Thiết kế bộ điều khiển PID cho hệ thống lái trợ lực điện EPS

Cdng trinh Khoa hqc THIET KE BQ DIEU KHIEN PI0 CHO HE THONG LAI TRO Lire DIEN EPS NGUYEN TUAN ANH Vifn Mdi Irirdng vd An lodn Giao Ihong Trudng Dgi hpc Giao thong Van tdi Tdm tdt: Do cd nhieu iru diem noi bgt so vdi h$ thdng ldi trg Igr: thuy luc, h? thdng Idi frpluc dien hay he thong ldi di4n EPS (Electric Power Steering) ngdy cdng dugc su dung rgng rai tren cdc logi to hien dgi thdi gian gdn ddy Mgt nhirng yeu cdu guan trgng ddi vdi he thong trg lgc ldi Id phdi cung cdp gid trj mo men trg luc phii hgp Iheo tdc dg chuyin dgng vd md men ddnh ldi dudi tdc dung cda lire cdn quay vong Trong hdi bdo bg diiu khiin PID dugc thiel ke dua Iren md hinh dgng luc hgc cua he thdng ldi EPS vd mo hinh dgng luc hgc tdng qudt cda td vdi quan hi phi tuyen giUa luc cdn quay vong vd gdc Igch ben cua cdc bdnh xe ddn hudng Cdc kit qud mo phong su dung phdn mim Mallab-Simulink cho thdy h$ thong EPS vdi bg dieu khien PID thiel ki ldm viec hiiu qud vd dn dinh cdc diiu hen chuyen dgng khdc Summary: In recent years, electric power steering (EPS) systems have been used more popular on model vehicles due to their noticeable advantages compared lo hydraulic power steering (HPS) syslems One of the most important task of steering system is to provide assistance torque appropriated to vehicle speed and driver steering torque In this article an PID controller is designed on the base of an EPS column-type model integrated with vehicle dynamic model where nonlinear relation between lateral tire-force and tire side-slip angle Is considerated The simulation results using Matlab-Simulink software show that the EPS system with the designed PID controller works effectively and robustly in different speed and frequency conditions DAT VAN DE He thdng ldi ddng vai trd quan trgng viec ddm bao quy dao chuyen ddng cua d td theo mong mudn cua ngudi Iai De giam md men cdn thilt tac dung Ien vdnh tav lai, tren cac logi d td trudd ddy thudng sd dung he thdng ldi trg lyc thuy lyc HPS (Hydraclic Power Steering) hogt dgng nhd bam thuy Iuc din dgng tir dgng ca ddt Trong nhiing ndm gan day he thdng Iai trg lyc dien EPS Hinh Sa he thong ldi dien EPS (^Electric Power Steering) cdng dugc su I- Vdnh tay ldi; 2- Cdm bien mo men; dyng rgng rai thay the cho he thdng ldi trg lyc 3- Bo gidm loc dong ca dien; 4- True vit ca cdu ldi; thuy lyc O he thdng Idi EPS, md men trg lyc 5- Thanh rdng ca cdu ldi; 6- Dgng ca dign trg luc; Idi dugc tgo nhd mdt d^ng co dien hogt 7- Bg diiu khiin EPS Tgp chi KHOA HOC GIAO THONG V ^ TAI So 48 - 10/2015 29 Cdng trinh Khoa hqc ddng dgc lap su dyng ndng lugng dc quy So vdi he thdng Idi trg Iuc thuy Iuc, he thdng ldi trgf luc dien EPS cd nhilu uu dilm ndi bat nhu hieu sudt cao, kit cdu nhd ggn, de dang thay th6 sda chua, giam tieu hao