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IFAC-PapersOnLine 49-9 (2016) 099–104 H active anti-roll bar control to prevent rollover H∞ active anti-roll bar control to prevent rollover ∞ of heavy vehicles: a robustness analysis ∞ of heavy vehicles: a robustness analysis Van-Tan Vu ∗ Olivier Sename ∗ Luc Dugard ∗ Peter Gaspar ∗∗ Van-Tan Vu ∗ Olivier Sename ∗ Luc Dugard ∗ Peter Gaspar ∗∗ Van-Tan Vu ∗ Olivier Sename ∗ Luc Dugard ∗ Peter Gaspar ∗∗ Univ. Grenoble Alpes, GIPSA-lab, F-38402 Grenoble Cedex, France ∗ Univ. Grenoble Alpes, GIPSA-lab, F-38402 Grenoble Cedex, France CNRS,∗ Univ. GIPSA-lab, Grenoble F-38402 Alpes, GIPSA-lab, Grenoble Cedex, F-38402 France. Grenoble E-mail: Cedex,Van-Tan.Vu, France CNRS,∗ Univ. GIPSA-lab, Grenoble F-38402 Alpes, GIPSA-lab, Grenoble Cedex, F-38402 France. Grenoble E-mail: Cedex,{Van-Tan.Vu, France CNRS, GIPSA-lab,olivier.sename, F-38402 luc.dugard [email protected] Cedex, France. E-mail: {Van-Tan.Vu, olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr{ ∗∗ Systemsolivier.sename, and Control luc.dugardLaboratory,}@gipsa-lab.grenoble-inp.fr Institute for Computer Science and ∗∗ Systems and Control Laboratory,} Institute for Computer Science and Control,∗∗ Systems Hungarian and Control Academy Laboratory, of Sciences, Institute Kende for u. Computer 13-17, H-1111 Science Budapest, and Control, HungarianHungary. Academy E-mail: of Sciences, [email protected] Kende u. 13-17, H-1111 Budapest, Control, HungarianHungary. Academy E-mail: of Sciences, [email protected] Kende u. 13-17, H-1111 Budapest, Hungary. E-mail: [email protected] Abstract: Rollover of heavy vehicle is an important road safety problem world-wide. Although rollovers Abstract: Rollover of heavy vehicle is an important road safety problem world-wide. Although rollovers areAbstract: relativelyRollover rare events, of heavy they vehicle are usually is an important deadly accidents road safety when problem theyworld-wide. occur. In order Although to improve rollovers roll arestability, relatively most rare of modern events, heavy they are vehicles usually are deadly equipped accidents with passive when they anti-roll occur. bars In orderto reduce to improve roll motion roll stability,are relatively most rare of modern events, heavy they are vehicles usually are deadly equipped accidents with passive when they anti-roll occur. bars In orderto reduce to improve roll motion roll duringstability, cornering most ofor modern riding heavy on uneven vehicles roads. are This equipped paper with proposes passive an anti-rollH approach bars to to reduce design rollactive motion anti- duringroll bars cornering using the or yaw-roll riding on model uneven of roads. a single This unit paper heavy proposes vehicle. an TheH∞ controlapproach signals to design are theactive torques anti- duringroll bars cornering using the or yaw-roll riding on model uneven of roads. a single This unit paper heavy proposes vehicle. an TheH∞ controlapproach signals to design are theactive torques anti- generatedroll bars using by the the actuators yaw-roll at model the front of a and single rear unit axles. heavy Simulation vehicle. The results∞ control in both signals frequency are the and torques time generatedroll bars using by the the actuators yaw-roll at model the front of a and single rear unit axles. heavy Simulation vehicle. The results control in both signals frequency are the and torques time domainsgenerated are by provided the actuators to compare at the two front diff anderent rear cases: axles. passive Simulation anti-roll results bars and in bothH active frequency anti-roll and bars. time domains are provided to compare two different cases: passive anti-roll bars and H∞ active anti-roll bars. Itdomains is shown are that provided the use to compare of two H twoactive different (front cases: and passive rear) anti-roll anti-roll bars bars drastically and H∞ active improves anti-roll the bars. roll It is shown that the use of two H∞ active (front and rear) anti-roll bars drastically∞ improves the roll Itstability is shown of the that single the use unit of heavy two vehicleH∞ active to prevent (front and rollover. rear) anti-roll bars drastically improves the roll stability of the single unit heavy vehicle∞ to prevent rollover. stability of the single unit heavy vehicle∞ to prevent rollover. