Introduction to vehicle dynamics control
Olivier Sename et Soheib Fergani
Gipsa-lab Grenoble and LAAS-CNRS Toulouse, France
July 2-7, 2017
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 1 Outline
1. Introduction 2. Models 3. Intro to Towards global chassis control 4. Active safety using coordinated steering/braking control Active safety Objective Basics on vehicle dynamics Partial non linear Vehicle model Lateral stability control Simulations 5. Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive controller synthesis Implementation & test validation on the INOVE test bench 6. LPV FTC for Vehicle Dynamics Control Towards global chassis control The LPV FTC VDC... approach Simulations on a full NL vehicle model 7. Conclusions and future work
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 2 Introduction Outline
1. Introduction 2. Models 3. Intro to Towards global chassis control 4. Active safety using coordinated steering/braking control Active safety Objective Basics on vehicle dynamics Partial non linear Vehicle model Lateral stability control Simulations 5. Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive controller synthesis Implementation & test validation on the INOVE test bench 6. LPV FTC for Vehicle Dynamics Control Towards global chassis control The LPV FTC VDC... approach Simulations on a full NL vehicle model 7. Conclusions and future work
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 3 Introduction
Road safety: an international stake Worldwide, 1.24 million people of road traffic deaths per year (+ 50 million of injuries) a. For • people aged 5-29 years, road traffic injuries is the leading cause of death. Various causes: speed, alcohol, drugs, non safe driving,... • Recognized importance of smart and safe cars: passive safety (airbags, belt..) and active • (ABS, ESP....)
aWorld health organization 2013
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 4 Introduction
Road safety: an international stake Worldwide, 1.24 million people of road traffic deaths per year (+ 50 million of injuries) a. For • people aged 5-29 years, road traffic injuries is the leading cause of death. Various causes: speed, alcohol, drugs, non safe driving,... • Recognized importance of smart and safe cars: passive safety (airbags, belt..) and active • (ABS, ESP....)
aWorld health organization 2013
Among the 5 pillars towards road safety Safer vehicles: Electronic Stability Control is part of the minimum standards for vehicle construction (ex European and Latin New Car Assessment Programs - NCAP)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 4 Introduction Challenges in chassis control
Today’s vehicles. . . Growth of controlled organs: suspensions, ABS, ESC, ABC, braking distribution, active • Vehicle vertical steering, tire pressure, TCS Z motion Increasing number of sensors & actuators Yaw • Heavy networking • C
Roll Y X Pitch Vehicle lateral Vehicle longitudinal motion motion
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 5 Introduction Challenges in chassis control
Complexity to synchronize all the controllers to improve Driving comfort (and pleasure) • Active safety • Need for fault tolerance in case of actuator/sensor malfunctions
Ferrari VDC
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 6 Introduction Introduction
This course has been mainly written thanks to: the Post-doctoral work of [Moustapha Doumiati (2010)] • the PhD dissertations of [Damien Sammier (2002), Alessandro Zin (2005), • Poussot-Vassal(2008), Sébastien Aubouet (2010), Anh Lam DO (2011), Soheib Fergani (2014)]. the authors’ works since 1995 • interesting books cited below •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 7 Introduction Collaborations & associated studies
ANR INOVE 2010-2014
Modelling and control of a hydraulic semi-active damper- PhD thesis of Sébastien Aubouet 2010