nhien ii?u khdng phai trich cdng sudt dan ddng bam thiiy lyc, tang kha nang dn dinh quy dao vd cam gidc lai nhd h? thdng dilu khiln dign tu [5, 6] He thdng EPS dugc chia thdnh ba logi ca ban phy thuOc vdo phdn tu tdc ddng cua ddng co dien trg Iuc: 1) ddng ca di?n tdc dyng vao try Idi (EPS column-type), 2) dgng eg dien tdc dyng vao true ddn dgng rang (EPSpinion-type), va 3) dgng ca dien tac dung tryc tilp vdo rdng CO cdu !ai (EPS rack-type) Hinh gidi thi?u cac bg phan co ban cua h? thdng EPS loai dgng CO dien tdc dyng vao try ldi Bg dilu khiln EPS tinh todn cudng ddng dien tdi uu dieu khiln dgng co trg lyc dya trSn tin hieu tir cdm biln tdc chuyln dpng cua d td vd cam bien md men tren try lai Md men trg lyc tir dgng ca di$n dugc truyen din try,ldi thdng qua bg giam tdc loai true vit - banh vit Hieu qua cua he thdng EPS phy thugc vdo chdt lugng Iam vi?c cua bd dieu khien EPS Trong thai gian gdn day mgt sd tac gia da gidi thi6u cdc phuong phdp dilu khien khdc dya tren md hinh he thdng EPS dgc lap vdi cac gid thiet vl lyc can quay vdng, Mehrabi [5] dd so sdnh chdt lugng Iam vi$c eiia he thdng EPS dilu khien LQG va PID, Ahmed [2] dp dyng phuang phdp dieu khien bin vung H2 va H-infinity Mdt sd tac gia khac kit hgp mo hinh he thdng EPS vdi mo hinh chuyln dgng mgt vit ciia d td de xac dinh lyc cdn quay vdng vdi lyc ngang tdc dyng len cdc bdnh xe dan hudng quan he tuyen tinh vdi gdc l?ch ben cua Idp, Marouf [4] dp dung phuang phdp dilu khiln.trugt SMC, Li [3] thilt kl bd dilu khiln dua tr6n md hinh T-S Fu22y, Zhang [7] kit hgp phuong phdp dilu khiln Fuzzy vd PID Dua tren md hinh dgng Iuc hgc cua he thdng EPS vd md hinh dgng luc hgc tdng quat ciia td cd xet den quan h6 phi tuyin giita lyc ngang va gdc lech ben cCia cac banh xe dan hudng [I], bai bao gidi thieu phuong phap thilt kl bd dilu khien PID dam bao cho he thdng EPS lam viec hi?u qua vd dn djnh cdc dilu kien chuyln dgng khdc Chdt lugng ldm viec cua h6 thdng EPS vai bg dieu khien PID thilt kl dugc ddnh gia qua cac kit qua md phdng sir dung phdn mem Matlab-Simulink XAY DlTNG MO HINH He thdng EPS gidi thiSu tren Hinh I cd thi dugc md hinh hda nhu Hinh Trong do: Tj, T„ T„, Ta [Nm] tuong irng la md men ngudi Iai tdc dyng len vdnh tay lai, md men dugc tir cdm biln trSn try ldi, md men cCia ddng ca dign vd md men trg lyc Idi; 6s, d„, dp Irad] la gdc quay vdnh tay Iai, gdc quay dgng ca dien, gdc quay cua tryc vit ca cdu lai; Jt, Jm [kgm^] Id md men quan tinh khdi lugng cua vanh tay ldi vd dgng ca dien; Mr [kg], Xr [m] Id khii lugng va djch chuyln cua rang co cau lai; 30 F- M; K., Hinh Md hinh he thdng tdi EPS Tap chi KHOA HQC GIAO THONG V ^ N TAI S - 10/2015 Cong trinh Khoa hqc iv[N] la Iuc can quay vdng quy ddn ve rdng co cdu Idi Cac thdng sd khdc ciia mo hinh dugc gidi thieu Bdng I Ap dyng nguyen Iy D'AIambert ddi vdi vanh tay