Vehicle Chassis Control Using Adaptive Semi-Active Suspension

Transcription

1 Poceedings of the 17th Wold Congess The Intenational Fedeation of Automatic Contol Vehicle Chassis Contol Using Adaptive Semi-Active Suspension V. Sankaanaayanan, Sinan Oncu, Dince Ocan, and Levent Güvenç Automotive Contol and Mechatonics Reseach Cente İstanbul Technical Univesity, TURKEY. Abstact: This pape pesents an adaptive semi-active contol stategy to impove the stability and pefomance of a light commecialvehicle equipped with fou continuously vaying dampes. A choice between ide comfot o oad holding of the vehicle is made automatically using a ule based adaptive algoithm based on vaious factos such as oll ate and yaw ate. The damping facto o the contolle configuation of each dampe is modified using a ule based adaptive algoithm and this technique is named Individual Damping Contol () in this pape. The vehicle oll and yaw stability ae analyed using this technique. Simulation esults on a highfidelity ealistic compute model of a light commecial vehicle ae pesented to validate the poposed technique. 1. INTRODUCTION Semi-active suspension system is used in automobiles to impove ide comfot and oad holding and these can be achieved using contol methods like sky-hook Kanopp et al., 1974 and gound-hook Valasek et al., 1997 m espectively. It is a well known fact that ide comfot and oad holding pefomance cannot be impoved simultaneously. The equiementofgoodide comfotand oadholding vaies basedonsevealfactos. Fo example, on snowy oads, vehicle handling is moe impotant than comfot since poo oad holding affects the stability of the vehicle. Thus, automatic switching between these two pefomance goals is an ideal solution to utilie the semiactive suspension effectively. Hybid contol which is the combination of sky-hook and gound-hook methods can solve this poblem. A simple hybid contol algoithm can be witten as F sa = βf gd (1 β)f sky whee, F sa, F sky, F gd ae semi-active, sky-hook and goundhook dampe foces espectively and β is a facto which mixes the two contol foces. The main aim of this pape is to popose a ule based adaptive contol stategy which contols each semi-active suspension dampe sepaatelyto impove the stability and comfot of the vehicle using the most adequate compomise solution. This can be achieved eithe by changing the damping facto of each dampe o by changing the contolle configuation of each dampe fom sky-hook to gound-hook o by changing the β value of each dampe in the hybid contolle o a combination of all. To poceed with this idea, diffeent paametes and vaious simula- This wok was suppoted by the Euopean Commission Famewok Pogam poject AUTOCOM(INCO-1646). tions have been caied out in this pape. The sky-hook and gound-hookcontolles ae designed based on quate ca models. The necessity to impove vehicle handling is identified using oll ate and yaw ate. The est of the pape is oganied as follows. Section intoduces the mathematical model of the full ca and a quate ca model which ae used to design individual suspension contolles. Section 3 pesents the design of the ule based adaptive algoithm. Simulation esults and conclusions ae pesented in the subsequent sections.. MATHEMATICAL MODELS.1 Full ca suspension model The full ca suspension model as in Sankaanaayanan et al., 7, consists of a spung mass (actual ca body), thee unspung masses in which two ae font ties and a single ea axle which connects the two ea ties. The whole system has 7 degees of feedom and those ae vetical motion of the spung mass, oll motion of the spung mass φ, pitch motion of the spung mass θ, vetical motion of the two font unspung masses 11, 1, vetical motion of the ea unspung mass u and the oll motion of the ea unspung mass φ u. The dynamics equation of the suspension model can be expessed as M = f s11 f s1 f s1 f s f d11 f d1 f d1 f d I yy θ = a(fs11 f s1 f d11 f d1 ) b(f s1 f s f d1 f d ) I xx φ = c(fs11 f s1 f d11 f d1 ) d(f s1 f s f d1 f d ) m = f s11 f d11 f t /8/$. 8 IFAC /876-5-KR

