Development of Active Suspension System for Automobiles using PID Controller

Transcription

1 Procding of th World Congr on Enginring 8 Vol II WCE 8, July - 4, 8, London, UK Dvlopnt of Supnion Syt for Autoobil uing PID Controllr Moulwaran Snthil kuar, Mbr, IAENG Abtract-Th ain ai of upnion yt i to iolat a vhicl body fro road irrgulariti in ordr to axiiz pangr rid cofort and rtain continuou road whl contact in ordr to provid road holding Th prnt work ai at dvloping an activ upnion for th quartr car odl of a pangr car to iprov it prforanc by uing a proportional intgral drivativ (PID controllr Th controllr dign dal with th lction of proportional, drivativ gain and intgral gain paratr (Kp, Ki, and Kd Th rult how that th activ upnion yt ha rducd th pak ovrhoot of prung a diplacnt, prung a acclration, upnion travl and tir dflction copard to paiv upnion yt Indx Tr- upnion, Quartr car odl, PID controllr, Rando road, Stp road NOTATION Ai : aplitud of ith in wav, c : daping cofficint, N / F ; actuator forc, kn Kp : proportional gain Kd : drivativ gain Ki : intgral gain k : pring tiffn, kn/ k : tir tiffn, kn/ : quartr car prung a, kg : unprung a, kg ω : wavin of road ω n : fundantal natural frquncy, Hz ω n : cond natural frquncy, Hz S : tatic dflction of th tir pring,, : Laplac oprator ψi : uniforly ditributd pha angl in th rang btwn and π Ωi : wav nubr T : ti, c W : road profil, x : prung a vrtical diplacnt, : unprung a vrtical diplacnt, x Manucript rcivd on Octobr, 7 (Moulwaran nthil kuar i with Dpartnt of Mchanical Enginring, PSG Collg of Tchnology, Coibator 64 4, India (Phon: ; fax: ; -ail: nthil_kuar@hotailco ẋ : prung a acclaration,/ x -x : upnion travl, x -w : tir dflction, z( : ditanc along th road, INTRODUCTION Supnion yt hav bn widly applid to vhicl, fro th hor-drawn carriag with flxibl laf pring fixd in th four cornr, to th odrn autoobil with coplx control algorith Th ain ai of upnion yt i to iolat a vhicl body fro road irrgulariti in ordr to axiiz pangr rid cofort and rtain continuou road whl contact in ordr to provid road holding [] Dand for bttr rid cofort and controllability of road vhicl lik pangr car ha otivatd to dvlop nw typ of upnion yt lik activ and i activ upnion yt Th lctronically controlld upnion yt can potntially iprov th rid cofort a wll a th road handling of th vhicl [] An activ upnion yt ha th capability to adjut itlf continuouly to changing road condition By changing it charactr to rpond to varying road condition, activ upnion offr uprior handling, road fl, rponivn and afty [3] In thi papr an attpt i ad to dvlop an activ upnion with PID controllr to iprov th prforanc of upnion yt and prforanc i vrifid with MATLAB 7 MATHEMATICAL MODELING In thi work, a quartr car odl with two dgrof-frdo i conidrd intad of full odl It not only lad to iplify th analyi but alo rprnt ot of th fatur of th full odl A Supnion Syt Th two dgr of frdo quartr odl hown in Figur i th ot coonly ud odl in th dign tudi for paiv upnion yt ISBN: WCE 8

2 Procding of th World Congr on Enginring 8 Vol II WCE 8, July - 4, 8, London, UK ( Kd C( + ( Kp + Ki (5 k x Figur Quartr car odl of paiv upnion According to Nwton cond law and fr body diagra approach, th quation of otion for th yt ar writtn a, For prung a ( x+ c x x + k ( x x ( For unprung a x c( x x k( x x k( w x B Supnion Syt ( upnion yt ploy hydraulic or pnuatic actuator, which provid th dird forc in th upnion yt Hnc, clarly xtrnal forc i introducd into th yt by th an of hydraulic actuator [3] For activ upnion hown in Figur, uing th Nwton cond law of otion and fr-body diagra concpt, th following quation of otion ar drivd ( x c ( x x k( x x k( w x + F x+ c x x + k ( x x F (3 (4 A proportional-intgral-drivativ controllr (PID controllr[7] i a coon fdback loop coponnt in indutrial control yt Th diffrnc (or "rror" ignal i thn ud to adjut o input to th proc in ordr to bring th proc' aurd valu back to it dird tpoint PID controllr do not rquir advancd athatic to dign and can b aily adjutd (or "tund" to th dird application, unlik or coplicatd control algorith bad on optial control thory Figur 3 i th block diagra of th PID controllr Kp a th proportional gain, Ki a th intgral gain and Kd a th drivativ gain which ar th paratr to b varid to tun th controllr for th rquird prforanc of th yt Figur Quartr car odl of activ upnion 3 PID CONTROLLER DESIGN (t Kp t Ki ( t dt Kd d(t dt I P D Figur 3 PID controllr + u(t With th t point a zro, th rror ignal (aurd variabl t point i fd to th controllr Fro th block diagra hown in Figur 4, upnion travl (X -X i givn by, nud nuc nu ( X W ( X X (6 dnd dnc nud dnd F ( W ( ( Kd C( ( X ( X ( ( + ( Kp + Ki ( W ( ( F ( ISBN: WCE 8

