LPV Active Braking Control to Improve Vehicle Roll Stability

7th IFAC Symposium on System Structure and Control 7th IFAC Symposium on System Structure and Control 7th IFAC Symposium on System Structure and Control 7th IFAC Symposium on Structure and Sinaia, Romania, September 9-11, 2019 7th IFAC Symposium on System System and Control Control Available online at www.sciencedirect.com Sinaia, Romania, September 9-11,Structure 2019 Sinaia, Romania, September 9-11,Structure 2019 7th IFAC Symposium on System and Sinaia, Romania, September 9-11,Structure 2019 7th IFAC Symposium on System and Control Control Sinaia, Sinaia, Romania, Romania, September September 9-11, 9-11, 2019 2019

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IFAC PapersOnLine 52-17 (2019) 54–59

The Design an H /LPV Active Braking Control ∞ The Design of of an H /LPV Active Braking Control ∞ The of an H /LPV Active Braking Control ∞ The Design Design of an H /LPV Active Braking Control ∞ to Improve Vehicle Roll Stability The Design of an H /LPV Active Braking Control ∞ to Improve Vehicle Roll Stability The Design of an H /LPV Active Braking to Improve Vehicle Roll Stability ∞Vehicle Roll Stability Control to Improve ∗∗ Olivier Sename ∗∗ ∗∗ Vehicle Stability ∗∗ ∗∗ ∗∗∗ Van Tan Tan to Vu Improve LucRoll Dugard Peter Gaspar Gaspar ∗∗∗ ∗∗ Olivier ∗∗ ∗∗ Van Vu Dugard Vehicle Stability ∗∗ Luc ∗∗ Peter ∗∗∗ Van Tan to Vu Improve Olivier Sename Sename LucRoll Dugard Peter Gaspar ∗∗∗

Van Luc Peter Van Tan Tan Vu Vu ∗∗ Olivier Olivier Sename Sename ∗∗ Luc Dugard Dugard ∗∗ Peter Gaspar Gaspar ∗∗∗ ∗∗ ∗∗ ∗∗∗ ∗ Olivier ∗∗ Luc ∗∗ Peter ∗∗∗ Van Tan Vu Sename Dugard Gaspar ∗∗ Department Van Tan Vu Olivier Sename Luc Dugard Peter Gaspar of Automotive Mechanical Engineering, University of Transport of Automotive Mechanical Engineering, University of Transport ∗ Department of Automotive Mechanical Engineering, University of Transport ∗ Department and Communications, Vietnam. E-mail: [email protected] of Automotive Hanoi, Mechanical Engineering, University of Transport and Communications, Hanoi, Vietnam. E-mail: [email protected] ∗∗ Department ∗∗ + and Communications, Hanoi, Vietnam. E-mail: [email protected] Department of Automotive Mechanical Engineering, University Transport ∗∗ + Univ. Grenoble Alpes, CNRS, Grenoble INP , GIPSA-lab, Department of Automotive Mechanical Engineering, University of of38000 Transport and Communications, Hanoi, Vietnam. E-mail: [email protected] Grenoble Alpes, CNRS, Grenoble INP 38000 ∗∗ Univ. + ,, GIPSA-lab, Univ. Grenoble Alpes, CNRS, Grenoble INP GIPSA-lab, 38000 + and Communications, Hanoi, Vietnam. E-mail: [email protected] ∗∗ + Univ. Grenoble Alpes, CNRS, Grenoble INP , GIPSA-lab, 38000 + Grenoble, France. Institute of Engineering Univ. Grenoble Alpes. E-mail: and Communications, Hanoi, Vietnam. E-mail: [email protected] Univ. Grenoble Alpes, CNRS, Grenoble INP , GIPSA-lab, 38000 + ∗∗ + Grenoble, France. Institute of Engineering Univ. Grenoble Alpes. E-mail: + Grenoble, France. of Engineering Univ. Grenoble Alpes. E-mail: Grenoble Alpes, CNRS, Grenoble INP ,, GIPSA-lab, 38000 ∗∗ Univ. + Institute Grenoble, France. Institute of Alpes. E-mail: {olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr Univ. Grenoble Alpes, CNRS, GrenobleUniv. INP+Grenoble GIPSA-lab, 38000 Grenoble, France. Institute of Engineering Engineering Univ. Grenoble Alpes. E-mail: {olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr + ∗∗∗ {olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr + Grenoble, France. Institute of Engineering Univ. Grenoble Alpes. E-mail: ∗∗∗ Institute for Computer Science and Control, Hungarian Academy of Grenoble, France. Institute of Engineering Univ. Grenoble Alpes. E-mail: {olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr for Computer Science and Control, Hungarian Academy of ∗∗∗ Institute for Computer Science and Control, Hungarian Academy of {olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr ∗∗∗ Institute Sciences, Budapest, Hungary. E-mail: [email protected] {olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary. E-mail: [email protected] ∗∗∗ Sciences, Budapest, Hungary. E-mail: [email protected] Institute for Computer Science and Control, Hungarian Academy ∗∗∗ Institute Sciences, Budapest, Hungary. E-mail: [email protected] for Computer Science and Control, Hungarian Academy of of