2 w11 w1 w c s (t) - Damping factos k t - Sping constants of the ties w ij - Road inputs CG - Cente of gavity of the spung mass a, b - Distance fom CG to font and ea espectively c, d - Distance fom CG to ight and left espectively e, g - Distance fom Cente of gavity of the unspung mass to ight and left espectively. Quate ca model w1 The linea dynamics of a quate ca model as shown in Fig. can be witten as Fig. 1. Full ca suspension model xs m 1 1 = f s1 f d1 f t1 Ms M u u = f s1 f s f d1 f d f t1 f t I u φu = e(f s1 f d1 f t1 ) g(f s f d f t ) Ks B(t) xu The kinematic equations can be witten as s11 s1 s1 s 1 = u u The sping foces ae a c a d b c b d e g f sij = k sij ( sij ij ) i, j = 1, The semi-active damping foces ae f dij = c sij (t)(ż sij ż ij ), i, j = 1,, c sij (t) (c min, c max ) IR The sping foces due to ties ae f tij = k tij ( ij w ij ), i, j = 1, ( ) sinθ sinφ sinφ u whee, 11 - Font ight (FR) 1 - Font left (FL) 1 - Rea ight (RR) - Rea left (RL) - Vetical displacement of the spung mass s - Vetical displacement of the individual spung masses - Vetical displacement of unspung masses θ - Pitch angle φ - Roll angle φ u - Roll angle of the unspung mass M - Mass of the spung mass I xx - Inetia of the spung mass with espect to x axis I yy - Inetia of the spung mass with espect to y axis m - Mass of the font unspung masses M u - Mass of the ea single unspung mass I u - Inetia of the unspung mass f s - Sping foces f d - Damping foces f t - Sping foce due to ties k s - Sping constants Fig.. Quate ca suspension model Mu Ku M s ẍ s B(t)(ẋ s ẋ u ) K s (x s x u ) = M u x u B(t)(ẋ s ẋ u ) K s (x u x s ) K u (x u ) = whee, x s - Position of the spung mass, x u - Position of the unspung mass, M s - Mass of the spung mass, M u - Mass of the unspung mass, < B min B(t) B max - Vaying damping coefficient, K s - Sping constant of the suspension sping, K u - Sping constant of the tie, - Road distubance. Futhe the semi-active suspension foce can be defined as F sem = B(t)(ẋs ẋ u ) 3. SEMI-ACTIVE SUSPENSION CONTROL STRATEGIES 3.1 Sky-hook The aim of the sky-hook contol technique of Kanopp et al is to minimie the vetical motion of the spung mass by connecting a vitual dampe between the body and the sky as shown in Fig. 3, hence named skyhook. In pactice, since it is not possible to connect a dampe between the body and the sky, the adjustable dampe is appoximated to mimic the vitual dampe. The necessay damping foce can epesented as { C F sky = sky ẋ s if ẋ s (ẋ s ẋ u ) C min (ẋ s ẋ u ) if ẋ s (ẋ s ẋ u ) < This technique cetainly impoves the ide comfot but may lead to poo handling. 4678

3 4. RULE BASED ADAPTIVE CONTROL STRATEGY Ks Csky Ms Mu Ku B(t) xs xu The aim of the ule based adaptive contol stategy is to impove the stability o comfot based on the diving and oad based equiements. To design such a stategy, vaious contol methods have been studied in this section using standad maneuves. The oll stability and yaw stability of the vehicle ae investigated using fish-hook and µ-split maneuves espectively. Semi-active suspensions cannot actively stabilie the oll and yaw motions but they can impove the pefomance of the active contolles such as anti-oll bas and Electonic Stability Pogam (ESP). This section dedicated to study the oll and yaw stability impovement using vaious contolle configuation. 4.1 Contolle configuation Fig. 3. Sky-hook contol 3. Gound-hook The gound-hook contol algoithm is developed to educe the tie motion, that is, to impove oad holding (handling), by vitually connecting a dampe between the gound and the tie as shown in Fig. 4. Since this is not xs Let the damping facto of each dampe be epesented as whee B(t) FL, B(t) FR, B(t) RL, B(t) RR < B min < B(t) < B max. Similaly, the β value of individual dampes can be expessed as β(t) FL, β(t) FR, β(t) RL, β(t) RR Ks Ms Mu Ku Fig. 4. Gound-hook contol B(t) possible in pactice, the adjustable damping foce that is necessay can be expessed as { C F gd = gd ẋ u if ẋ u (ẋ s ẋ u ) C min (ẋ s ẋ u ) if ẋ u (ẋ s ẋ u ) < 3.3 Hybid The combination of sky-hook and gound-hook is called hybid contol technique and the coesponding semiactive damping foce can be witten as F hyb = B(t)(ẋs ẋ u ) = βf sky (1 β)f gd (1) whee, C sky, C gd > C min = B min >, β, 1. The value of β detemines the contibution of the individual sky-hook and gound-hook contol actions buied inside the hybid contol algoithm. xu Cgd whee β(t), 1 (1) Configuation-1 All passive dampes, that is, B(t) FL = B(t) FR = B(t) RL = B(t) RR = = B minb max () Configuation- All soft dampes, that is, B(t) FL = B(t) FR = B(t) RL = B(t) RR = B min (3) Configuation-3 All had dampes, that is, B(t) FL = B(t) FR = B(t) RL = B(t) RR = B max (4) Configuation-4 All sky-hook, that is, β(t) FL = β(t) FR = β(t) RL = β(t) RR = 1 in (1) (5) Configuation-5 All gound-hook, that is, β(t) FL = β(t) FR = β(t) RL = β(t) RR = in (1) (6) Configuation-6-1(fo oll stability) B F R (t) = B RR (t) = 1 sign( φ φ set) B min B F L (t) = B RL (t) = 1 sign( φ φ set) B max (7) Configuation-7 -(fo yaw stability) 1 sign( φ φ set) 1 sign( φ set φ ) 1 sign( φ φ set) 1 sign( φ set φ ) B max B min 4679