3 Procding of th World Congr on Enginring 8 Vol II WCE 8, July - 4, 8, London, UK nup X( ( Clod loop tranfr function of upnion travl nud * dnc* nup (7 dnd( dnp* dnc + nup* nuc nup X W A Tuning of PID Controllr Thr ar vral thod for tuning a PID loop [6] Ziglr and Nichol [7] uggtd rul for tuning PID controllr (aning to t valu Kp, Kd, Ki Such rul uggt a t of valu of Kp, Kd, and Ki that will giv a Tabl opration of th yt Kp 355; Kd 36 and Ki 7 4 RESULTS AND DISCUSSIONS Calculation Natural Frqunci Th olution of th abov diffrntial quation of otion can b aud a in th following for, x X in( ω t; x X in( ωt (3 Figur 4 Block diagra of clod loop yt Fro th block diagra hown in Figur 4, prung a diplacnt X i givn by nud nuc nup X W ( X dnd dnc (8 nup X( Clod loop tranfr function prung a diplacnt, nuddnc * * nup ( c + k (9 nuddnpdnc * * *( c + k * nupnucdnd * * * Fro th block diagra hown in Figur 4, prung a acclration X i givn by nud nuc nup X W ( X X dnd dnc ( nup X ( Clod loop tranfr function of prung a acclration nud * dncnup * ( c + k nud * dnpdncc * *( + k * nup * nuc * dn ( Fro th block diagra hown in Figur 4, tir dflction (X -W i givn by By olving abov two quation, w will gt th two undapd natural frqunci of th yt, k ( k + k ( k + k k kk ω + ± + (4 4 Tabl Paratr valu ud in th quartr carodl Sprung a 5 kg Unprung a 5 kg k Supnion pring contant 8,6 N/ c Supnion daping cofficint, N/ k Tir pring contant 96, N/ Th abov paratr ar takn fro rfrnc [5] Uing th abov givn paratr valu and quation th natural frqunci of th yt ar calculatd and hav bn obtaind a: ω n 83 rad/ (3 Hz; ω n 6556 rad/ (4 Hz Th tatic dflction of th tir pring, S, can b calculatd a 5 A Ti Doain Analyi Th tranint rpon of both paiv and activ upnion yt ar dtrind in ti doain Ti doain analyi i carrid out for diffrnt road input lik tp input (pot hol, and rando road input nud nuc nup X W W ( X X dnd dnc ( ISBN: WCE 8

4 Procding of th World Congr on Enginring 8 Vol II WCE 8, July - 4, 8, London, UK ( nt c pla D i M a g n S pru STEP INPUT Th tp input charactriz a vhicl coing out of a pot hol Th pot hol ha bn rprntd in th following annr [8] for th tp hight of 8 w 8 t t > (5 Road input Fro Figur 6, pak ovrhoot of prung a acclration for paiv yt i 799 / a for th activ upnion yt it i 8 / l( a v n tr n i o S up Figur 7 Supnion travl V ti Figur 5 Sprung a diplacnt V ti 4 5 Fro Figur 5, pak ovrhoot of prung a diplacnt for paiv yt i 68 a for th activ upnion yt it i 66 n ( o c t i fl d r T i c n (/ o ra ti l A cc Figur 6 Sprung a acclration V ti Figur 8 Tir dflction V ti Fro Figur 7, axiu longation of upnion pring for paiv yt i 436 a for th activ upnion yt it i 6 Fro Figur 8, axiu tir dflction for paiv yt i 346 a for th activ upnion yt it i 33 6 RANDOM ROAD INPUT Apart fro inuoidal bupy and pot-hol typ of road, a ral road urfac takn a a rando xciting function i ud a input to th vhicl Road profil can b approxiatd by PSD in th for of ISBN: WCE 8

