Active Return-to-Center Control Based on Torque and Angle Sensors for Electric Power Steering Systems

Transcription

1 Aticle Active Retun-to-Cente Contol Baed on Toque and Angle Seno fo Electic Powe Steeing Sytem Pan-Pan Du, Hao Su *, Gong-You Tang College of Infomation Science and Engineeing, Ocean Univeity of China, Qingdao266100, China; (P.-P.D.); (G.-Y.T.) * Coepondence: afeedom@163.com; Tel.: Abtact: Thi pape peent a complete contol tategy of the active etun-to-cente (RTC) contol fo electic powe teeing (EPS) ytem. We fit etablih the mathematical model of the EPS ytem and analyze the ouce and influence of the elf-aligning toque (SAT). Second, baed on the feedback ignal of teeing column toque and teeing wheel angle, we give the tigge condition of a tate witch between the teeing ait tate and the RTC tate. In ode to avoid the udden change of the output toque fo the diving moto when the tate witche fequently between the teeing ait tate and the RTC tate, we deign an unditubed tate witching logic algoithm. Thi tate witching logic algoithm enue that the output value of the RTC contolle i et to an initial value and inceae in given tep up to a maximum value afte enteing the RTC tate, and the output value of the RTC contolle will educe in given tep down to zeo when exiting the RTC tate. Thi theefoe enue mooth witch contol between the two tate and impove the dive teeing feeling. Thid, we deign the RTC contolle, which depend upon the feedback ignal of the teeing wheel angle and the angula velocity. In addition, the contolle inceae the auxiliay contol function of the RTC toque baed on vehicle peed. The expeimental eult how that the active RTC contol method doe not affect the baic ait chaacteitic, which effectively educe the eidual angle of the teeing wheel at low vehicle peed and impove the RTC pefomance of the vehicle. Keywod: electic powe teeing ytem; toque eno; angle eno; tate witch; active etunto-cente contol 1. Intoduction Electic powe teeing (EPS) ytem have the advantage of afety, enegy aving, and envionmental potection. It ha become the mainteam of powe teeing technology fo paenge ca becaue of it impotant ole in the enhancement of handling tability and afety [1]. The EPS ytem add a moto and deceleation mechanim on the bai of the taditional mechanical teeing mechanim. Theefoe, the fiction of the teeing ytem will inceae and the etun-to-cente (RTC) pefomance will educe. In the unning poce of a vehicle, when the dive manually tun the teeing wheel back to cente, it often need to coect the diection ubtantially o fequently. The vehicle dive cannot get a comfotable contol feeling and i pone to fatigue, thu impacting taffic afety. When the dive tun the teeing wheel to cente, the ait moto can apply the coeponding RTC toque to the teeing ytem, which can olve the poblem that the teeing wheel cannot etun to cente becaue of the fiction of the mechanical pat, and make the opeation tack of the teeing wheel and the unning tack of the vehicle the ame, thu geatly educing the buden on, and poviding a comfotable and table diving expeience fo, the dive [2] by the autho(). Ditibuted unde a Ceative Common CC BY licene.