Sciences, Budapest, Hungary. E-mail: [email protected] Sciences, Budapest, Hungary. E-mail: [email protected] Budapest, Hungary. E-mail: [email protected] Abstract: The The active activeSciences, braking control control system is an an active active safety system designed designed to to prevent prevent accidents accidents and and Abstract: braking system is safety system Abstract: The active braking control system is an active safety system designed to prevent accidents and Abstract: The activemanoeuvers braking control control system isby angenerating active safety safety system designed to prevent prevent accidents and to stabilize dynamic of aasystem vehicle an artificial yaw moment using differential Abstract: The active braking is an active system designed to accidents and to stabilize dynamic manoeuvers of vehicle by generating an artificial yaw moment using differential to stabilize dynamic manoeuvers of a vehicle by generating an artificial yaw moment using differential Abstract: The active braking control system is an active safety system designed to prevent accidents and braking forces. In this paper, the yaw-roll model of a single unit heavy vehicle is used for studying Abstract: The active braking control system is an active safety system designed to prevent accidents and to stabilize dynamic manoeuvers of a vehicle by generating an artificial yaw moment using differential braking forces. In this this paper, the theofyaw-roll yaw-roll model of aa single single unit heavy vehicle is used used for studying braking forces. In paper, model of unit heavy vehicle is for studying to stabilize dynamic manoeuvers a vehicle by generating an artificial yaw moment using differential the active braking system by using the longitudinal braking force at each wheel. The grid-based LPV to stabilize dynamic manoeuvers of a vehicle by generating an artificial yaw moment using differential braking forces. In this paper, the yaw-roll model of a single unit heavy vehicle is used for studying the active braking system by using the longitudinal braking force at each wheel. The grid-based LPV the active braking system by using the longitudinal braking force at each wheel. The grid-based LPV braking this paper, the model aa single unit vehicle is for studying the activeforces. braking system by using using the longitudinal braking force atheavy each wheel. The The grid-based LPV /LPV controller by considering the parameter dependant weighting approach isbraking usedIn to system synthesize the Hyaw-roll braking forces. In this paper, theH yaw-roll model of ofbraking single unit at heavy vehicle is used used forweighting studying the active by the longitudinal force each wheel. grid-based LPV ∞ /LPV controller by considering the parameter dependant approach is used to synthesize the ∞ /LPV controller by considering the parameter dependant weighting approach is used to synthesize the H the active braking system by using the longitudinal braking force at each wheel. The grid-based LPV /LPV controller by considering the parameter dependant weighting approach is used to synthesize the H ∞ function for the lateral acceleration. The braking monitor designs are proposed to allow the active braking the active braking system by using the longitudinal braking force at each wheel. The grid-based LPV approachfor is used to synthesize the H∞The /LPV controller by designs considering the parameter dependant weighting function the lateral acceleration. braking monitor are proposed to allow the active braking function for the lateral acceleration. The braking monitor designs are proposed to allow the active braking /LPV controller by considering the parameter dependant weighting approach is used to synthesize the H ∞ system to react when the normalized load transfer at the rear axle reaches the criteria of rollover ±1. /LPV controller by considering the parameter dependant weighting approach is used to synthesize the H function for the lateral acceleration. The braking monitor designs are proposed to allow the active braking ∞load transfer at the rear axle reaches the criteria of rollover ±1. The system react when the normalized The system to tofor react when the normalized loadbraking transfermonitor at the the rear axleare reaches the criteria criteria ofthe rollover ±1. The function the lateral acceleration. The designs proposed to allow active braking system to react when the normalized load transfer at axle reaches the of rollover ±1. The simulation results indicate that the active braking system satisfies the adaptation vehicle rollover in an function for the lateral acceleration. The designs proposed to of allow active braking system to react when the normalized loadbraking transfermonitor at the rear rear axleare reaches the criteria ofthe rollover ±1. The simulation results indicate that the active braking system satisfies the adaptation of vehicle rollover in an simulation results indicate that the active braking system satisfies the adaptation of vehicle rollover in an system to react when the normalized load transfer at the rear axle reaches the criteria of rollover ±1. simulation results indicate that the active braking system satisfies the adaptation of vehicle rollover in an emergency situation, with low braking forces andsystem improved handling performance ofofthe the vehicle. system to react when the normalized load transfer at the rear axle reaches the criteria rollover ±1.inThe The simulation results indicate that braking the active braking satisfies the adaptation of vehicle rollover an emergency situation, with low forces and improved handling performance of vehicle. simulation results indicate that the active braking system satisfies the adaptation of vehicle rollover in an emergency situation, with low braking forces and improved handling performance of the vehicle. simulation results indicate that the active braking system satisfies the adaptation of vehicle rollover in an emergency situation, with low braking forces and improved handling performance of the vehicle. emergency situation, with low braking forces and improved handling performance of the vehicle. emergency situation, with low braking forces and improved handling performance of the vehicle. control, LPV Keywords: Active braking system, H Copyright © Vehicle 2019. Thedynamics, Authors. Published by Elsevier Ltd. Rollover, All rights reserved. ∞ LPV system. system. Keywords: Vehicle dynamics, Active braking system, Rollover, H ∞ control, Keywords: Vehicle dynamics, Active braking system, Rollover, H control, LPV LPV system. system. Keywords: Vehicle dynamics, Active braking system, Rollover, H ∞ control, Keywords: Vehicle dynamics, Active braking system, Rollover, H ∞ control, LPV system. Keywords: Vehicle dynamics, Active braking system, Rollover, H control, LPV system. ∞ control, LPV Keywords: Vehicle dynamics, Active braking system, Rollover, H ∞ lateral inertialsystem. duction of of the the force by by means means of of speed speed reduction reduction 1. INTRODUCTION 1. INTRODUCTION duction lateral inertial force 1. duction of the lateral inertial force by means of speed reduction and the combined reduction of the lateral force component, by 1. INTRODUCTION INTRODUCTION duction of the lateral inertial force by means of speed reduction and the the combined combined reduction of theby lateral force component, by and reduction of the lateral force component, by 1. INTRODUCTION duction of the lateral inertial force means of speed reduction 1.1 Context and the reduction of the lateral force component, by means ofcombined manipulating the tyre tyre slip. These two effects together 1. INTRODUCTION duction of the lateral inertial force by means of speed reduction 1.1 Context and the combined reduction of