Iai, rang co cdu lai vd dgng co dien trg luc ta nhan'dugc he phuong trinh md ta dgng lyc hgc ciia he thdng EPS nhu sau: (1) (2) (3) Trong do: (4) T, = K , ( e , - e p ) , U p i (5) T„=K|I„ (6) Cucmg dp dong dien /„ cung cap cho dong ca dien dugc xac djnh tir djnh luat Kirchhoff theo phucmg trinh: (7) U'Rnilm+Linlm+KeOm Ket hgrp cac phuang trinh (l)-(6), sau mot so bien doi ta co: JJ,+B,9, (8) J„e„+B„0„+K„|9| M.x.tB, 'p[ 'r) 'p { '?) H8 phucfng trinh (8) co the dugc bieu dien cr dang ma tran: (9) Mq + Bq + Kq = h , voi q = [Sg, On,, Xf]^ la vec to toa dp suy rpng, h = [TJ, Tjn- -Ffi^ la vec to ngoai Iuc suy rpng va cac ma tran: Tap chi KHOA HOC GIAO THONG VAN TAI So 48 - 10/2015 31 Cong trinh Khoa hqc Ks 0 J„, B, 0 Mr Bm 0" , K- 0 K„ Ks KmGn, Br •^s^'^m^m I Phuong trinh ma tran (9) ti6p tuc dugc bilu diln a d^ng khong gian trang thai: J x - A^psX + Bepsiu + Beps2W (10) [y = Q p s " + Depsl" + Deps2»' Trong X = [e^, en,, Xf, 03, B^, ii,f la vec ta trgng thai, y = [TJ, Ta,9s, 6^, X ^ / la vec ta thdng sd ra, u = T^, la tin hieu dieu khiln, w = [Td,Fr]^ld vec to tin hieu vao, vd cdc ma diin trang thdi dugc xdc djnh nhu sau: 0(3x1) 0(3x1) 1/Js 0(3xl)' 0(3x3) 1(3x3) Bepsi = -M"'K -M"'B "KJ -Ks'fp K-niGm I - ^n,Gm''p 0 ^epsi ^c =0(6x1)' L>eps2 =0(6x2)- Gid trj lyc can quay vdng quy din vl rang ca cdu lai Fr dugc xdc djnh tir lyc ngang Fy tac dung len cdc bdnh xe ddn hudng theo cdng thdc: P ^ F y K + "k) (11) O day «r vd «* Id cac kich thudc dugc xdc djnh tren Hinh 3, n^ Id khoang each tii rang co cdu ldi din tdm tru dimg Quan he phi tuyen gitra Iuc ngang Fy phu thudc vdo gdc lech ben ciia cdc bdnh xe din hudng dugc xac djnh theo cdng thdc Pacejka dua tren md hinh dgng luc hgc tdng qudt cua d td kit hgp md hinh chuyln dOng ciia d td mat phdng (3 bdc tu do) va md hinh dao dgng ciia d td khdng gian (7 bgc ty do), [1] i QJ , " ' " ] '^^ r.,^ •' •* J •/' Z , ^ ,;• ' ~~i ^^ V -I^-^ f ' ^\^ i / ^ IP | j r \ n\ /7, ' / ^ r*l"" ' Hinh Sa dd xdc djnh l^rc cdn quay vdn 32 Tap chi KHOA HOC GIAO THONG VijJV TAI S6 48 - 10/2015 Cdng trinh Khoa hqc Myc tieu cua bg dilu khiln EPS id dilu chinh di?n dp U(t) cung cdp cho dgng ca dlSn trg lyc de dam bao sai sd e(t) nhd nhat giifa cudng dg ddng dien thyc te /„(/) va cudng dg ddng dien tdi uu iJ" (t) dugc xac djnh theo tin higu tdc chuyen dgng cua d td vd md men dugc tren tryc ldi, Hinh 4, [6] Gid trj dien dp U(t) dugc xdc djnh bdng phuang phdp dilu khiln PID nhu sau: Hinh Ddc linh ddng ca dl4n trg luc de(t) U(t)=Kpe(t) + K | j ^ e M d T + K o - ^ (12) Trong cac tham sd cua bg dilu khien PID dugc xac dinh tir bdi todn tdi uu: ^nji"^^e(t)=|C(t)-/,(t)| (13) Ung dyng thugt toan tdi uu ^Hsqnonlin" phdn mim Matlab Simulink, ta nhgn dugc gia tri cdc thdng sd tdi uu cua bg dilu khiln PID: Kp = 5,3; /^/ = 0,15; Kn = 0,001 Md hinh md phdng chuyln