2 2 of 12 Recently, expet and chola at home and aboad have done a lot of eeach on the RTC contol of EPS ytem. Fo EPS ytem with a teeing wheel angle eno intalled, ince the abolute poition of the teeing wheel can be obtained in eal-time, the eeach on thi kind of ytem mainly focue on the ealization method of RTC contol. Thi eeach take the teeing wheel angle a an input ignal, and mainly adopt the Popotional Integal Deivative (PID) contol method [3] o othe impoved PID algoithm [4,5] to make the teeing wheel etun to cente. Becaue the pice of an angle eno i highe, in ode to ave cot many eeache ue moto voltage and cuent to etimate moto peed, and then etimate the teeing wheel angle though integation and afte that, toque etimation [6], tet data tatitic [7], RTC toque compenation [8,9] and othe method ae ued to ealize RTC contol thee method have a cetain effect on the RTC ability of the EPS ytem. Howeve, it depend on the peciion of the ytem model and bing geat uncetainty to the RTC contol due to the lack of teeing wheel angle infomation. Moeove, the algoithm i complex and i pone to poblem and difficult to pomote. Fo vehicle equipped with an electonic tability pogam (ESP), the elevant vehicle taveling tate infomation can be obtained fom the eno ignal of the ESP uch a vehicle idelip angle and yaw ate, and the RTC toque can be etimated baed on thee ignal in ode to ealize RTC contol [10, 11], but thee method do not apply to vehicle without ESP intalled. With the development of eno technology, a compoite eno i ued to detect the toque and angle of the teeing wheel, and the pice of thee i gadually deceaing. The teeing ytem i vital to the afety of the ca; theefoe, it i not woth acificing afety to ave cot and the active RTC contol with angle eno ha gadually become mainteam [12 14]. At peent, the eeach on the active RTC contol of EPS ytem i mainly focued on the contol method. Thee i le eeach on the detemination method of the RTC tate. The mot common method fo detemining the RTC tate i to judge whethe the teeing wheel angle and the angula velocity ae in the ame diection good eult can be achieved fo the eleae-etun tate. Fo the complex teeing condition in which powe teeing tate and RTC tate witch fequently, howeve, RTC toque will have a cetain impact on the dive feel becaue the angula velocity of the teeing wheel cannot be mutated [15 17]. When the ait tate and the RTC tate ae witching becaue the diection of the ait toque and the RTC toque ae oppoite one anothe, if they ae not connected popely, the teeing poce will eult in a ene of futation and affect the feel fo the dive. It i theefoe impotant fo RTC contol, but to the bet of the autho knowledge, no liteatue ha been publihed in thi egad. The elf-aligning toque of the vehicle inceae with the inceae of vehicle peed [18], theefoe, the RTC toque hould vay with the vehicle peed. Mot eeach focue on the RTC pefomance at a fixed vehicle peed but doe not pay attention to the influence of vehicle peed. Thi pape conide the deficiency of cuent RTC contol fo EPS ytem, and a method baed on teeing wheel angle ignal i popoed to accuately detemine the RTC tate of the vehicle. An RTC contol tategy fo the EPS ytem i deigned to enue unifomly mooth tanition of the toque fo the teeing wheel to avoid affecting the feel fo the dive. 2. Model of EPS Sytem The mechanical tuctue of EPS ytem i hown in Figue 1, which mainly compoe of toque-angle eno, teeing wheel, teeing column, wom gea, ack and pinion, the ait moto, the electonic contol unit (ECU), and o foth. It baic opeating pinciple can be ummaized a follow: when the vehicle i in the tating o unning tate, the input toque and the angle of the teeing wheel ae detected though the toqueangle eno placed on the teeing column, and thee ignal will be tanmitted to an ECU fo poceing, and then dive the ait moto to povide an ait toque o a RTC toque [19,20].

3 3 of 12 Figue 1. Mechanical tuctue of Electic Powe Steeing (EPS) ytem. The dynamic model of an EPS ytem i govened by the elationhip between teeing mechanim, the electic moto dynamic behavio and the oad/tie contact foce. Fom Figue 1, following Newton econd law, a nonlinea dynamic model of the EPS ytem can be deived. The mathematical model of the EPS ytem can be decibed a: J θ = T T B θ (1) d T = K( θ θ p) (2) p J mθm = Tm Km( θm G ) B mθm (3) p M p + B p + TSAT + Ffic gn( p ) = ( T + TG) / p (4) whee J i the teeing column moment of inetia; θ i the otation angle of the teeing wheel; T d i the teeing wheel toque; T i the meauement of the toque eno; B i the teeing column vicou damping; K i the teeing column tiffne; θ i the otation angle of the pinion; p J m i the moto moment of inetia; θ m i the otation angle of the moto haft; T m i the electomagnetic toque povided by electic moto; K m i the moto tiffne; B m i the moto vicou damping; G i the moto gea atio; p i the ack poition; i the pinion adiu; M p i the ma of the ack; vehicle; B i the ack vicou damping; F i the fiction toque of the teeing ytem. fic T SAT i the elf-aligning toque of the In ode to analyze the lateal dynamic of the vehicle and etimate the elf-aligning toque (SAT) of the font wheel, a bicycle model i ued. The pinciple ketch map of the bicycle model i hown in Figue 2. Thi model include eveal impotant excluion and implification. Thee implification geatly educe the model complexity and degee of feedom, but do not ignificantly affect the vehicle lateal dynamic.