the lateral force component, by means of manipulating the slip. These two effects together 1.1 and the combined reduction of the lateral force component, by means manipulating the slip. These two together 1.1 Context Context are enough enough to prevent prevent rollover on both combination and also and theof reduction of on the lateral force component, by means ofcombined manipulating the tyre tyre slip. These two effects effects together are to rollover both aaa combination and also 1.1 Context Vehicle rollover accidents have been extremely hazardous to the means of manipulating the tyre slip. These two effects together are enough to prevent rollover on both combination and also 1.1 Context Vehicle rollover accidents accidents have have been been extremely extremely hazardous hazardous to to the the means a single unit vehicles. of manipulating the tyre slip. These two effects together are enough to prevent rollover on both a combination and also Vehicle rollover aa single unit Vehicle rollover accidents have been hazardous to occupants of the vehicle and identified as the most fatal vehicle enough tovehicles. prevent Vehicle rollover accidents have been extremely extremely hazardous to the the are unit occupants of the vehicle and identified as the most fatal vehicle are enough prevent rollover rollover on on both both aa combination combination and and also also a single single unittovehicles. vehicles. Vehicle rollover accidents have been extremely hazardous to the occupants of the vehicle and identified as the most fatal vehicle crashes. Loss of roll stability is the main cause of rollover acciVehicle rollover accidents have been extremely hazardous to the a single unit vehicles. occupants of the vehicle and identified ascause the most fatal vehicle crashes. Loss of roll stability is the main of rollover acci1.2 Related works a1.2 single unit works vehicles. occupants of the vehicle and identified as the most fatal vehicle Related crashes. Loss of roll stability is the main cause of rollover accidents involving vehicles. According the Japan Traffic occupants of the vehicle and identified ascause theto most fatal vehicle crashes. Loss of heavy roll stability is the main of rollover acci- 1.2 dents involving heavy vehicles. According to the Japan Traffic 1.2 Related Related works works crashes. Loss of roll stability is the main cause of rollover accidents involving heavy vehicles. According to the Japan Traffic 1.2 Related Among the works literature on on active active braking braking system system in in order order to to Accidents Databases, rollover accidents were nearly 1/5 of all crashes. Loss of roll stability is the main cause of rollover accidents involving heavy vehicles. According to the Japan Traffic Among the literature Accidents Databases, rollover accidents were nearly 1/5 of all 1.2 Related works Among the literature on active braking system in order to Accidents Databases, rollover accidents were nearly 1/5 of all dents involving heavy vehicles. According to the Japan Traffic Among the literature on active braking system in order to Accidents Databases, rollover accidents were nearly 1/5 of all prevent the rollover situation of heavy vehicles, let us mention the accidents. Federal National Highway dentssingle-vehicle involving heavy vehicles.The According to the Japan Traffic Among the literature on active braking system in order to Accidents Databases, rollover accidents were nearly 1/5 of all prevent the rollover situation of heavy vehicles, let us mention the single-vehicle accidents. The Federal National Highway Among the literature on braking system in order to Accidents Databases, rollover accidents were nearly 1/5 of the rollover situation of vehicles, let us mention the single-vehicle accidents. Federal National Highway some few works below: Traffic Safety Administration has statistics that in the United Among the literature on active active braking system to Accidents Databases, rollover The accidents were nearly 1/5 of all all prevent prevent the rollover situation of heavy heavy vehicles, let in us order mention the single-vehicle accidents. The Federal National Highway some few few works below: Traffic Safety Administration has statistics that in the United prevent the rollover situation of heavy vehicles, let us mention the single-vehicle accidents. The Federal National Highway some works below: Traffic Safety Administration has statistics that in the United • In (Palkovics et al. (1999)), the authors discuss some of States, there were 333, 000 heavy vehicles involved in traffic prevent the rollover situation of heavy vehicles, let us mention the single-vehicle accidents. The Federal National Highway some few works below: Traffic Safety Administration has statistics that in the United States, were 333, 000 heavy vehicles involved in traffic • In In (Palkovics et al. al. (1999)), (1999)), the the authors authors discuss discuss some some of of States, there there were 333, 000were heavy vehicles involved inrollover traffic some (Palkovics et few works Traffic Safety Administration has statistics that in United States, there were 333, 000 heavy vehicles involved in traffic ••• In (Palkovics et al. (1999)), authors discuss some of the problems of general crashes during 2012. There 3, 921 people killed in few works below: below: Traffic Safety Administration has statistics that in the the United States, there were 333, 000were heavy vehicles involved inrollover traffic some In (Palkovics etthe al.commercial (1999)), the thevehicle authorsstability discussin some of crashes during 2012. There 3, 921 people killed in the problems ofet the commercial vehicle stability insome general crashes during 2012. There were 3, 921 people killed in rollover the problems of the commercial vehicle stability in general States, there were 333, 000 heavy vehicles involved in traffic • In (Palkovics al. (1999)), the authors discuss of crashes during 2012. There 3, people killed in problems of stability general and heavy vehicles in particular, and offer ain solution crashes and 104, 000 people injured. In 2013, more 4, 500 States, there were 333, 000were heavy vehicles involved traffic • the In al.commercial (1999)), thevehicle authors discuss of during 2012. There were 3, 921 921 people killedthan ininrollover rollover the problems ofetthe the commercial vehicle stability insome general crashes and 104, 000 people injured. In 2013, more than 4, 500 and(Palkovics heavy vehicles vehicles in particular, particular, andstability offer solution crashes during 2012. There were 3, 921 people killed in rollover the problems of the commercial vehicle general and 104, 000 people injured. In 2013, more than 4, 500 and heavy in and offer aaain solution for detecting and avoiding rollover by using the existing persons were killed in road traffic accidents involving heavy crashes during 2012. There were 3, 921 people killed in rollover the problems of the commercial vehicle stability in general and 104, 000 people injured. In 2013, more than 4, 500 and heavy vehicles in particular, and offer solution persons were killed in road traffic accidents involving heavy for detecting and avoiding rollover by using the existing crashes 104, 000 people injured. In 2013, more than 4, 500 and heavy vehicles in particular, and offer aa solution persons were killed in road traffic accidents involving heavy for detecting and avoiding rollover by using existing sensors and actuators of the electronic braking system. An vehicles in EU, constituting almost of all road accident crashes and and 104, 000 people In18% 2013, than 4, 500 and heavy vehicles in particular, and offerthe solution persons were killed in road injured. traffic accidents involving heavy for detecting and