreater the power torque source in the while power the source mode while shifted. the mode shifted.

Figure 6. Driving cycle. Figure 6. Driving cycle. After we added the control methods, the curve diﬀerence between the half-shaft vibration and the foundationalAfter we modeladded was the observed,control methods, as shown the in curve Figure difference7. In addition, between due the to thehalf torque-shaft vibration of the power and the foundational model was observed, as shown in Figure 7. In addition, due to the torque of the power source changing greatly during acceleration and deceleration, as shown in the brown and blue frames, it resulted in significant vibration. Appl. Sci. 2020, 10, 1712 9 of 13 source changing greatly during acceleration and deceleration, as shown in the brown and blue frames, Appl.itAppl. resulted Sci.Sci. 20202020 in,, 1010 signiﬁcant,, xx FORFOR PEERPEER vibration. REVIEWREVIEW 99 ofof 1313

ComparisonComparison ofof TreactTreact betweenbetween controlscontrols 15001500 OriginalOriginal 10001000 PIDPID PCPC PC-PIDPC-PID 500500

-500-500 Torque(N-m) Torque(N-m) -1000-1000

-1500-1500

-2000-2000

-2500-2500 00 55 1010 1515 2020 2525 3030 3535 Time(s)Time(s) FigureFigure 7. 7. Half-shaftHalf-shaft torquetorque comparisoncomparison with with different didifferentﬀerent control control methods methods inin timetime domain.domain.

TheThe comparisoncomparison during duringduring vehicle vehiclevehicle acceleration accelerationacceleration and andand deceleration decelerationdeceleration are areare shown shownshown in Figuresinin FiguresFigures8 and 88 and9and. The 9.9. The PCThe PCwasPC waswas able ableable to reduce toto reducereduce 593 593593 N-m, N-m,N-m, about aboutabout 22.5% 22.5%22.5% of ofof the thethe peak-to-peak peak-to-peakpeak-to-peak torque torquetorque vibration vibratvibrationion duringduring acceleration, acceleration, butbut the the PC PC mainlymainly workedworked whilewhile thethe internalinternal combustioncombcombustionustion engineengine waswas running.runninrunning.g. Thus, Thus, there there was was no no vibrationvibration reductionreduction during duringduring deceleration. deceleradeceleration.tion. PID PIDPIDand andand PC-PID PC-PIDPC-PID were werewere able ableable to toto reduce reducereduce 1055 10551055 N-m, N-m,N-m, about aboutabout 40% 40%40% of oftheof thethe peak-to-peak peak-to-peakpeak-to-peak torque torquetorque value valuevalue during duringduring acceleration; acceleration;acceleration; and wereandand werewere able to ableable reduce toto reducereduce 419 N-m, 419419 about N-m,N-m, 14% aboutabout during 14%14% duringdeclaration.during declaration.declaration. The overall TheThe overall eoverallffect of effecteffect vibration ofof vibrationvibration reduction reductionreduction performed performedperformed better than betterbetter PC. thanthan However, PC.PC. However,However, the analysis thethe analysisofanalysis peak-to-peak ofof peak-to-peakpeak-to-peak vibration vibrationvibration reduction reductionreduction during deceleration duringduring decelerationdeceleration in the time inin domain thethe timetime was domaindomain almost waswas identical almostalmost to identicalPC.identical Therefore, toto PC.PC. the Therefore,Therefore, frequency thethe domain frequencyfrequency response domaindomain was responseresponse needed to waswas compare neededneeded the toto di comparecomparefference betweenthethe differencedifference them. betweenThebetween effect them.them. of the TheThe Peak-to-Peak effecteffect ofof the vibrationthe Peak-to-PeakPeak-to-Peak reduction vibrvibr inationation half-shaft reductionreduction torque inin under half-shafthalf-shaft each control torquetorque methodunderunder eacheach was controlcompared,control methodmethod as shown waswas compared,compared, in Table1. asas shownshown inin TableTable 1.1.

ComparisonComparison ofof TreactTreact betweenbetween controlscontrols 15001500 OriginalOriginal PIDPID 10001000 PCPC PC-PIDPC-PID

500500

00 Torque(N-m) Torque(N-m)

-500-500

-1000-1000

-1500-1500 88 8.58.5 99 9.59.5 1010 10.510.5 1111 11.511.5 1212 12.512.5 1313 Time(s)Time(s) FigureFigure 8. 8. VehicleVehicle half-shaft half-shaft torque torque during during acceleration acceleration inin timetime domain.domain. Appl. Sci. 2020, 10, 1712 10 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 13

Comparison of Treact between controls 1000 Original PID 500 PC PC-PID 0

-500

-1000 Torque(N-m)

-1500

-2000

-2500 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 Time(s) Figure 9. Vehicle half-shaft torque duringduring decelerationdeceleration inin timetime domain.domain.