Global chassis control using LPV/H∞ control - PhD the- sis Soheib Fergani 2014, Alessandro Zin 2005, Charles Poussot 2008
Magneto-rheological dampers - PhD thesis of Charles Poussot 2008, Sébastien Aubouet 2010
Modelling and control of semi-active suspensions - Post Doc Charles Poussot 09, PhD thesis of Ahn-Lam Do 2011
Skyhook and H∞ control of semi-active suspensions - PhD thesis of Damien Sammier 2002
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 8 Models Suspension system
Objective Link between unsprung and sprung masses •
Involves vertical( z ,z ) dynamics • s us
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 9 Models Suspension system
Objective Link between unsprung (m ) and sprung (m ) masses • us s
Involves vertical( z ,z ) dynamics • s us
Passive suspension system
ms,zs { }
mus,zus { }
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 9 Models Suspension system
Objective Link between unsprung (m ) and sprung (m ) masses • us s
Involves vertical( z ,z ) dynamics • s us
Semi-active suspension system dissipates energy through an adjustable damping coefficient −−−→
ms,zs { }
mus,zus { }
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 9 Models Suspension system
Objective Link between unsprung (m ) and sprung (m ) masses • us s
Involves vertical( z ,z ) dynamics • s us
Active suspension system dissipate and generate energy working as an active actuator −−−−−−−−→
ms,zs { }
mus,zus { }
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 9 Models Vehicle model - dynamical equations
Full vertical model
Mainly influenced by the vehicle suspension systems. • Describes the comfort and the roadholding performances. •
z¨s = Fsz f l + Fsz f r + Fszrl + Fszrr /ms − z¨usi j = Fszi j Ftzi j /musi j ¨ − θ = (Fszrl Fszrr )tr + (Fsz f l Fsz f r )t f /Ix − − φ¨ = (Fsz + Fsz )lr (Fsz + Fsz )l f /Iy rr rl − f r f l
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 10 Models Wheel & Braking system
Objective Link between wheel and road • Influences safety performances • Involves longitudinal (v) rotational (ω) and slipping (λ = v Rω ) dynamics • max−(v,Rω)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 11 Models Wheel & Braking system
Objective Link between wheel and road (z , µ) • r Influences safety performances • Involves longitudinal (v) rotational (ω) and slipping (λ = v Rω ) dynamics • max−(v,Rω)
Extended quarter vehicle model
Normalized longitudinal tire force
Dry 1 Cobblestone
0.8 n
/F 0.6 tx
F Wet
0.4
0.2 Icy
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 λ
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 11 Models Vehicle model - dynamical equations
Full vertical model
Mainly influenced by the vehicle suspension systems . • Describes the comfort and the roadholding performances . •
z¨s = Fsz f l + Fsz f r + Fszrl + Fszrr /ms − z¨usi j = Fszi j Ftzi j /musi j ¨ − θ = (Fszrl Fszrr )tr + (Fsz f l Fsz f r )t f /Ix − − φ¨ = (Fsz + Fsz )lr (Fsz + Fsz )l f /Iy rr rl − f r f l
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 12 Models Vehicle model - dynamical equations
Full vertical and longitudinal model
Mainly influenced by the vehicle suspension systems and the braking system. • Describes the comfort and the roadholding performances and the the stability and security • issues.
x¨s = (Ftx f r + Ftx f l ) + (Ftxrr + Ftxrl ) /m z¨s = Fsz f l + Fsz f r + Fszrl + Fszrr /ms − z¨usi j = Fszi j Ftzi j /musi j ¨ − θ = (Fszrl Fszrr )tr + (Fsz f l Fsz f r )t f /Ix − − φ¨ = (Fsz + Fsz )lr (Fsz + Fsz )l f +mhx¨s /Iy rr rl − f r f l vi j Ri jωi j λi j = − max(vi j,Ri jωi j) ω˙i j =( RFtx (µ,λ,Fn) + Tb )/Iw − i j i j
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 12 Models Wheel & Steering system
Objective Wheel / road contact • Influences safety performances • Involves lateral (y ), side slip angle (β) and yaw (ψ) dynamics • s