4 B F L (t) = B RR (t) = 1 sign( set) B min B F R (t) = B RL (t) = 1 sign( set) B max 1 sign( set ) 1 sign( set) B min 1 sign( set) 1 sign( set ) B max ollate deg/sec passive soft had idc1 sky hook gound hook 1 This configuation is designed to impove the oll stability by individually changing the damping coefficient of the vehicle based on the oll ate. If the oll ate is moe than the theshold value and positive, that is, in the clock-wise diection with espect to the x-axis, as shown in Fig. 5, the ight side dampes ae made had and left side dampes ae made soft and visa vesa fo negative oll ate. Soft Fig φ Had The aim of is to educe the yaw ate of the vehicle using semi-active suspension dampes. The damping facto of the diagonal dampes ae modified based on the yaw ate as shown in Fig. 6. Fig. 6. Soft 4. Roll stability Had Roll ove possibilities ae moe citical in commecial vehicles, especially in heavy tucks, which can be avoided using anti-oll bas. Semi-active suspension can also help pevent oll ove accidents to some extent as tansient oll behavioucanbe impoved. Popelydesignedsemi-active suspension system can impove the oll stability compaed with passive suspension. The main cause of oll ove is the high speed with sudden steeing of the vehicle. This situation can be detected with the steeing angula ate togethe with speed of the vehicle o oll ate. In this pape, the fish-hook maneuve is consideed fo oll stability analysis using vaious contolle configuation pesented in the pevious section. The actual vehicle s paametes ae enteed into a high-fidelity, ealistic vehicle simulato fo this pupose. Fish-hook maneuve is tested with all the contolle configuations. The simulation esults ae pesented in Figs. 7, time Fig. 7. Roll ate in fish-hook maneuve ollate deg/sec gound hook had idc1 passive soft sky hook time Fig. 8. Roll ate in fish-hook maneuve - oomed It can be seen fom the figues that, 1 significantly educe the oll ate of the vehicle in the fish-hook maneuve. 4.3 Yaw stability Yaw stability of the vehicle is impoved using ESP (Electonic Stability Pogam) which conventionally uses individualbaking concepto ecently using active steeingo stee-by-wie. In this section, the yaw stability of the vehicle using stee-by-wie togethe with is investigated. Yaw stability contolles have been studied using stee-bywie methods ecently by Oncu et al., 7, Kaaman et al., 6. An ESP contolle implementation appoach based on the distubance obseve is shown in Fig. 9. is tested in the vehicle with µ-split maneuve and the esults ae compaed with passive suspension without ESP, with ESP and ESP. The simulation esults ae pesented in Figs. 1, 11. Fom the figues, it can be easily seen that, impoves the yaw stability of the ESP contolle as compaed with ESP alone. 4.4 Supevisoy contolle Based on vaious contolle configuation and simulation esults, it is clealy seen that, 1 woks bette to impove the oll stability and woks bette to impove the yaw stability. The aim is to design a ule based adaptive algoithm which switches between the contol stategies in subsection 4.1 to achieve the necessaycombination of comfot and holding. In othe wods, the algoithm has to switch to sky-hook fo comfot, 1 fo oll stability 468