4 4 of 12 Figue 2. Bicycle model. The lateal foce i a nonlinea function of the wheel lip angle. Howeve, when a ca i in the nomal unning tate, the lip angle i vey mall; theefoe, the lateal foce can be appoximated with a linea function of lip angle. The font and ea lateal foce of the wheel i: F Y1 Y1 1 F = K α = K α Y2 Y2 2 (5) whee F Y1 and F Y 2 ae font and ea lateal foce of the wheel, K Y1 and K ae font and ea Y 2 tie coneing tiffne, α 1 and α 2 ae font and ea lip angle of the wheel. Accoding to the coodinate elation of Figue 2, aω α1 = ( δ ξ) = β + δ u v bω bω α2 = = β u u whee δ i the font wheel tuning angle, ξ i the angle between the X-axi and the velocity at the midpoint of the font haft, β i the idelip angle of the vehicle cente of ma, a and b ae the ditance fom font and ea tie to vehicle cente of ma, ω i the yaw ate of the vehicle cente of ma, u and v ae the longitudinal and latitudinal velocity of the vehicle at cente of ma. SAT i mainly geneated by the eactive foce of the font lateal foce; becaue the font lateal foce i popotional to the font lip angle, the SAT can be appoximated with a linea function of the font lip angle. aω TSAT = KSATα1 = KSAT ( δ β ) (7) u whee K i the tiffne of the elf-aligning toque. It can be een that SAT inceae with an SAT inceae in vehicle peed. In thi pape, a pemanent magnet buhle DC moto i ued a the ait moto. The dynamic model of the moto i: di() t La + Rit a () = Ua() t E() t (8) dt (6)

5 whee L a i the electic inductance of the moto, moto amatue cuent, a () U t i the moto amatue voltage, () of the moto amatue. Accoding to the moto theoy, the following expeion i given: Et () = Ke ( Φ) nt () T () t = K ( Φ)() i t m 5 of 12 R a i the electic eitance of moto, it () i the Et i the back electomotive foce whee Φ i the magnetic field tength of the moto tato, Ke ( Φ ) and Kt ( Φ ) ae poitive numbe dependent on the magnetic field tength Φ, nt () i peed of the moto haft, Tm () t i the moto toque. Auming that Φ i contant, then Ke ( Φ ) and Kt ( Φ ) ae contant, and denoted a K e and K t, epectively [21,22]. The moto toque T () t i applied to the teeing column though the wom gea educe, Ta m () t i the toque acting on the teeing column and can be expeed a: whee K i eduction atio of the wom gea. The toque acting on the teeing wheel i: t T () t = K T () t (10) a m T () t = T () t T () t (11) d a whee T () t i the toque acting on the teeing wheel and T () t i the eitance toque of the d teeing column caued by fiction between the tie and the gound. 3. Active RTC Contol Stategy Thee ae two impotant apect needed to olve the active RTC contol poblem of EPS ytem; one i the RTC tate judgment, and the econd i the RTC algoithm. The pimay goal of EPS ytem i to ealize powe teeing and the active RTC i ued to impove the pefomance of the vehicle and hould not affect the baic ait chaacteitic of EPS ytem RTC State Detemination Active RTC contol doe not wok in the teeing ait poce and it i tiggeed only when the vehicle ente the RTC tate. Theefoe, it i a pecondition of the active RTC contol to accuately judge the cuent unning tate of the teeing ytem. The mot commonly ued method i baed on the ign of teeing wheel angle and angula velocity when θθ < 0, it goe back to the RTC tate. Howeve, thi method doe not accuately detemine the opeation intention of the dive becaue in pactice, a teeing poce i not a imple eleae-etun poce. The teeing wheel may be etuning, but becaue of the dive intevention, the teeing wheel will emain tationay o un with egula powe teeing, and the ait tate and the RTC tate will be witched fequently. Becaue the angula velocity of the teeing wheel cannot be changed uddenly, the ditubance witch will be geneated. Ditubance toque caued by ditubance witching can affect the dive feel. Theefoe, it i neceay to ue teeing toque ignal to detect whethe o not the dive ha a an intention to change fom the RTC tate to a teeing tate. In the powe teeing contol tate, when the teeing toque exceed a etting toque value T d 0, the aited moto will povide ait toque, that i to ay, if the teeing toque exceed the etting toque value T d 0, it mean that the dive ha an intention to tun the teeing wheel. If thee i uch an intention, it i detemined that the RTC contol tate i witched to the powe teeing contol tate. When the vehicle i unning at low peed o i at et, it i not neceay and not uitable to ue active RTC contol. When diving at high peed, due to the mall teeing eitance, the paive RTC (9)