5 Procding of th World Congr on Enginring 8 Vol II WCE 8, July - 4, 8, London, UK ( n c a rb tu d i R oad Φ(ΩΦ(Ω (Ω/Ω -ω (6 ΩΠ/L in rad/ dnot th wav nubr andφ Φ(Ω in /(rad/ dcrib th valu of Ti ( n a c D p M a g n S pu Figur 9 Road roughn claification by ISO PSD at rfrnc wav nubr Ω rad/ Th drop in agnitud i odld by wavin ω By tting wavin to ω, ach cla i iply dfind by it rfrnc valu Φ Th ISO ha propod road roughn claification (cla A-H bad on th powr pctral dnity valu i a hown in Figur 9[9] A rando profil of ingl track can b approxiatd by uprpoition of N in wav [9] Road profil z R ( N A ( Ω - i in ψ (7 i i i ach in wav i dtrind by it aplitud A i and it wav nubr Ω i By diffrnt t of uniforly ditributd pha angl ψ i, i (N in th rang btwn and π diffrnt profil can b gnratd which ar iilar in th gnral apparanc but diffrnt in dtail Figur Sprung a diplacnt V ti c n (/ o ra ti l A cc According to quation (7 th profil z z( wa gnratd by N in wav in th frquncy rang fro cycl/ (68rad/ to cycl/ (683rad/ Th aplitud A i, i (N wr calculatd and th MATLAB function rand wa ud to produc uniforly ditributd rando pha angl in th rang btwn and π Fro Figur, pak ovrhoot of prung a diplacnt for paiv yt i 5 a for th activ upnion yt it i 47 Fro Figur, pak ovrhoot of prung a acclration for paiv yt i 435 / a for th activ upnion yt it i 556 / Fro Figur, axiu longation of upnion pring for paiv yt i 536 a for th activ upnion yt it i 367 Fro Figur 3, axiu tir dflction for paiv yt i, a for th activ upnion yt it i 7784 Uually for rando vibration th valu ar aur in RMS valu, which ar hown in Tabl Fro Figur 4, that th activ upnion yt i bttr than th paiv upnion yt in tr of pak ovrhoot and ttling ti for th prung a diplacnt and prung a acclration (Rid cofort, upnion travl(rattl pac and tir dflction(road holding for both tp and rando road profil Figur Sprung a acclration V 7 CONCLUSIONS ti In thi papr, a PID controllr ha bn dignd for a quartr car odl of a pangr car to iprov th rid cofort and road holding ability Ziglr and Nichol tuning rul ar ud for riou of tuning to iprov th rid cofort and road holding ability For tp input th of 8, th prung a diplacnt ha bn rducd by 4779% which how th iprovnt in rid cofort and prung ISBN: WCE 8

6 Procding of th World Congr on Enginring 8 Vol II WCE 8, July - 4, 8, London, UK a acclration rducd by 8993%Th upnion travl ha bn rducd by 7464% and tir dflction ha rducd by 8973% For rando road input, th axiu acclration of th prung a ha bn rducd by 87% which how th iprovnt rid cofort Th axiu prung a diplacnt ha bn rducd by 786% Th axiu upnion travl ha bn rducd by 7645% which will iprov th lif of th upnion yt upnion rducd th tir dflction by 63% which how th bttr road holding ability of th activ upnion yt Thrfor, it i concludd that th activ upnion yt ha bttr prforanc capabiliti ovr paiv upnion yt n ( o c t i fl d r T i Figur 3 Tir dflction V ti a v n o n S up Figur Supnion travl V ti Tabl Pak RMS valu of rando vibration Paratr Sprung a diplacnt( Sprung a acclration(/ upnion upnion 435* * -3 76* -3 5* -3 Supnion travl ( 568* -3 39* -3 REFERENCES Lin, JS and Kanllakopoulo, I, 997, Nonlinar Dign of Supnion, IEEE Control Syt Magazin, Vol 7, No3, pp45-59 Croby,M and DCKarnopp, 973, Th activ dapr a nw concpt for hock and vibration control, Shock Vibration Bull, Part H, Wahington DC, pp R Rajaani and JK Hdrick, Prforanc of Autootiv Supnion with Hydraulic Actuator: Thory and Exprint Procding of t h Arican control confrnc Jun Eailzadh, E and Taghirad, HD, 994, Vhicl Supnion with Optial Stat-Fdback Control, Procding of CSME, Vol, pp Lin, JS and Kanllakopoulo, I, 997, Modular Adaptiv Dign for Supnion, Procding of th 36th IEEE Confrnc on Dciion and Control, San Digo, CA, pp Jacqulin wilki, Michal Johnon and Rza Katbi, 3, Control Enginring: an Introductory Cour, Pal grav Publihr 7 Ogata, K, 996, Modrn Control Enginring, Prntic-Hall, 3rd dition 8 Wong, JY, 988, Thory of Ground Vhicl, John Wily and Son Inc, Nw York 9 Prof Dr Gorg Rill Vhicl dynaic, Univrity of applid cinc, Octobr 6 % Rduction in pak valu Sprung a diplacnt Supnion travl Stp input Sprung a acclration Tir dflction 63 Rando input Figur 4 Prforanc of activ upnion yt for diffrnt road input ISBN: WCE 8