5 Sky-hook Supevisoy contolle 1 Vehicle Fig. 9. Yaw stability contol using stee-by-wie and distubance obseve Yaw Rate ad/s ESP With out ESP With ESP Road taveled m Fig. 1. Yaw ate compaison Fig. 1. Adaptive algoithm wheneve oll ate o yaw ate is moe than the theshold value. It can be seen fom Fig. 17 that, up to 1 sec, the sky-hook contol foce is applied since thee is no oll ate and yaw ate at this time which can be seen fom Figs.15, 16. But fom 1 to sec, the vehicle handling is impoved though both 1 and based in the magnitude of the oll and yaw ate. Similaly fom 41 to 45 sec, the handling is impoved. The oll ate and yaw ate of the vehicle is impoved wheneve the supevisoy contolle also called contolleswitches fom sky-hookto eithe 1 o which can be clealyseen fom Figs. 15, 16. The body acceleation is educed wheneve the contolle switched to sky-hook which can be seen fom Fig width of the oad Body acceleation m/s 5 5 length of the oad Fig. 11. Stoboscopic plots. 1-without ESP, -with ESP, 3-ESP and fo yaw stability. This can be epesented as in a block diagam fom as shown in Fig. 1 and can be witten as a fomula as follows 1 if φ > φ set & φ > F sem = if > set & > φ () F sky othewise To simulate the ule based adaptive contolle, a test oad is ceated using the same softwae which is used fo simulation. This oad consists of oad bumps to test the suspension fo comfot, and a sudden tun and a µ-split maneuve to test handling of the vehicle. The simulation esults with ule based adaptive contolle ae compaed with passive suspension and the esults ae pesented in Figs The ide comfot of the vehicle is impoved Time s Fig. 13. Body acceleation 5. CONCLUSION A ule based adaptive semi-active suspension contolle algoithm is developed to impove the ide comfot and oad holding of a light commecial vehicle. Vaious semiactive suspension contol algoithms ae studied to design the adaptive contolle. A new method has been poposed to impove the handling of the vehicle by changing the damping facto of each dampes based on oll ate and yaw ate which is named Individual Damping Contol. The ule based adaptive contolle automatically switches between contolles to impove eithe ide comfot o oad holding. The simulation esults shows that, the poposed adaptive contolle has bette pefomance compaed to a passive suspension system. 4681

6 Time s Switch value Time s Fig. 14. Body acceleation-oomed Roll Rate ad/s Time s Fig. 15. Roll ate Fig. 17. Switch value. 1-Sky-hook, -1, 3- ings of the IEEE Intelligent Vehicle Symposium, Tokyo, Japan, 6. D. Kanopp, M.J. Cosby, and R.A. Hawood. Vibation Contol Using Semi-Active Foce Geneatos. Tansaction of the ASME Jounal of Engineeing fo Industy, 96:619 66, S. Oncu, S. Kaaman, Levent Güvenç, S.S. Esolma, E.S. Otuk, and M. Sinal. Robust Yaw Stability Contolle Design fo a Light Commecial Vehicle Using a Hadwae in the Loop Steeing Test Rig. In Poceedings of theieee Intelligent Vehicle Symposium, Istanbul, 7. V. Sankaanaayanan, M. Engin Emekli, B. Aksun Güvenç, L. Güvenç, E. S. Ötük, Ş. S. Esolma, I. E. Eyol, and M. Sinal. Obseve Based Semi-Active Suspension Contol Applied to a Light Commecial Vehicle. In Poceedings of the IEEE/ASME confeence on Adanced Intelligent Mechatonics, Switeland, 7. M. Novak Valasek, M., Z. Sika, and O. Vaculin. Extended Goundhook New Concept of Semi-Active Contol of Tucks Suspension. Vehicle System Dynamics, 9:89 33, Yaw ate in ad/sec Time s Fig. 16. Yaw ate 6. ACKNOWLEDGEMENT The authos thank the membes of the chassis goup of Fod Otosan, Tukey fo useful discussions in the couse of this wok. REFERENCES S. Kaaman, S. Oncu, L. Güvenç, Ş. S. Esolma, E. Cetin, and A. Kanbolat. Robust velocity scheduled yaw stability contol of a light commecial vehicle. In Poceed- 468