6 6 of 12 toque of the ca i ufficient to make the teeing wheel etun to cente, o it doe not need active RTC contol. Moeove, it may even need damping contol at the time of etun. Theefoe, active RTC contol i only executed within a et vehicle peed ange. The vehicle doe not need active RTC contol when it top, o the minimum vehicle peed V min i uually et to 0 Km/h. Accoding to Equation (7), a vehicle peed inceae SAT inceae, when the vehicle peed exceed a cetain value, the SAT can make the teeing wheel etun to cente o it doe not need active RTC contol at thi time, and thi cetain value i defined a the maximum vehicle peed V max, V max can be detemined by a eal vehicle tet. Baed on the above analyi, the judgment algoithm of the RTC tate put fowad i a follow. 1. Vehicle peed hould be in a cetain ange, that i, Vmin < V < Vmax. 2. The toque T acting on the teeing wheel i le than a cetain thehold T d d 0, that i, Td < Td0. 3. The ign of teeing wheel angle θ and angula velocity θ i oppoite, that i, θ θ < The teeing wheel angle θ i geate than the peet dead zone Δ, that i, θ >Δ. The flow chat of judging tate witch i hown in Figue 3. θ >Δ V < V < V min max θ θ < 0 T < T d d Contol Sytem Stuctue Figue 3. Flow chat of judging tate witch. The tuctue of the EPS contol ytem popoed in thi pape i hown in Figue 4. θ T θ dm e θ et I θ I t I e I I am Ui U a E I a K t Tm T a T T d θ d T dm Figue 4. Stuctue of the EPS contol ytem.

7 7 of 12 When the dive tun the teeing wheel, the EPS contolle get teeing wheel toque Td () t and teeing wheel angle θ d () t though a toque-angle eno placed on the teeing column. The meaued value of the toque and angle ae ued a input to the ait contolle and RTC contolle. The EPS contolle ue the deied teeing wheel toque T () t and the actual meauement of the toque ignal T () t to calculate the eo of the toque contol loop: dm e () t = T () t T () t (12) T dm The EPS contolle ue the deied teeing wheel angle θ () t and the actual meauement of the angle ignal θ () t to calculate the eo of the angle contol loop: dm eθ () t = θdm () t θ () t (13) The um of the output of the ait contolle and the output of the RTC contolle i ued a the input of the cuent contolle: I()= t It(t)+ Iθ () t (14) The EPS contolle ue the output cuent of the moto I a () t and the meauement of the moto cuent I () t to calculate the eo of the cuent contol loop: am e () t = I () t I () t (15) I am The toque acting on the teeing wheel can be obtained by: T () t = T () t T () t (16) d a whee Td () t i the toque acting on the teeing wheel and T () t i the eitance toque of the teeing ytem RTC Contol Stategy When the toque T d, acting on the teeing wheel, i le than a cetain thehold T, that i d 0 Td < Td0, the teeing ytem will put RTC foce on the teeing wheel. When the value of T d 0 i malle (geneally 2 3 (N.m) fo a ca), mall change in toque may affect the dive feel, epecially when the ait tate and the RTC tate ae witching. If the RTC toque and the ait toque ae not connected popely, the teeing poce will eult in a ene of futation and affect the dive feel. In ode to avoid udden change in the toque affecting the dive feel, we divide a complete RTC poce into thee tage. The RTC poce i hown in Figue 5, whee 0~T0 i the gadually inceaing tage of RTC toque, T0~T1 i the maintenance tage of RTC toque, T1~T2 i the gadually educing tage of RTC toque. Figue 5. Retun-to-Cente (RTC) poce.