avoiding avoiding rollover bybraking using the existing vehicles in the the EU, constituting almost 18% of more all road accident sensors and actuators actuators of the the electronic braking system. An vehicles in the EU, constituting almost 18% of all road accident sensors and of electronic system. An persons were killed in road traffic accidents involving heavy for detecting and rollover by using the existing vehicles in the EU, constituting almost 18% of all road accident sensors and actuators of the electronic braking system. An integrated control of yaw, roll and vertical vertical dynamics based fatalities for that year et al. (2016)). persons were killed in(Evgenikos road traffic accidents involving heavy for detecting and of avoiding rollover bybraking using the existing vehicles in the EU, constituting almost 18% of all road accident sensors andcontrol actuators of the electronic system. An fatalities for that year (Evgenikos et al. (2016)). integrated yaw, roll and dynamics based fatalities for that year (Evgenikos et al. (2016)). integrated control of yaw, roll and vertical dynamics based vehicles in the EU, constituting almost 18% of all road accident sensors and actuators of the electronic braking system. An fatalities for that year (Evgenikos et (2016)). integrated of yaw, roll and vertical dynamics based on semi-active suspension and an active differential Because of the high center of gravity, the disturbance effects vehicles in the EU, constituting almost of all road accident sensors andcontrol actuators of the electronic system. An fatalities for that year (Evgenikos et al. al.18% (2016)). integrated control of yaw, roll and vertical dynamics based Because of the high center of gravity, the disturbance effects on aaa semi-active semi-active suspension andvertical anbraking active differential fatalities for that year (Evgenikos et al. (2016)). integrated control of yaw, roll and dynamics based Because of the high center of gravity, the disturbance effects on suspension and an active differential braking system was presented by (Soltani et al. (2017)). A such as gusts of wind, irregular road surfaces, and abrupt mafatalities for that year (Evgenikos et al. (2016)). integrated control of yaw, roll and vertical dynamics based Because of the high center of gravity, the disturbance effects on a semi-active suspension and an active differential such as gusts of wind, irregular road surfaces, and abrupt mabraking system was presented by (Soltani et al. (2017)). A such as as gusts gusts ofhigh wind,center irregular road surfaces, surfaces, and abrupt abrupt mabraking system wassuspension presented by (Soltani et al.differential (2017)). A Because of the of gravity, the disturbance effects on aa semi-active and an active such of wind, irregular road and mabraking system was presented by (Soltani et al. (2017)). A coordinated control of the two systems is proposed, using noeuvers, heavy vehicles have a proclivity to rollover accidents. Because of the high center of gravity, the disturbance effects on semi-active suspension and an active differential such as gusts of wind, irregular road surfaces, and abrupt mabraking system was presented by (Soltani et al. (2017)). A noeuvers, heavy vehicles have a proclivity to rollover accidents. coordinated control of the two systems is proposed, using noeuvers, heavy vehicles have a proclivity to rollover accidents. coordinated control of the two systems is proposed, using such gusts of wind, irregular road surfaces, and mabraking system was presented by (Soltani et al. A noeuvers, heavy have to accidents. coordinated control of the two systems is proposed, using a fuzzy fuzzy controller controller and an adaptive sliding mode controller. Thus, is necessary to develop fast safety control systems such as asit gusts of vehicles wind, irregular roadand surfaces, and abrupt abrupt mabraking system was presented (Soltani et al. (2017)). (2017)). A noeuvers, heavy vehicles have aa proclivity proclivity to rollover rollover accidents. coordinated control ofan theadaptive twoby systems is mode proposed, using Thus, it is necessary to develop fast and safety control systems and sliding controller. Thus, it is necessary to develop fast and safety control systems aaaWith fuzzy controller and an adaptive sliding mode controller. noeuvers, heavy vehicles have a proclivity to rollover accidents. coordinated control of the two systems is proposed, using Thus, it is necessary to develop fast and safety control systems fuzzy controller and an adaptive sliding mode controller. the active braking system, in the emergency situation to detect and prevent vehicle rollover, so they will enhance noeuvers, heavy vehicles have a rollover, proclivity to they rollover accidents. coordinated control ofan the two systems is mode proposed, using Thus, it is and necessary to vehicle develop fast and safety control systems aWith fuzzy controller and adaptive sliding controller. to detect prevent so will enhance the active braking system, in the emergency situation Thus, it necessary to develop fast safety control systems aWith fuzzy controller and adaptive sliding mode controller. to detect and prevent rollover, so will the active braking system, in the situation the vehicle can avoid rollover by reducing the roll angle, vehicle stability. Rollover prevention detection such as Thus, it is is necessary to vehicle develop fast and andand safety control systems aWith fuzzy and an an adaptive mode controller. to detect and prevent vehicle rollover, so they they will enhance enhance thecontroller active braking system, in sliding the emergency emergency situation vehicle stability. Rollover prevention and detection such as the vehicle can braking avoid rollover by reducing the roll roll angle, to detect and prevent vehicle rollover, so they will enhance With the active system, in the emergency situation vehicle stability. Rollover prevention and detection such as the vehicle can avoid rollover by reducing the angle, lateral acceleration and the lateral load transfer ratio. active steering, active braking, active suspension and active to detect and prevent vehicle rollover, so they will enhance With the active braking system, in the emergency situation vehicle stability. Rollover prevention and detection such as the vehicle can avoid rollover by reducing the roll angle, active steering, active braking, active suspension and active the lateral acceleration and the lateral load transfer ratio. active steering, active braking, active suspension and active the lateral acceleration and the lateral load transfer ratio. vehicle stability. Rollover prevention and detection such as vehicle can avoid by the roll angle, active steering, active braking, active suspension and active lateral and the lateral load • the In (Jo (Jo et acceleration al. (2008)), in order order toreducing enhance vehicle roll anti-roll bar systems have been studied extensively vehicle stability. Rollover prevention and detection such as the vehicle can(2008)), avoid rollover rollover reducing thevehicle roll ratio. angle, active steering, active braking, active suspension and(Gaspar active lateral acceleration and the by lateral load transfer transfer ratio. anti-roll bar systems have been studied extensively (Gaspar In et al. in to enhance roll anti-roll bar systems have been studied extensively (Gaspar ••• the In (Jo et al. (2008)), in order to enhance vehicle roll active steering, active braking, active suspension and active lateral acceleration and the lateral load transfer ratio. anti-roll bar systems have been studied extensively (Gaspar In (Jo et al. (2008)), in order to enhance vehicle roll stability, the reference yaw rate is designed and combined et al. (2004),Vu et al. (2017)). Among