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 13 Models Wheel & Steering system
Objective Wheel / road contact • Influences safety performances • Involves lateral (y ), side slip angle (β) and yaw (ψ) dynamics • s
Bicycle model
ys −→v 6 Fty 1 f F K * tx f ] β - - xs ψ
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 13 Models Vehicle model - dynamical equations
Full vertical and longitudinal model
x¨s = (Ftx f r + Ftx f l ) + (Ftxrr + Ftxrl ) /m z¨s = Fsz f l + Fsz f r + Fszrl + Fszrr /ms − z¨usi j = Fszi j Ftzi j /musi j ¨ − θ = (Fszrl Fszrr )tr + (Fsz f l Fsz f r )t f /Ix − − φ¨ = (Fsz + Fsz )lr (Fsz + Fsz )l f + mhx¨s /Iy rr rl − f r f l
vi j Ri jωi j λi j = − max(vi j,Ri jωi j) ω˙i j = ( RFtx (µ,λ,Fn) + Tb )/Iw − i j i j
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 14 Models Vehicle model - dynamical equations
Full model A very complex model with dynamical correlations. •
Subject to several external disturbances. •
x¨s = (Ftx + Ftx )cos(δ)+( Ftx + Ftx ) (Fty + Fty )sin(δ) + mψ˙ y˙s /m f r f l rr rl − f r f l ˙ y¨s = (Fty f r + Fty f l )cos(δ) + (Ftyrr + Ftyrl ) + (Ftx f r + Ftx f l )sin(δ) mψx˙s /m − z¨s = Fsz f l + Fsz f r + Fszrl + Fszrr /ms − z¨usi j = Fszi j Ftzi j /musi j − θ¨ = (Fsz Fsz )tr + (Fsz Fsz )t f mhy¨s + (Iy Iz)ψ˙ φ˙ /Ix rl − rr f l − f r − − ¨ ˙ ˙ φ = (Fszrr + Fszrl )lr (Fsz f r + Fsz f l )l f + mhx¨s+(Iz Ix)ψθ /Iy − − ψ¨ = (Fty + Fty )l f cos(δ) (Fty + Fty )lr + (Ftx + Ftx )l f sin(δ) f r f l − rr rl f r f l +(Ftxrr Ftxrl )tr + (Ftx f r Ftx f l )t f cos(δ) (Ftx f r Ftx f l )t f sin(δ) − − − − +(Ix Iy)θ˙φ˙ /Iz vi j −Ri jωi jcosβi j λi j = − max(vi j,Ri jωi jcosβi j) ω˙i j = ( RFtx (µ,λ,Fn) + Tb )/Iw − i j i j x˙i j βi j = arctan y˙i j
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 14 Models Vehicle model - dynamical equations
Full model A very complex model with dynamical correlations. •
Subject to several external disturbances. •
x¨s = (Ftx + Ftx )cos(δ)+( Ftx + Ftx ) (Fty + Fty )sin(δ) + mψ˙ y˙s Fdx /m f r f l rr rl − f r f l − ˙ y¨s = (Fty f r + Fty f l )cos(δ) + (Ftyrr + Ftyrl ) + (Ftx f r + Ftx f l )sin(δ) mψx˙s Fdy /m − − z¨s = Fsz f l + Fsz f r + Fszrl + Fszrr +Fdz /ms − z¨usi j = Fszi j Ftzi j /musi j − θ¨ = (Fsz Fsz )tr + (Fsz Fsz )t f mhy¨s + (Iy Iz)ψ˙ φ˙+Mdx /Ix rl − rr f l − f r − − ¨ ˙ ˙ φ = (Fszrr + Fszrl )lr (Fsz f r + Fsz f l )l f + mhx¨s+(Iz Ix)ψθ+Mdy /Iy − − ψ¨ = (Fty + Fty )l f cos(δ) (Fty + Fty )lr + (Ftx + Ftx )l f sin(δ) f r f l − rr rl f r f l +(Ftxrr Ftxrl )tr + (Ftx f r Ftx f l )t f cos(δ) (Ftx f r Ftx f l )t f sin(δ) − − − − +(Ix Iy)θ˙φ˙+Mdz /Iz vi j −Ri jωi jcosβi j λi j = − max(vi j,Ri jωi jcosβi j) ω˙i j = ( RFtx (µ,λ,Fn) + Tb )/Iw − i j i j x˙i j βi j = arctan y˙i j
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 14 Models Vehicle model - synopsis
q ? ? Fsz xs z˙s,zs - i j - - Suspensions ys z˙us,zus zs - Chassis (vehicle dynamics) ? Ftx,y,z x¨s,y¨s - θ - - ψ˙ ,v, Wheels - λi j φ Fsz,zus βi j ψ 6 6 ωi j (tire, wheel dynamics)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 15 Models Vehicle model - synopsis
Fdx,y,z & Mdx,y,z (external disturbances)
q ? ? Fsz xs z˙s,zs - i j - - Suspensions ys z˙us,zus zs - Chassis (vehicle dynamics) ? Ftx,y,z x¨s,y¨s - θ - - ψ˙ ,v, Wheels - λi j φ Fsz,zus βi j ψ 6 6 ωi j (tire, wheel dynamics) (road characteristics) [µi j,zri j ]
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 15 Models Vehicle model - synopsis
Fdx,y,z & Mdx,y,z (external disturbances)
(suspensions control) ui j q ? ? Fsz xs z˙s,zs - i j - - Suspensions ys z˙us,zus zs δ -
(braking & steering control) [Tbi j ,δ] Chassis (vehicle dynamics) ? Ftx,y,z x¨s,y¨s - θ - - ψ˙ ,v, Wheels - λi j φ Fsz,zus βi j ψ 6 6 ωi j (tire, wheel dynamics) (road characteristics) [µi j,zri j ]
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 15 Intro to Towards global chassis control Towards global chassis control approaches (GCC)