dgng ciia d td vdi h6 th6ng EPS dugc dilu khiln PID Matlab-Simulink dugc gidi thieu tren Hinh Cac thdng sd ca bdn cua md hinh dgng luc hgc tdng quat ciia d td dugc cho tdi lieu [I] LJ-, Hinh S Md hinh mo phdng chuyen dgng cda d to vdi h? thdng EPS diiu khiin PID Bdng Thong sd ky thudt ciia hi thong lat EPS TT 1' Thong so Mo men quan tinh Idioi luong vanh tay lai va tru lai Mo men quan tinh Idioi lupng quy din ciia dong co dien Khoi lupng quy dan cua rang va banh xe dan huong He so can xo^n cua tru [ai He so can xoan ciia dpng co dien H6 s6 can ciia dan dpng lai Dp Cling xoan cua try lai Dp cirng xoan cua dpng co dien Dp cimg cua din dpng lai Tap chl KHOA H Q C GIAO THONG VAN TAI Ky hi£u ', J., M, B, B„ B, K, K K, Gii trj 0,0459 0,000452 32 0,361 0,00334 88,128 115 125 42057 S6 48 - 10/2015 Don vi kgm' kgm' kg Nm/rad/s Nm/rad/s Nm/rad/s Nm/rad Nm/rad N/m/rad 33 Cong trinh Khoa hqc Bang I Thdng sd k$ thugt cua h? thdng ldi EPS (tie Thong so TT 10 II 12 13 14 15 16 17 18 Kybifu Gia tri 0, Cm 20 16 0,0075 0,1 0,0015 0,02 0,04 Ty so truyen co cau lai Ty so truyen bp giam toe dpng ca dipn BSn kinh truc vit ca cau lai Dipn tro dpng co dien He s6 dipn cam dpng ca diSn H? so toe dp goc quay dpng co dien H^ s6 mo men dong ca dien Di?n ap dOng ca dien Cuang dp dpng dien fp R™ L„ Ke Ki U l,u Don vl m n H V/rad/s Nm/A V A KET QU^ KHAO SAT D I danh gid hi$u qua trg luc cua bd dilu khiln PID, d td dugc md phdng chuyln dgng a cdc chl dg vgn tdc khdng ddi tir 10 km/h din 160 km/h vdi tin hieu ddu vao la md men tac dyng ISn vdnh tay Iai tang ddn tir din Nm thdi gian 0,2 s Kit qud md phdng tren Hinh cho thdy dgng co dien trg Iuc khdng Iam viec gdc quay cua banh xe dSn hudng khdng thay ddi d gid trj 10° vdi mgi tdc dg chuyln ddng Khi he thdng EPS-PID hogt dgng, gid trj gdc quay ciia bdnh xe ddn hudng thay ddi ty I^ nghich vdi tdc dg chuyen dgng vd tdng dang ke so vdi trucmg hgp khdng cd trg lyc Cudng ddng dien dgng co trg lyc thay ddi theo tdc dg chuyln dgng tCr 13,5A xudng 2,5A Iam giam gid tri gdc quay cua bdnh xe dan hudng ttr 25° d van tdc 10 km/h xudng 13° d van tdc 160 km/h riioi pan mo ction9[a Hinh 6: Kit qud mo phdng md men ddnh ldi ldng ddn Mo men vanh Uy lai GDC quay banh xt Thoi gian mo phong (s| Thoi gian mo phong [s] Hinh Kit qud mo phong md men ddnh ldi thay doi dgng hinh sin 34 Tgp chi KHOA HOC GIAO THONG V ^ N TAI S - 10/2015 Cdng trinh Khoa hqc Hinh gidi thi|u kit qua md phdng md men tac dung Ien vanh tay Idi thay doi theo quy lugt hinh sin vdi cac tdn sd thay ddi d che tdc chuyen ddng 40 km/h Khi tan sd kich thich tang tir 0,5 Hz den 5,0 Hz, bien ldn nhdt ciia gdc quay bdnh xe ddn hudng giam dan, nhien tdn sd biln thien khdng thay ddi so vdi tin hieu kich thich Dap ung cua hS thdng d cdc che tdc vd tdn sd khac cho thdy he thdng lai trg lyc dien EPS cd the ldm viec hieu