them, the active braking active steering, active braking, active suspension and active the lateral acceleration and the lateral load transfer ratio. anti-roll bar systems have been studied extensively (Gaspar • In (Jo etthe al.reference (2008)), yaw in order todesigned enhanceand vehicle roll et al. (2004),Vu et al. (2017)). Among them, the active braking stability, rate is combined anti-roll bar systems have been studied extensively (Gaspar •• In (Jo et al. (2008)), in to enhance vehicle roll et al. et Among them, the active braking stability, yaw rate designed and combined into aa target yaw rate depending on the driving situation. system is considered as the most effective way to improve anti-roll bar systems have been studied extensively (Gaspar In etthe al.reference (2008)), in order order enhance vehicle roll et al. (2004),Vu (2004),Vu et al. al. (2017)). (2017)). Among them, the active braking stability, the reference yaw rate is isto designed and combined system is considered as the most effective way to improve into(Jo target yaw rate depending depending on the driving driving situation. et al. (2004),Vu et al. (2017)). Among them, the active braking stability, the reference yaw rate is designed and combined system is considered as the most effective way to improve into a target yaw rate on the situation. A yaw rate controller is designed to track the target yaw vehicle stability in emergencies. With increasing emphasis on et al. (2004),Vu et al. (2017)). Among them, the active braking stability, the reference yaw rate is designed and combined system is considered as the most effective way to improve into a target yaw rate depending on the driving situation. vehicle stability stability in emergencies. emergencies. With increasing emphasis on A yaw yaw rate controller controller is designed designedonto tothe track the target target yaw vehicle in With increasing emphasis on A rate is track the yaw system is as the effective way to improve into aa target yaw rate depending driving situation. vehicle stability in emergencies. With increasing emphasis on A rate is track the target yaw rateyaw based oncontroller sliding mode controlonto theory. To generate the traffic safety in recent intensive efforts have put system is considered considered asyears, the most most effective way to been improve into target yaw ratemode depending the driving situation. vehicle stability in emergencies. With increasing emphasis on A yaw rateon controller is designed designed to track thegenerate target yaw traffic safety in recent years, intensive efforts have been put rate based sliding control theory. To the vehicle stability in emergencies. With increasing emphasis on A yaw rate controller is designed to track the target yaw traffic safety in recent years, intensive efforts have been put rate based on sliding mode control theory. To generate the total yaw from the proposed yaw rate towards improving the braking performance. standards vehicle stability emergencies. With increasing emphasis on A yaw ratemoment is designed to track thegenerate target yaw traffic safety in in recent years, intensive effortsSafety have been put rate based oncontroller slidingrequired mode control theory. To the towards improving the braking performance. Safety standards total yaw moment required from the proposed yaw rate traffic safety in years, intensive efforts have been put rate based on sliding mode control theory. To the towards improving the performance. Safety standards total yaw required from the proposed yaw rate controller, each brake pressure is properly distributed that specify performance requirements of various types of brake traffic safety in recent recent years, intensive efforts have been put rate based on sliding mode control theory. To generate generate the towards improving the braking braking performance. Safety standards total yaw moment moment required from the proposed yaw with rate that specify performance requirements of various types of brake controller, each brake pressure is properly properly distributed with that specify performance requirements of various types of brake controller, each brake pressure is distributed with towards improving the braking performance. Safety standards total yaw moment required from the proposed yaw rate that specify performance requirements of various types of brake controller, each brake pressure is properly distributed with effective control wheel decision. system have been introduced in many countries (Yakub and towards improving the braking performance. Safety standards total yaw moment required from the proposed yaw rate that specify performance requirements of various types of brake controller, each brake pressure is properly distributed with system have been introduced in many (Yakub and effective control control wheelpressure decision. system have been introduced in manyofcountries countries (Yakub and effective wheel decision. that performance requirements various of each brake is distributed with system have been in (Yakub and effective control wheel decision. •• controller, In (Gaspar et al. (2004)), the authors proposed aa combined Mori (2015)). that specify specify requirements various types types of brake brake controller, each is properly properly distributed with system haveperformance been introduced introduced in many manyofcountries countries (Yakub and effective control wheelpressure decision. Mori (2015)). In (Gaspar (Gaspar et al. al. brake (2004)), the authors authors proposed combined system have been introduced in many countries (Yakub and effective control wheel decision. Mori (2015)). • In et (2004)), the proposed a combined control structure between active anti-roll system In order to prevent aa vehicle rollover situation, the rollover resystem have been introduced in many countries (Yakub and control wheel decision. Mori (2015)). • effective In (Gaspar et al. (2004)), thethe authors proposed abar combined In order to prevent vehicle rollover situation, the rollover recontrol structure between the active anti-roll bar system Mori (2015)). •• In (Gaspar et (2004)), the authors proposed aabar combined In order to prevent aa vehicle rollover situation, the rollover recontrol structure between active anti-roll system and the active system. The main objective of sponsible of forces has to be reduced, which means the reMori (2015)). In et al. al.braking (2004)), thethe authors proposed combined In order topair prevent vehicle rollover situation, the rollover control structure between the active anti-roll bar system sponsible pair of forces has to be reduced, which means the reand(Gaspar the structure active braking system. The main main objective of this this In order to prevent a vehicle rollover situation, the rollover recontrol between the active anti-roll bar system sponsible pair of forces has to be reduced, which means the and the active braking system. The objective of In order topair prevent a vehicle situation, rollover control between the active anti-roll bar system sponsible of forces has torollover be reduced, whichthe means the reand the structure active braking system. The main objective of this this sponsible pair of forces has to be reduced, which means the reand the active braking system. The main objective of this 2405-8963 Copyright © 2019. Authors. Published Elsevier All rights and reserved. sponsible pair of IFAC forces hasThe to be reduced, whichbymeans theLtd. re-102 the active braking system. The main objective of this Copyright © 2019 Copyright 2019 IFAC 102 Control. Peer review© under responsibility of International Federation of Automatic Copyright © 2019 IFAC 102 Copyright © 2019 IFAC 102 10.1016/j.ifacol.2019.11.026 Copyright © 2019 IFAC 102 Copyright © 2019 IFAC 102