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Vehicle dynamics, Active anti-roll bar control, Rollover, Roll stability, H control, Keywords: Vehicle dynamics, Active anti-roll bar control, Rollover, Roll stability, H∞ control, Keywords:µ-analysis. Vehicle dynamics, Active anti-roll bar control, Rollover, Roll stability, H∞ control, µ-analysis. ∞ µ-analysis. ∞ 1. INTRODUCTION 1.2 Related works 1. INTRODUCTION 1.2 Related works 1. INTRODUCTION 1.2 Related works Some of the control methods applied for active anti-roll bar Somecontrol of on the heavy control vehicle methods are briefly applied presented for active below: anti-roll bar 1.1 Context controlSome of on the heavy control vehicle methods are briefly applied presented for active below: anti-roll bar 1.1 Context controla- Optimal on heavy control: vehicleSampson are brieflyet al presented(see Sampson below: and Cebon 1.1 Context a- Optimal control: Sampson et al (see Sampson and Cebon (1998),a- Optimal Sampson control: andSampson Cebon (2002))et al (see have Sampson proposed and a Cebon state The rollover is a very serious problem for heavy vehicle safety, (1998),feedback Sampson controller and which Cebon was (2002)) designed have by finding proposed an optimal a state The rollover is a very serious problem for heavy vehicle safety, feedback(1998), Sampson controller and which Cebon was (2002)) designed have by finding proposed an optimal a state whichThe rollover can result is a very in large serious financial problem and for environmental heavy vehicle conse-safety, controllerfeedback controller based on a which linear was quadratic designed regulator by finding(LQR) anfor optimal single whichquences. can In result order in to large improve financial roll stability,and environmental most of modern conse- controllerunit and articulated based on a heavy linear vehicles. quadratic regulator (LQR) for single quences.which can In result order in to large improve financial roll stability,and environmental most of modern conse- controllerunit and articulated based on a heavy linear vehicles. quadratic regulator (LQR) for single heavyquences. vehicles In order are to equipped improve with roll stability,passive anti-roll most of barsmodernto Theunit andLQR articulatedwas also applied heavy vehicles. to the integrated model including an heavyreducevehicles roll motion. are The equipped passive with anti-rollpassive bar has anti-roll the advantages bars to TheelectronicLQR was servo-valve also applied hydraulic to the damperintegrated model model and including a yaw-roll an reduceheavyvehicles roll motion. are The equipped passive with anti-rollpassive bar has anti-roll the advantages bars to TheelectronicLQR was servo-valve also applied hydraulic to the damperintegrated model model and including a yaw-roll an toreduce reduce roll the motion. body roll The acceleration passive anti-roll and roll bar angle has the during advantages single modelelectronic of a servo-valve single unit heavy hydraulic vehicle. damper The modelinput control and a yaw-rollsignal is towheel reduce lifting the body and cornering roll acceleration maneuvers. and roll However, angle during the passive single modelthe input of currenta single of unit the heavy electronic vehicle. servo-valve The input (Vu control et al., signal 2016). is wheelto reduce lifting the body and cornering roll acceleration maneuvers. and roll However, angle during the passive single themodel input of currenta single of unit the heavy electronic vehicle. servo-valve The input (Vu control et al., signal 2016). is wheelanti-roll lifting bar also and has cornering drawbacks. maneuvers. During corneringHowever, maneuvers,the passive theb-Neural input current network of the control: electronicBoada servo-valve et al.