8 8 of 12 At the beginning of the RTC tate, the RTC toque will inceae gadually, the RTC toque will maintain it value when it inceae to the et value, and when exiting the RTC tate (cloe to cente o enteing the ait tate), the RTC toque will educe gadually, thu enuing that the toque i unifomly mooth. When witching fom the ait tate to the RTC tate, the output value of the RTC contolle i I θ 1 when the meaued RTC toque i the mallet (le than the toque that the dive can peceive, uually 0.3 (N.m)), and thi value i et to the output lowe limit; the output value of the RTC contolle i I θ 2 when the meaued RTC toque i the laget, and thi value i et to the output uppe limit. The output tep of the RTC contolle i Δ I θ. I θ 1, I θ 2 and Δ I θ need oad teting to be meaued. Afte enteing the RTC tate, the output value of the RTC contolle i et to I θ 1, and then inceaed in tep Δ I θ until eaching the maximum value. Iθ1 + ΔIθ, Iθ1 Iθ( t) Iθ2 Iθ () t = (17) Iθ2, Iθ( t) > Iθ2 When exiting the RTC tate, the output value of the RTC contolle will educe in tep zeo. Δ I θ until Iθ 2 ΔIθ, 0 Iθ( t) Iθ2 Iθ () t = (18) 0, Iθ ( t) < 0 Accoding to Equation (7), at the ame vehicle peed, the SAT inceae with the font wheel tuning angle, that i to ay, the etun peed of the teeing wheel inceae with the angle of the teeing wheel, which i conitent with the dive diving habit. In ode to keep thi diving habit, the output value of the RTC contolle I θ 2 hould inceae with the teeing wheel angle. In ode to avoid the ovehoot when the teeing wheel i nea the cente, I θ 2 hould educe apidly when appoaching the cente. The coeponding elationhip between the RTC toque and the teeing wheel angle i hown in Figue 6, and thi cuve can be detemined by eal vehicle tet. Figue 6. Relationhip between the RTC toque and the teeing wheel angle. The maximum output value of the RTC contolle I θ 2 will alo change baed on the vehicle peed. The fate the peed, the malle the RTC toque. The coeponding elationhip cuve between the RTC toque and the vehicle peed ae hown in Figue 7.

9 9 of 12 Figue 7. Coeponding elationhip between the RTC toque and the vehicle peed. 4. Active RTC Contol of Real Vehicle Teting The tet vehicle i an electic vehicle equipped with an EPS ytem a hown in Figue 8. In ode to tet the RTC contol effect, the ait chaacteitic tet i caied out fit to invetigate whethe the active RTC contol hould affect the baic ait chaacteitic of EPS ytem while impoving the RTC pefomance of the vehicle, then tet the RTC contol effect and the effect of the RTC contol algoithm on the RTC pefomance of the vehicle i invetigated Ait Chaacteitic Teting Figue 8. Expeimental vehicle. The teeing toque cuve of the teeing wheel with active RTC contol and paive RTC contol ae hown in Figue 9. Fom the compaion cuve of the toque of the teeing wheel, we ee that the contol effect of active RTC contol i baically the ame a that of paive RTC contol. It i hown that the popoed method in thi pape ha no effect on the baic ait chaacteitic, and it will not affect the baic ait chaacteitic becaue of the addition of RTC contol.