2019 IFAC SSSC Sinaia, Romania, September 9-11, 2019

Van Tan Vu et al. / IFAC PapersOnLine 52-17 (2019) 54–59

proposal is to allow the active anti-roll bar system to work in the normal driving situation and the active braking system is only activated when the vehicle comes close to a rollover situation. 1.3 Paper contribution The active braking system is crucial in view of autonomous driving to accomplish the task of obstacle avoidance. With the aim of applying advanced control method to complete this system, hence the contributions of this paper are the following: • A parameter dependant weighting function of the lateral acceleration is used to permit performance adaptation to the rollover risk of heavy vehicles, characterized by the normalized load transfers at the rear axle. The grid-based LPV approach is used to synthesize the H∞ /LPV active braking controller by using the LPVToolsTM toolbox. • We propose two Braking Monitor Designs in order to satisfy simultaneously the improved vehicle performance and prevention of vehicle rollover in an emergency situation. To fit better with the real world application, the objective of the braking monitor designs is to allow the active braking system to react when the normalized load transfer at the rear axle reaches the criteria of rollover ±1 by reducing the lateral acceleration. 2. THE LPV MODEL OF A SINGLE UNIT HEAVY VEHICLE USING AN ACTIVE BRAKING SYSTEM

Fig. 1. Vehicle model (Gaspar et al. (2004)). In this section, the yaw-roll model of a single unit heavy vehicle (two-axle vehicle) is used for studying the active braking system by using the four longitudinal braking forces at each wheel (Fb, f l , Fb, f r , Fb,rl , Fb,rr ). The vehicle model is shown in Figure 1 with the parameters and values presented in (Gaspar et al. (2004)). The braking force Fbi j , originating from the brake system and developed on the tyre-road interface is the primary retarding force. When the braking force is below the limit of tyre-road adhesion force, the braking force Fbi j , is given by (J.Y.Wong (2001)): Tbi j − ∑ Iα (1) Fbi j = r where Tbi j is the applied brake torque, I the rotating inertia connected with the wheel being decelerated, α the corresponding angular deceleration, and r the rolling radius of the tyre. The maximum braking force that the tyre-road contact can support is determined by the normal load and the coefficient of road adhesion. With four-wheel brakes, the maximum braking 103

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forces at the front axle are given by (assuming the maximum braking force of the vehicle Fbimax = µGi ): µG f µG[lr + h(µ + fr )] Fb, f lmax = Fb, f rmax = = (2) 2 2L at the rear axle: µG[l f − h(µ + fr )] µGr = (3) Fb,rlmax = Fb,rrmax = 2 2L where µ is the coefficient of road adhesion, G the vehicle weight, G f ,r the total axle loads, fr the rolling resistance coefficient, h the height of CG from ground, L the wheelbase, l f ,r the distance from CG to the front and rear axles. The yaw moment control generated by the active braking system, depends linearly on the difference between the left and right braking forces. In order to simplify building the control models, it is assumed that the braking forces are equal at the front and rear wheels on each side, so Fb, f l = Fb,rl , Fb, f r = Fb,rr . Therefore the yaw moment control Mz is defined as:    Mz = Mz,rr + Mz,rl     l 2f + lw2  lw  Mz,rr = Fb,rr (1 + sin(arctan( ) − δ f )) (4) l lf w    2  2  l f + lw  lw   sin(arctan( ) + δ f ))  Mz,rl = Fb,rl (1 + lw lf where lw is the half of the vehicle’s width, δ f the steering angle. Using the nonlinear functions in equation (4) will result in higher control efficiency, but it complicates the problem. Because the magnitude value of δ f is not too large compared to other parts, so to simplify the control design, we can use the approximate linear formula of Mzi (Gaspar et al. (2004)). The yaw moment (4) can be linearized as follows: (5) Mz = 2lw (Fb,rr − Fb,rl ) The motion differential equations of the yaw-roll vehicle model using the active braking system are defined as follows:                                                                     

l f ψ˙ lr ψ˙ ˙ − ms hφ¨ = µC f (−β + δ f − ) + µCr (−β + ) mv(β˙ + ψ) v v l f ψ˙ ˙ ψ l r )l f − µCr (−β + )lr −Ixz φ¨ + Izz ψ¨ = µC f (−β + δ f − v v +2Fb,rr − 2Fb,rl ˙ − k f (φ − φu f ) (Ixx + ms h2 )φ¨ − Ixz ψ¨ = ms ghφ + ms vh(β˙ + ψ) 2 t t t B A A −b f (φ˙ − φ˙u f ) + 4kAO f 2 φ − 4kAO f 2 φu f − kr (φ − φur ) c c t2 t tB −br (φ˙ − φ˙ur ) + 4kAOr A 2 φ − 4kAOr A2 φur c c l f ψ˙ ˙ −rµC f (−β + δ f − ) = mu f v(r − hu f )(β˙ + ψ) v +mu f ghu f .φu f − ku f φu f + k f (φ − φu f ) + b f (φ˙ − φ˙u f ) t2 t tB +4kAO f A 2 φ − 4kAO f A2 φu f c c lr ψ˙ ˙ − mur ghur φur −rµCr (−β + ) = mur v(r − hur )(β˙ + ψ) v −kur φur + kr (φ − φur ) + br (φ˙ − φ˙ur ) t2 t tB +4kAOr A 2 φ − 4kAOr A2 φur c c (6)

where kAO f ,r are respectively the torsional stiffness of the anti-roll bar at the two axles, tA half the distance of the two suspensions, tB half the distance of the chassis and c the length of the anti-roll bar’s arm (Vu et al. (2017)). It is assumed that the driving throttle is constant during a lateral manoeuver and the forward velocity depends only on the braking forces. The differential equation of the forward velocity is:

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mv˙ = −2Fb,rr − 2Fb,rl (7) It is worth noting that the motion differential equation of the vehicle model depends on the forward velocity and its inverse, moreover, the forward velocity is a constantly changing parameter. Therefore in this case the forward velocity is chosen as a varying parameter. We also would like to emphasize here that, considering the forward velocity is a varying parameter, it is extremely important for vehicle brake system. Because during the braking process, this parameter changes very quickly, this cannot be met with the lower-level control methods. The motion differential equation can be written in the following LPV statespace representation: x˙ = A(ρ1 ).x + B1 (ρ1 ).w + B2 (ρ1 ).u (8) where ρ1 = v is the varying parameter, the state vector T  x = β ψ˙ φ φ˙ φu f φur v , the exogenous disturbance w = T T [ δ f ] , and the control input u = [ Fb,rr Fb,rl ] . 3. THE PROPOSED H∞ /LPV ACTIVE BRAKING SYSTEM The main objective of the active braking control system is to maximize the vehicle roll stability to prevent a rollover phenomenon in an emergency. The most important criteria is used to assess the vehicle roll stability being the normalized load transfer at the two axles R f ,r , which is defined as follows (Hsun-Hsuan et al., 2012): k u f φu f kur φur Rf = , Rr = ∆Fzr = (9) G f lw Gr lw where G f ,r are the total axle loads, ku f ,r the stiffness of the tyres, φu f ,r the roll angles of the unsprung masses at the two axles, lw the half of the vehicle’s width. The normalized load transfer R f ,r = ±1 value corresponds to the largest possible load transfers. The roll stability is achieved by limiting the normalized load transfers within the levels corresponding to wheel lift-off.

absolute value of the normalized load transfer at the rear axle. Because vehicle rollover is affected by the suspension stiffness to load ratio, so the wheels at the rear axle often lift off first. This aims to satisfy the two following goals: the first goal is to design the the parameter dependent weighting function to allow performance adaptation to the rollover risk of vehicle, the second goal is to design the monitor to allow the active braking system to be only activated when the vehicle reaches the critical rollover situation. This approach can ensure the active braking system works closest to the real situation of vehicles. 4. THE BRAKING MONITOR DESIGN In the previous section, the proposed H∞ /LPV active braking system aims to prevent vehicle rollover; the varying parameter ρ2 is changed according the absolute value of the normalized load transfer at the rear axle (ρ2 = f (|Rr |)). According to Figure 2, in order to satisfy simultaneously the improved vehicle performance and prevention of vehicle rollover in an emergency situation (critical state), in this section we propose the two following LPV Braking Monitor Designs.