(2007) (Vu et al., proposed 2016). anti-rollwheel lifting bar also and has cornering drawbacks. maneuvers. During corneringHowever, maneuvers,the passive b- Neural network control: Boada et al. (2007) proposed itanti-roll transfers bar the also vertical has drawbacks. forces of oneDuring side cornering of suspension maneuvers, to the ab- reinforcement Neural network learning control: algorithmBoada using et al. neural (2007) networks proposed to itother transfers one, creating the vertical therefore forces a ofmoment one side against of suspension lateral force. to the aimprove reinforcement the roll stability learning for algorithm a single usingunit heavy neural vehicle. networks to otherit transfers one, creating the vertical therefore forces a ofmoment one side against of suspension lateral force. to the improvea reinforcement the roll stability learning for algorithm a single usingunit heavy neural vehicle. networks to otherIn order one, to creating overcome therefore the drawbacks a moment of theagainst passive lateral anti-roll force. bar improvec- Robust the control roll stability(LPV) for: aGaspar single unitet al heavy(see vehicle. Gaspar et al. Inother order one, to creating overcome therefore the drawbacks a moment of theagainst passive lateral anti-roll force. bar c- Robust control (LPV): Gaspar et al (see Gaspar et al. systems,In order to several overcome schemes the drawbacks with possible of the active passive intervention anti-roll into bar c-(2005a), Robust Gaspar control et al.(LPV) (2004): Gaspar and Gasparet al et(see al. (2005b)) Gaspar et have al. systems,the vehicle several dynamics schemes have with been possible proposed. active One intervention of them intoem- (2005a),applied Linear Gaspar Parameter et al. (2004) Varying and Gaspar(LPV) ettechnique al. (2005b)) for have the thesystems, vehicle several dynamics schemes have with been possible proposed. active One intervention of them intoem- applied(2005a), Linear Gaspar Parameter et al. (2004) Varying and Gaspar(LPV) ettechnique al. (2005b)) for have the ploysthe vehicleactive dynamics anti-roll bars have, that been is, proposed. a pair of hydraulic One of them actuators em- appliedactive anti-roll Linear bar Parameter combined Varying with an active(LPV) braketechnique control for on the ploys active anti-roll bars, that is, a pair of hydraulic actuators active anti-roll bar combined with an active brake control on the ployswhichactive generate anti-roll a stabilizing bars, that moment is, a pair to balance of hydraulic the overturning actuators singleactive anti-rollunit heavy bar vehicle. combined The with forward an active velocity brake iscontrol considered on the as whichmoment. generate Lateral a acceleration stabilizing moment makes vehicles to balance with the conventional overturning singlethe varying unit heavy parameter. vehicle. The forward velocity is considered as moment.which generate Lateral a acceleration stabilizing moment makes vehicles to balance with the conventional overturning thesingle varying unit heavy parameter. vehicle. The forward velocity is considered as passivemoment. suspension Lateral acceleration tilt out of makescorners. vehicles The center with of conventional the sprung the varying parameter. passive suspension tilt out of corners. The center of the sprung 1.3 Paper contribution masspassive shifts suspension outboard tilt of out the of vehicle corners. centerline, The center which of the creates sprung a 1.3 Paper contribution massdestabilizing shifts outboard moment of that the reduces vehicle roll centerline, stability. whichThe lateral creates load a Based1.3 Paper on the contribution model presented in (Gaspar et al. (2004)), this destabilizingmass shifts outboard moment of that the reduces vehicle roll