Some facts In most vehicle control design approaches, the vehicle-dynamics control sub-systems • (suspension control, steering control, stability control, traction control and, more recently, kinetic-energy management) are traditionally designed and implemented as independent (or weakly interleaved) systems. The global communication and collaboration between these systems are done with empirical • rules and may lead to unappropriate or conflicting control objectives. So, it is important to develop new methodologies (centralized control strategies) that force the • sub-systems to cooperate in some appropriate "optimal" way.
Global chassis control This approach combines several (at least 2) vehicle sub-systems in order to improve the • general behavior of the vehicle ; in particular, the GCC methodology is developed to improve comfort and safety properties, according to the vehicle situation, taking into account the actuators constraints and the knowledge (if any) of the environment of the vehicle. The objective is then to make the sub-systems collaborate towards the same goals, according • to the vehicle situation (constraints, environment, ...) in order to fully exploit the potential benefits coming from their interconnection.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 16 Intro to Towards global chassis control Towards global chassis control approaches (GCC)
The GCC strategies are de- veloped in 2 steps:
Renault Mégane Coupé
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 17 Intro to Towards global chassis control Towards global chassis control approaches (GCC)
The GCC strategies are de- veloped in 2 steps: The monitoring • approach → collaborative based Renault strategy. Mégane Coupé
Coordination strategy Monitoring system
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 17 Intro to Towards global chassis control Towards global chassis control approaches (GCC)
The GCC strategies are de- veloped in 2 steps: The monitoring Steering controller • approach → collaborative based Renault strategy. Mégane Coupé Braking controller
Developping • coordinated control strategies achieve Suspension controller close loop→ performance and actuators coordination.
Main objective: Improve the overall dynamics of the car • Coordination strategy and the vehicle safety in critical driving Monitoring system situations.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 17 Intro to Towards global chassis control Towards Global chassis control approaches
Two main approaches, one considering the vehicle as a MIMO system, the other developing a "super controller" for the local actuators. Some references : Lu and DePoyster (2002), Shibahata (2005), Chou and d’Andréa Novel (2005), Andreasson and Bunte (2006), Falcone et al. (2007a), Falcone et al. (2007b), Gáspár et al. (2008), Fergani and Sename (2016)...
Vehicle considered as a MIMO system This approach consists in considering the vehicle as a global MIMO system and in designing • a controller that solves all the dynamical problems by directly controlling the various actuators with the available measurements. No local controller is considered (no inner loop). See, for instance Lu and DePoyster (2002), Chou and d’Andréa Novel (2005), Andreasson and Bunte (2006), Gáspár et al. (2008), Fergani et al (2016).
High level reference super controller The second approach consists in designing a controller which aims at providing somehow, • the reference signals to local controllers, which have been previously designed to solve a local subsystem problem (e.g. ABS). Thus, this controller, more than a controller, "monitors" the local controllers. Therefore, such a controller solves the global vehicle dynamical problems, playing the role of "super controller". See also Falcone et al. (2007a).