Fig. 3. The varying parameter ρ2 = f (|Rr |). 4.1 The first braking monitor design (1st LPV ): The value of the varying parameter ρ2 is always equal to the absolute value of the normalized load transfer at the rear axle ρ21 = |Rr |. It means that, the active braking system always operates even when the lateral acceleration is small. This is unrealistic, because when the active braking system is in use, it will reduce the various vehicle performance characteristics, which are highlighted by the increased energy consumption, the reduced longevity of the engine, the increased wear of the tyres and the brake actuators. The main purpose of this design is to evaluate the adaptability of the LPV active braking system when the varying parameter receives continuously the value from the roll stability criteria.

Fig. 2. The closed-loop interconnection structure.

4.2 The second braking monitor design (2nd LPV ):

According to the control objective, we propose a control scheme for the active braking system of heavy vehicles as shown in Figure 2. The H∞ /LPV control structure includes the nominal model G(ρ1 ), the controller K(ρ1 , ρ2 ), the performance output z, the control input u, the measured output y, the measurement noise n. The steering angle δ f is the disturbance signal, set by the driver. Wδ ,Wz (ρ2 ),Wn are the weighting functions for the steering angle, the performance output, the noises. The use of the two varying parameters (ρ1,2 ) has an important implication for adapting to vehicle’s situation. The role of ρ1 is to help the vehicle model and the controller change according to the forward velocity, which is of great significance at high motion speeds because the dynamic vehicle characteristics are far different when moving at low motion speeds. Meanwhile we select the value of the varying parameter ρ2 depending on the

The previous research results have demonstrated that most of heavy vehicles are equipped with the passive anti-roll bar system to maintain roll stability. This passive system does not consume energy and its structure is quite simple. However, the main problem we need to consider is that when the vehicle is in a critical state (approaching to the threshold of rollover), the passive anti-roll bar system does not provide enough of the necessary restoring torque. This requires the addition of the anti-roll torque of proactive systems in critical states, not in normal states. Moreover, vehicle rollover often occurs when the lateral acceleration reaches around 0.5g (Palkovics et al. (1999)). So to fit better with the real world application, the active braking system should be only activated when the vehicle reaches the critical rollover situation to reduce the lateral acceleration. The

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objective of this braking monitor is to allow the active braking system to react when the normalized load transfer at the rear axle reaches the criteria of rollover ±1. Therefore, in this design the varying parameter ρ2 is chosen as follows:  1 0 when |Rr | ≤ RCrit    1 |Rr | − RCrit 1 2 when RCrit < |Rr | < RCrit ρ22 = |Rr | 2 1  RCrit − RCrit   2 |Rr | when |Rr | ≥ RCrit (10) 2 1 The values of RCrit are chosen so that they respond to and RCrit the emergency situation, satisfying the time delay of the braking system and limiting the influence of the switch point. Here, the 1 2 authors propose RCrit = 0.8. = 0.75 and RCrit To better understand the value of the varying parameter ρ2 in the two cases (the 1st LPV and 2nd LPV braking monitor designs), let us look at the diagram in Figure 3. In the 1st LPV braking monitor design, the value of ρ2 is always equal to the absolute value of the normalized load transfer at the rear axle. Meanwhile the 2nd LPV braking monitor design, when the absolute value of the normalized load transfer at the rear axle is less than 0.75, the vehicle roll stability is determined by the passive anti-roll bar system, the active braking system is only activated when this value is greater than 0.75, meaning when the vehicle is close to the critical rollover situation. 5. THE H∞ /LPV CONTROL DESIGN 5.1 Performance specifications for the H∞ /LPV control design The purpose of choosing weighting functions and performance output in Figure 2 is to enhance vehicle roll stability and avoid actuator saturation, over the desired frequency range up to 4rad/s, which represents the limited bandwidth of the driver (Gaspar et al. (2004), Sampson and Cebon (2003)). These weighting functions can be considered as penalty functions, that is, weights which should be large in the frequency range where small signals are desired and small where larger performance outputs can be tolerated. According to the considered performance objectives, the weighting functions Wz (ρ2 ) = diag[WzFb,rr ,WzFb,rl ,Wzay (ρ2 )] are selected as follows:  1 1   , WzFb,rl = ,  WzFb,rr = ζFb,rr ζFb,rl (11) sχay + 2   (ρ ) = ρ W  zay 2 2 sϑay + τay Here, the parameters in equations (11) are chosen as: ζFb,rr = ζFb,rl = 8270; χay = 0.5; ϑay = 0.2; τay = 90. The varying parameter is defined as ρ2 = f (|Rr |). We stress that the interest of parameter dependant weighting functions Wzay (ρ2 ) is to allow performance adaptation to the rollover risk of heavy vehicles. For example, as far as the normalized load transfer at the rear axle is concerned, when the varying parameter ρ2 → 1, the gain of the weighting function Wzay is large, and therefore the lateral acceleration is penalized, this leads to vehicle roll stability improvement. The weighting function for the steering angle is selected as Wδ = π/180 in order to manage the maximum expected command. The weighting function for sensor noise models in the control design Wn is selected as a diagonal matrix of 0.01(m/s2 ) for the lateral acceleration ay and 0.01(0 /sec) for the derivative of the roll angle φ˙ (Gaspar et al., 2004). 5.2 The solution of the H∞ /LPV control problem According to Figure 2, the concatenation of the nonlinear model (8) with the performance weighting functions has a partitioned 105

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representation in the following form:      x(t) x(t) ˙ A(ρ) B1 (ρ) B2 (ρ) w(t) z(t) = C1 (ρ) D11 (ρ) D12 (ρ) u(t) y(t) C2 (ρ) D21 (ρ) D22 (ρ)

(12)

T where the performance output vector z(t) = [ ay Fb,rr Fb,rl ] , the exogenous input w(t) = [ δ f n ], the control input u(t) =  T [ Fb,rr Fb,rl ], the measured output vector y(t) = ay φ˙ . The LPV model of the active braking system (12) uses the varying parameters ρ = [ρ1 , ρ2 ], which are known in real time. The parameter ρ1 = v is measured directly, while the parameter ρ2 = f (|Rr |) can be estimated by the unsprung mass at the rear axle φur . The H∞ /LPV controller in Figure 2 is defined in the form (13). The control goal is to minimize the induced L2 norm of the closed-loop LPV system ∑CL = LFT (G, K), with zero initial conditions, which is shown in equation (14).      AK (ρ) BK (ρ) x˙K (t) xK (t) = (13) u(t) CK (ρ) DK (ρ) y(t)

where AK (ρ), BK (ρ), CK (ρ), DK (ρ) are continuous bounded matrix functions.  z 2 (14)  ∑CL (ρ) 2→2 = sup sup ρ∈P w∈L2  w 2 ¯ ρ≤ν ˙ ν≤ w2 =0