centerline, stability. whichThe lateral creates load a Based on the model presented in (Gaspar et al. (2004)), this responsedestabilizing is reduced moment by that active reduces anti-roll roll stability. bars which The lateral generate load a paperBased proposes on the model an H presentedcontrol method in (Gaspar for active et al. (2004)),anti-roll bar,this response is reduced by active anti-roll bars which generate a paper proposes an H∞ control method for active anti-roll bar, responsestabilizing is moment reduced to by counterbalance active anti-roll the bars overturning which generate moment a thatpaper focuses proposes on an theH uncertainties∞ control method due to for the active vehicle anti-roll forward bar, stabilizing moment to counterbalance the overturning moment that focuses on the uncertainties∞ due to the vehicle forward instabilizing such a way moment that the to counterbalancecontrol torque leans the overturning the vehicle moment into the velocitythat focuses and theon the sprung uncertainties∞ mass variations. due to Hence the vehicle the following forward incorners such a(see way Sampson that the and control Cebon torque (2003), leans Gaspar the vehicle et al. (2004)). into the contributionsvelocity and the are sprungbrought: mass variations. Hence the following cornersin such a(see way Sampson that the and control Cebon torque (2003), leans Gaspar the vehicle et al. (2004)). into the contributionsvelocity and the are sprungbrought: mass variations. Hence the following Othercorners methods (see Sampson can be and used Cebon (active (2003), steering, Gaspar electronic et al. (2004)). brake -contributionsWe design anareH brought:robust controller for active anti-roll bar Othermechanism,...) methods but can they be usedare beyond (active the steering, scope of electronic this paper. brake system- We design on the an singleH∞ unitrobust heavy controller vehicle. Thefor active aim is toanti-roll maximize bar mechanism,...)Other methods but can they be usedare beyond (active the steering, scope of electronic this paper. brake system- We design on the an singleH∞ unitrobust heavy controller vehicle. Thefor active aim is toanti-roll maximize bar mechanism,...)The disadvantage but of they the are active beyond anti-roll the scope bars of is this that paper. the maxi- thesystem roll on stability the single to∞ prevent unit heavy rollover vehicle. of heavy The aim vehicles. is to maximize The nor- Themechanism,...) disadvantage but of they the are active beyond anti-roll the scope bars of is this that paper. the maxi- thesystem roll on stability the single to prevent unit heavy rollover vehicle. of heavy The aim vehicles. is to maximize The nor- mumThe disadvantage stabilizing moment of the active is limited anti-roll physically bars is by that the the relative maxi- malizedthe roll stability load transfer to prevent and the rollover limitation of heavy of the vehicles. torque generated The nor- mumroll angle stabilizing between moment the body is and limited the axle physically (Sampson by the and relative Cebon bymalized actuators load in transfer various and maneuver the limitation situations of the are torque considered. generated rollmum angle stabilizing between moment the body is and limited the axle physically (Sampson by the and relative Cebon bymalized actuators load in transfer various and maneuver the limitation situations of the are torque considered. generated (2002)).roll angle between the body and the axle (Sampson and Cebon by- The actuators performance in various analysis, maneuver made situations in frequency are considered. domain, shows (2002)). - The performance analysis, made in frequency domain, shows (2002)). - The performance analysis, made in frequency domain, shows 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. CopyrightPeer review © under 2016 responsibilityIFAC of International Federation of Automatic99 Control. Copyright © 2016 IFAC 99 Copyright10.1016/j.ifacol.2016.07.503 © 2016 IFAC 99 2016 IFAC SSSC 100June 22-24, 2016. Istanbul, Turkey Van-Tan Vu et al. / IFAC-PapersOnLine 49-9 (2016) 099–104