Table 1. Comparison of the vibration deduction results of each control method and basic model Table 1. Comparison of the vibration deduction results of each control method and basic model (original) in the time domain. (original) in the time domain.

Peak-to-PeakPeak-to-Peak Vibration Vibration Peak-to-PeakPeak-to-Peak Vibration Vibration VibrationVibration Reduction Reduction (Acc. in N-m) (Dec. in N-m) (Acc./Dec. in N-m) (Acc. in N-m) (Dec. in N-m) (Acc./Dec. in N-m) BasicBasic model model 26372637 30073007 -/- -/- PC PC 20432043 30073007 594594/419/419 PID 1582 2588 1055/419 PID 1582 2588 1055/419 PC-PID 1611 2588 1025/419 PC-PID 1611 2588 1025/419 The half-shaft torque that was added to the control methods was then applied to the Fast Fourier TransformThe half-shaft (FFT) to torquefurther that confirm was addedthe effect to the of vibration control methods reduction. was The then observation applied to theof the Fast half-shaft Fourier Transformtorque and (FFT) curve to was further shown confirm in Fi thegure eff ect10. ofWith vibration PC, the reduction. amplitude The at observation 16 Hz, the ofengine the half-shaft damper torquenatural andfrequency, curve waswas shownreduced in by Figure 60%, and10. the With amplitude PC, the amplitudeat 11 Hz, the at half-shaft 16 Hz, the natural engine frequency, damper naturalwas also frequency, reduced wasby about reduced 25%. by 60%,This andresult the was amplitude mainly atcaused 11 Hz, by the the half-shaft PC addressing natural frequency, only the wasvibration also reduced derived by from about the 25%. internal This combustion result was mainly engine. caused When by the the speed PC addressing difference only between the vibration the two derivedends of the from damper the internal decreased, combustion the elastomer engine. vibrat Whenion the would speed be diff reduced.erence between Therefore, the twothe vibration ends of the in damperthe internal decreased, combustion the elastomer engine damper vibration reduced, would be and reduced. the vibration Therefore, reduction the vibration was also in the able internal to be combustionobserved in the engine half-shaft damper natural reduced, frequency. and the However, vibration the reduction result of was PC alsoat 5 Hz able was to belimited. observed By adding in the half-shaftPID, the overall natural vibration frequency. was However, able to thebe resultreduced of PCby atmore 5 Hz than was 75%. limited. In PID By adding control, PID, there the was overall no vibrationsimilarity wasto the able PC to control be reduced method, by morewhich than addressed 75%. In only PID specific control, vibration there was source, no similarity but instead to the to PCreduce control vibration method, according which addressedto the condition only specificof the output vibration axis, source,so the overall but instead vibration to reduce reduction vibration effect accordingwas ideal. to the condition of the output axis, so the overall vibration reduction effect was ideal. It was observed that low-frequency vibration was basically neutralized while adding the PC-PID curve. The overall vibration was able to reach over 75%, while the vibration reduction range at 16 Hz was about 8% higher than the effect of PID control. The range of vibration reduction of each control method at each frequency is shown in Table2. The two-mode power-split hybrid system was developed by vehicle manufactures, and the simulation model was accurately represented by the driveline system. The control strategies could be implemented in the vehicle without difficulty, and the benefits of vibration reduction could be expected. Appl. Sci. 2020, 10, 1712 11 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 13

Figure 10. Half-shaft torque comparison with diﬀerent control methods in frequency domain. Figure 10. Half-shaft torque comparison with different control methods in frequency domain.

TableIt 2.wasComparison observed ofthat the low-frequency vibration deduction vibration of di wasﬀerent basically control neutralized methods in while the frequency adding the domain. PC- PID curve. The overall vibration was able to reach over 75%, while the vibration reduction range at 16 Hz was about 8% higher than thePC effect (%) of PID control. PID (%) The range PC-PIDof vibration (%) reduction of each control method at each frequency is shown in Table 2. 5 Hz 4.3% 78.2% 78.2%

Table 2. Comparison11 Hz of the vibration24.7% deduction of different 94.7% control methods 92.9%in the frequency domain.