10 10 of 12 Figue 9. Ait chaacteitic tet Active RTC Teting The dive dive the tet ca in a taight line and ecod the zeo line of the meaued vaiable, then tun the teeing wheel to 180. Afte that, we fix the teeing wheel angle, keep the vehicle peed teady, and tat ecoding tet data. Afte ome time, the dive eleae the teeing wheel and ecod the elationhip cuve between teeing wheel angle and time. The RTC cuve of the teeing wheel ae hown in Figue 10. Figue 10. RTC cuve of the teeing wheel. It can be een fom the tet cuve that the eidual angle of the teeing wheel can be educed effectively afte the active RTC contol i added, and the RTC pefomance i impoved. Figue 11 how the moto cuent chaacteitic at the time of etun. The dive tun the teeing wheel to 180 and hold on, then eleae the teeing wheel. It can be een fom the cuve of the moto cuent that the moto povide the ait cuent duing the ait tate. When enteing the RTC tate, the active RTC contol method povide compenation cuent to help the teeing wheel etun to cente. At the beginning of the RTC contol, the RTC cuent inceae gadually. A the teeing wheel appoache the cente, the RTC cuent deceae gadually. Thi i conitent with the contol tategy we deigned. The RTC contol tet eult how that the active RTC contol method i only executed when the teeing ytem i in a RTC tate, and thi method obviouly educe the eidual angle of the teeing wheel and effectively olve the poblem of the lack of paive RTC toque at low vehicle peed.

11 11 of 12 Figue 11. Moto cuent chaacteitic. 5. Concluion Though the analyi of the RTC poce, the method of judging the RTC tate of the vehicle i decibed in detail. Active RTC contol i applied only when the teeing ytem i in an RTC tate to avoid affecting the dive feel. In ode to avoid udden change in the toque, the RTC toque gadually inceae and educe, thu enuing that the toque i unifomly mooth. The contol tategy of the EPS ytem inceae the RTC auxiliay contol function baed on the vehicle peed in addition to the feedback ignal of teeing wheel angle and angula velocity. The advantage of the popoed algoithm can be ummaized in Table 1. In ode to veify the actual contol effect of active RTC contol, a eal vehicle tet i caied out. The expeimental eult how that the active RTC contol method doe not affect the baic ait chaacteitic, which effectively educe the eidual angle of the teeing wheel at low vehicle peed and impove the RTC pefomance of the vehicle. Table 1. Advantage of the algoithm. Popoed Algoithm Befoe Afte Add toque ignal to judge the RTC tate Unditubed tate witch RTC contol with vehicle peed 1. It cannot accuately detemine the opeation intention of the dive. 2. The ditubance toque will be geneated and affect the dive feel. 1. The RTC toque and the ait toque ae not connected popely. 2. The teeing poce will eult in a ene of futation RTC velocity of the teeing wheel i too fat at high vehicle peed. 1. It can accuately detemine the opeation intention of the dive though the toque. 2. RTC contol cannot affect the dive feel. 1. It can avoid udden change in the toque. 2. The RTC toque gadually inceae and educe and make the toque unifomly mooth. RTC velocity of the teeing wheel will low down at high vehicle peed. Acknowledgment: Thi wok i uppoted in pat by the National Natual Science Foundation of China unde Gant , , and , and in pat by the Natual Science Foundation of Shandong Povince, China unde Gant ZR2017QF017 and ZR2015FM004. Autho Contibution: The main idea wa popoed by Hao Su and Pan-Pan Du; Pan-Pan Du and Gong-You Tang conceived and deigned the expeiment; Pan-Pan Du wote the pape. Conflict of Inteet: The autho declae no conflict of inteet.

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