that the H active anti-roll bar control drastically reduces the mv(β˙ + ψ˙) mshφ¨ = Fyf + Fyr normalized∞ load transfer, compared to the passive anti-roll bar. − Ixzφ¨ + Izzψ¨ = Fyfl f Fyrlr It also shows that the H active anti-roll bar control is robust  − 2 − ∞  ¨ ¨ ˙ ˙ w.r.t. the forward velocity and the sprung mass variation. The  (Ixx + msh )φ Ixzψ = msghφ + msvh(β + ψ)  − robust stability analysis of the designed controller is performed  k f (φ φtf) b f (φ˙ φ˙tf) + MAR f + U f  − − − − using the µ- analysis method.  kr(φ φtr) br(φ˙ φ˙tr) + MARr + Ur (1)  − − − − - In time domain, we use a double lane change as the heavy  rF = m v(r h )(β˙ + ψ˙) + m gh .φ k φ  yf uf uf uf uf tf tf tf vehicle maneuver. The simulation results indicate that the Root  − − ˙ ˙ −  +k f (φ φtf) + b f (φ φtf) + MAR f + U f Mean Square (RMS) of the H active anti-roll bar control have  − − ∞  rFyr = murv(r hur)(β˙ + ψ˙) murghurφtr ktrφtr dropped from 15% to 50% compared to the passive anti-roll  − − − − bar with all the forward velocities considered in interval from  +kr(φ φtr) + br(φ˙ φ˙tr) + MARr + Ur  − − 50Km/h to 110Km/h.   The paper is organised as follows: Section 2 gives the model In (1) the lateral tire forces Fyf and Fyr in the direction of of a single unit heavy vehicle. Section 3 gives the H robust velocity at the wheel ground contact points are modelled by control synthesis to prevent rollover of heavy vehicles.∞ Section a linear stiffness as: 4 illustrates the robustness analysis in the frequency domain F = µC α using the µ- tool. Section 5 presents the simulations in time yf f f (2) F = µC α domain. Finally, some conclusions are drawn in section 6.  yr r r with tire side slip angles: 2. SINGLE UNIT HEAVY VEHICLE MODEL l ψ˙ α = β + δ f f − f − v  ˙ (3)  lrψ αr = β +  − v  The moment of passive anti-roll bar impacts the unsprung and sprung masses at the front and rear axles as follows (Vu et al., 2016):

2 tAtB tA MAR f = 4kAO f φ 4kAO f φuf (4) c2 − c2 2 tAtB tA MARr = 4kAOr φ 4kAOr φur (5) c2 − c2 where kAO f , kAOr are respectively the torsional stiffness of the anti-roll bar at the front and rear axles, tA half the distance of the two suspensions, tB half the distance of the chassis and c the length of the anti-roll bars’s arm. Using the previous equation, the single unit heavy vehicle is represented by the linear system in the state space form (6): x˙ = Ax+ Bu (6) y = Cx  with the state vector: T x = β ψφ˙ φφ˙ uf φur the input vector:   T u = δ f U f Ur and the output vector:   Fig. 1. Yaw-Roll model of single unit heavy vehicle (see Gaspar T y = β ψφ˙ φφ˙ uf φur et al. (2004)). Remark: Note that matrix A mainly depends on the forward velocity (V) and the sprung mass (ms). The design of H Fig 1 illustrates the combined yaw-roll dynamics of the vehicle ∞ modelled by a three-body system, in which ms is the sprung controller will be done considering the nominal matrix A and mass, muf the unsprung mass at the front including the front the effect of uncertainties will be analysed in section 4. wheels and axle, and mur the unsprung mass at the rear with 3. H ROBUST CONTROL SYNTHESIS TO PREVENT the rear wheels and axle. The parameters and variables of the ∞ yaw-roll model are shown in (Gaspar et al. (2004)). ROLLOVER OF HEAVY VEHICLES In the vehicle modelling, the differential equations of motion 3.1 Control objective, problem statement of the yaw-roll dynamics of the single unit vehicle, i.e. the lateral dynamics, the yaw moment, the roll moment of the The objective of the active anti-roll bar control system is sprung mass, the roll moment of the front and the rear unsprung to maximize the roll stability of the vehicle. An imminent masses, are formalized in the equations (1): rollover can be detected if the calculated normalized load

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