16 Hz PC60% (%) PID (%) 78.7% PC-PID (%) 86.2% 5 Hz 4.3% 78.2% 78.2% 5. Conclusions 11 Hz 24.7% 94.7% 92.9% 16 Hz 60% 78.7% 86.2% This research established a forward Two-Mode Hybrid System module with MATLAB/Simulink, and incorporatedThe two-mode elastomers power-split such hybrid as engine system damper, was developed half-shaft, by andvehicle tires manufactures, to present theand vibrationthe situationsimulation of the model driveline was whileaccurately driving. represented Previous by researchthe driveline majorly system. focused The co onntrol the strategies driveline could vibration causedbe implemented by the traction in motorthe vehicle during without start difficulty, and speed-up and the of benefits vehicle. of This vibration research reduction included could the be torque disturbanceexpected. from cylinder pressure of the internal combustion engine, and control strategies were applied on electric motors that had quick responses to eliminate the vibration caused by the torque disturbance5. Conclusions from the engine and driveline system. Vibration reduction control to the driveline was applied whileThis research the internal established combustion a forward engine Two-Mode was started Hybrid or System transmission module with was MATLAB/Simulink, shifting modes. At the sameand time, incorporated without changing elastomers the such power as engine demand, damper, three half-shaft, control methods and tires wereto present implemented. the vibration Such as Pulsesituation Cancellation, of the driveline which could while reducedriving. vibrationPrevious research by expecting majorly vibration focused on derived the driveline from vibration the operation of thecaused internal by the combustion traction motor engine during and start the and angular speed-up acceleration of vehicle. of This the research transmission included output, the torque and PID disturbance from cylinder pressure of the internal combustion engine, and control strategies were control, which was able to adjust the speed of the faster-responsive motor/generator to reduce the applied on electric motors that had quick responses to eliminate the vibration caused by the torque vibration that was created by the angular velocity of the transmission output. The two control methods disturbance from the engine and driveline system. Vibration reduction control to the driveline was aboveapplied were combinedwhile the internal at the end.combustion According engine to was the datastarted analysis or transmission in the previous was shifting sections, modes. the At following the conclusionssame time, can without be drawn: changing the power demand, three control methods were implemented. Such as Pulse Cancellation, which could reduce vibration by expecting vibration derived from the operation 1. The vibration of the half-shaft torque feedback under each control method was observed in of the internal combustion engine and the angular acceleration of the transmission output, and PID control,the time which domain, was able the to eff adjustect of the PC speed was obviousof the faster-responsive when the vehicle motor/generator accelerated to and reduce the the internal vibrationcombustion that enginewas created started by up,the theangular vibration velocity reduction of the transmission range of peak-to-peak output. The two value control of torque was able to reach up to 22.5%. On the whole, however, the PID vibration reduction effect was more significant. The vibration reduction range of peak-to-peak value was able to reach up to 40% when the vehicle accelerated, the convergence speed was also faster, and the torque output was smoother. In addition, the effect in the time domain was not much different from the PID; therefore, the difference will be need to be determined by the frequency response. Appl. Sci. 2020, 10, 1712 12 of 13

2. Apart from the observation of torque in the time domain, Fast Fourier Transform analysis of half-shaft torque of the vehicle was performed. In the frequency response of half-shaft torque, it was found that although the vibration was deduced with PC, and the vibration reduction at engine damper natural frequency, 16 Hz, was able to reach up to 60%. The vibration deduction at tire natural frequency, 5 Hz, was not obvious. The vibration reduction was relatively better in the PID frequency domain response. In the original vibration, sources of 5 Hz, 11 Hz, and 16 Hz were also effectively isolated, each reduced by 78.2%, 94.7%, and 78.7%, respectively, while the effect of vibration reduction of the PC-PID at 16 Hz increased another 8%, strengthening the effect of vibration reduction for the internal combustion engine. 3. The vibration reduction analysis of this research focused on the low-frequency vibration, which was directly related to the comfort of the human body. This research simulated the vibration situation when the power source was operated by estimating of the torque of the internal combustion engine derived from the cylinder pressure and adding elastomers such as a internal combustion engine damper, Half-Shaft, and tires to the driveline. There are a few more ideas for the modeling process as follows, which could be applied to improve accuracy in the future.

The internal combustion engine module is derived from cylinder pressure and a connecting rod mechanism. It can be improved by a more comprehensive engine model that includes the transient response. It will be able to present the impact of vibration more accurately. This model could be derived from the cranking ICE and the actual ignition. In the overall driveline, apart from the low-frequency vibration provided by the engine, there is a motor/generator that brings high-frequency vibration, and results in disturbance to the controller and sensor, which causes error in signal transduction. Therefore, adding an actual motor/generator model for processing high-frequency vibration analysis could be considered in the future.

Author Contributions: Conceptualization, H.-Y.H.; investigation, H.-Y.H.; methodology, T.-S.L.; project administration, J.-S.C.; software, J.-S.C.; validation, T.-S.L. and J.-S.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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