qua va dn djnh cac dieu kien khai thac vdi bd dieu khien PID thilt kl KET LUAN Hieu qua cua he thdng lai trg lyc dien chii yeu phu thudc vao chdt lugng ldm viec ciia bd dilu khien EPS De tgo cdm gidc Iai cho Idi xe, he thdng trg luc phai thay ddi dugc cudng dd md men trg luc phii hgp vdi tin hieu tdc chuyen dgng va md men tren true Idi, dieu ndy dugc thyc hien nhd bg dieu khien PID, Cac kit qua md phdng dua tren md hinh dgng luc hgc tdng qudt cua d td da cho thdy bg dilu khien PID vdi cac tham sd thiet ke dugc xdc dinh tir bai toan tdi uu dam bao h? thdng EPS lam vi$c hieu qua va dn djnh cac dieu kien chuyen ddng khdc D I cd thi ap dung b^ dieu khien PID thiet kl chl tgo he thdng EPS cdn tien hanh cdc thi nghiem kiem chirng vd ddnh gia thyc te Ngdy nhan bai ldn ddu: 28/10/2015 Ngdy nhdn bdi sira: 27/U/2015 Ngdy chdp nhdn dang bai: 30/10/2015 Tdi ii^u tham khao [ 11 Nguyen Tuan Anh, Mo hinh nghiin ciru chuyen dong tdng qudt cua to Tap chi Giao thong Van tai So 6: 28-30.2010 [2] H Ahmed, etal., Robust Fixed-Structure.Controller Design of Electric Power Steering Systems 2009 American Control Conference Hyatt Regency Riverfront, St Louis, MO, USA, pp, (445-450), 2009 [3] X Li, X P Zhao, J Chen, Controller Design for Electric Power Steering System Using T-S Fuzzy Model Approach International Journal of Automation and Computing 6(2), pp: (198-203), 2009 [4] Marouf A., et al Control of an Electric Power Assisted Steering System Using Reference Model 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA, pp: (6684-6690), 2011 [5].N Mehrabi, et al Optimal Disturbance Rejection Control Design for Electric Power Steering Systems 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDCECC), Orlando, FL, USA, pp: (6584-6589), 2011 [6].Zeng Qun, The Design of Power Assisted Characteristic Curve for Electric Power Steering System Joumal ofConvergence Information Technology(JCIT) Volume 7, Number 17, pp: (260-266), 2012 [7] H Zang, S Chen, Electric Power Steering Simulation Analyze Based on Fuzzy PID Current Tracking Control Joumal of Computational Information Systems 7:1, pp: (119-126), 2011 Phan bi$n: PGS-TS Cao Trong Hiln; PGS.TS Dao Mgnh Himg Tgp chi KHOA HQC GIAO THONG VAN TAI S6 48 - 10/2015 35 ... thilt kl bd dilu khien PID dam bao cho he thdng EPS lam viec hi?u qua vd dn djnh cdc dilu kien chuyln dgng khdc Chdt lugng ldm viec cua h6 thdng EPS vai bg dieu khien PID thilt kl dugc ddnh gia... (9) ti6p tuc dugc bilu diln a d^ng khong gian trang thai: J x - A^psX + Bepsiu + Beps2W (10) [y = Q p s " + Depsl" + Deps2»'' Trong X = [e^, en,, Xf, 03, B^, ii,f la vec ta trgng thai, y = [TJ,... tdng quat ciia d td dugc cho tdi lieu [I] LJ-, Hinh S Md hinh mo phdng chuyen dgng cda d to vdi h? thdng EPS diiu khiin PID Bdng Thong sd ky thudt ciia hi thong lat EPS TT 1'' Thong so Mo men