The existence of a controller that solves the parameter dependent LPV γ-performance problem can be expressed as the feasibility of a set of linear matrix inequalities (LMIs), which can be solved numerically. In this study, the authors use the grid-based LPV approach and the LPVToolsTM presented in (Hjartarson et al. (2015)) to synthesize the H∞ /LPV active braking control system. It requires a gridded parameter space for the two varying parameters ρ = [ρ1 , ρ2 ]. The H∞ controllers are synthesized for 12 grid points of the forward velocity in the range ρ1 = v = [20km/h, 130km/h] and 5 grid points of the normalized load transfer at the rear axle in a range ρ2 = f (|Rr |) = [0, 1]. 6. PERFORMANCE ASSESSMENT USING SIMULATION

In this section, the simulation results of a single unit heavy vehicle using the active braking system are shown in the time domain. The proposed 2nd LPV braking monitor design (dashdotted line) is compared with the passive anti-roll bar system (solid line) and the case of the 1st LPV braking monitor design (dashed line). The parameter values of the vehicle model are given in (Gaspar et al. (2004)). The double lane change manoeuver to avoid an obstacle is used in this scenario, with the steering angle as shown in Figure 4a. Figure 4 shows the time response of the vehicle. The initial forward velocity is 100 km/h as in Figure 4b. In the case of the passive anti-roll bar system, the forward velocity is kept constant at 100 km/h because there is no resistive force to reduce it. In the case of the 1st LPV braking monitor design, the forward velocity reduces continuously by 19 km/h from 0.5s to 6s. However, in the case of the 2nd LPV braking monitor design, the forward velocity only decreases when the normalized load transfer at the rear axle reaches its limitation with the reductions of 12 km/h. Figures 4e, f show the normalized load transfer at the two axles R f ,r . In the case of the 2nd LPV braking monitor design, the maximum absolute value of the normalized load transfer at the two axles is less than 1, this means that with this design the vehicle can avoid rollover. Additionally, in the case of the

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Fig. 4. Time response of the vehicle. passive anti-roll bar system, the normalized load transfers at the two axles exceed the limitation of ±1. So the use of the passive anti-roll bar in this scenario is not enough to prevent vehicle rollover. The simulation results indicate that, due to the braking monitor, the active braking system can be activated when the vehicle comes close to the rollover situation. In the normal situation, the vehicle can manoeuvre as in the case of using the passive anti-roll bar system. Therefore, the lateral acceleration ay in the case of the 2nd LPV braking monitor design is kept to less than the limitation of 0.5g (Palkovics et al. (1999)) as shown in Figure 4d. The maximum absolute value of the roll angle of sprung mass, lateral acceleration, suspension roll angles and normalized load transfers at both axles are listed in Table 1 for the two cases of the H∞ /LPV designs and the passive anti-roll bar system. From Figure 4 and Table 1, we can see that the 2nd LPV braking monitor design behaves better than the passive anti-roll bar system in term of avoiding vehicle rollover in a emergency situation. And it does not affect the various vehicle performance characteristics as in the case of the 1st LPV braking 106

monitor design. Table 1. Maximum absolute value of the signals. Signals |φ |max [deg] |ay |max [1/g] |R f |max |Rr |max |φ − φu f |max [deg] |φ − φur |max [deg]

Passive anti-roll bar 9.02 1.02 1.54 1.88 7.06 6.9

1st H∞ /LPV 1.88 0.21 0.57 0.20 1.07 1.68

2nd H∞ /LPV 4.23 0.50 0.99 0.79 2.75 3.62

Figures 5a, b show the time response of the wheel braking forces as the control input. It shows that, the time to maintain the braking force in the 1st LPV is very large (during the entire period of vehicle manoeuver - the lateral acceleration is different from zero). As mentioned above, this will affect the vehicle performance characteristics. Besides the roll stability criteria, it is necessary to evaluate the vehicle handling performance by using the phase plane β − β˙ (|β˙ + kβ β˙ β | < b) and the stability index λ (λ = |2.39β˙ + 9.55β |), where b = 24 and the slope of the reference region

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Fig. 5. Time responses of the (a,b) brake forces Fbrl,r , (c) phase - plane: β − β˙ and (d) stability index λ . boundaries kβ β˙ = 4 (Vu et al. (2017)). From Figure 5c, d, we can see that the handling performance is not satisfied for the passive anti-roll bar system. However, for the 2nd LPV braking monitor design, the trajectory of the phase plane β − β˙ is in the stability region boundaries and the stability index λ is still inside the limitation of 1. Therefore we can see that the vehicle handling performance is satisfied with the two proposed braking monitor designs. Therefore overall, the 2nd LPV can maintain the objective of preventing vehicle rollover situation and improving vehicle handling performance. 7. CONCLUSION In this paper, the active braking system is studied with the four longitudinal braking forces at each wheel by using the yawroll model of a single unit heavy vehicle. The grid-based LPV approach is combined with the LPVToolsTM toolbox to synthesize the H∞ /LPV parameter dependant weighting function controller. The braking monitor designs are proposed to allow the active braking system to react when the normalized load transfer at the rear axle reaches the criteria of rollover ±1. The simulation results indicate that the 2nd LPV braking monitor design satisfies simultaneously the adaptation of the vehicle to rollover in an emergency situation, with low braking forces and improved handling performance of the vehicle. Therefore, in order to avoid vehicle rollover, the braking monitor design is an effective solution in studying the active braking system. In the future, the characteristics of the brake actuators will be combined with the yaw-roll model. Studies on the nonlinear vehicle model and the comparison using nonlinear vehicle simulation packages (such as TruckSim) are also interesting topics. Acknowledgements: This work was supported by the project “Intelligent and autonomous vehicles for improving transport and road safety in Vietnam” from the French Embassy in Vietnam. REFERENCES Evgenikos, P., Yannis, G., Folla, K., Bauer, R., Machata, K., and Brandstaetter, C. (2016). Characteristics and causes of heavy goods vehicles and buses accidents in europe. Transportation Research Procedia, 14, 2158–2167. 107

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