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 18 Intro to Towards global chassis control A MIMO case: Suspension and braking
Characteristic of the solution Build a multivariable global chassis controller Shibahata (2004), (Poussot et al. 2011): Improve comfort in normal cruise situations • Improve safety in emergency situations (safety prevent comfort) • Supervise actuators and resources • The proposed design relies in the introduction of two parameters to handle the performance • compromise, actuator efficiency and well-coordinated action. The suspension performance moves from comfort to road holding characteristics when the • braking monitor identifies a normal or critical longitudinal slip ratio. Robust control theory approach (LPV/H ) • ∞ MIMO internal stability& no switching ⇒
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 19 Intro to Towards global chassis control Towards Global chassis control approaches
Some examples braking/suspension : non linear approach (Chou & d’Andréa Novel), LPV for heavy vehicles • (Gaspar, Szabo & Bokor), for cars (Poussot et al.) braking / steering : optimal control [Yang et al.], predictive [Di Cairano & Tseng, control • allocation [Tjonnas & Johansen], or LPV [Doumiati et al, 2013] braking /suspension/ steering: [Fergani, Sename, Dugard] •
LPV interest: on-line Adaption of the vehicle performances to various road conditions/types (measured, estimated) • to the driver actions • to the dangers identified thanks to some measurements of • the vehicle dynamical behavior to actuators/sensors malfunctions or failures •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 20 Intro to Towards global chassis control Towards Global chassis control approaches
In this presentation, 3 examples are provided for the topic:
F Active safety using coordinated steering/braking control.
F Road profile estimation and road adaptive vehicle dynamics control.
F LPV FTC for Vehicle Dynamics Control.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 21 Active safety using coordinated steering/braking control Outline
1. Introduction 2. Models 3. Intro to Towards global chassis control 4. Active safety using coordinated steering/braking control Active safety Objective Basics on vehicle dynamics Partial non linear Vehicle model Lateral stability control Simulations 5. Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive controller synthesis Implementation & test validation on the INOVE test bench 6. LPV FTC for Vehicle Dynamics Control Towards global chassis control The LPV FTC VDC... approach Simulations on a full NL vehicle model 7. Conclusions and future work
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 22 Active safety using coordinated steering/braking control Active safety
Vehicle safety systems: Prevent unintended behavior • Help drivers maintaining the vehicle control • Current production systems include: • • Anti-lock Braking Systems (ABS): Prevent wheel lock during braking • Electronic Stability Control (ESC): Enhances lateral vehicle stability • Braking based technique • 4 Wheel steering (4WS): Enhances steerability • Adding additional steering angle General structure:
Vehicle Active safety systems: Act on Actuators measures Sensors (suspensions, brakes, steer) Alert the driver
Any vehicle control system needs accurate information about the vehicle dynamics, and the more accurate information it gets, the more it can perform
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 23 Active safety using coordinated steering/braking control Active safety
Vehicle safety systems: Prevent unintended behavior • Help drivers maintaining the vehicle control • Current production systems include: • • Anti-lock Braking Systems (ABS): Prevent wheel lock during braking • Electronic Stability Control (ESC): Enhances lateral vehicle stability • Braking based technique • 4 Wheel steering (4WS): Enhances steerability • Adding additional steering angle General structure:
Vehicle Active safety systems: Act on Actuators measures Sensors (suspensions, brakes, steer) Alert the driver
Any vehicle control system needs accurate information about the vehicle dynamics, and the more accurate information it gets, the more it can perform
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 23 Active safety using coordinated steering/braking control Active safety
Vehicle safety systems: Prevent unintended behavior • Help drivers maintaining the vehicle control • Current production systems include: • • Anti-lock Braking Systems (ABS): Prevent wheel lock during braking • Electronic Stability Control (ESC): Enhances lateral vehicle stability • Braking based technique • 4 Wheel steering (4WS): Enhances steerability • Adding additional steering angle General structure:
Vehicle Active safety systems: Act on Actuators measures Sensors (suspensions, brakes, steer) Alert the driver
Any vehicle control system needs accurate information about the vehicle dynamics, and the more accurate information it gets, the more it can perform
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 23 Active safety using coordinated steering/braking control Objective
The presentation of today focuses on:
Yaw stability by active control • • Prevents vehicle from skidding and spinning out • Improves of the turning (yaw) rate response Undesired • Improves lateral vehicle dynamics motion • Involves Braking and Steering actuators
Desired trajectory
Figure: The objective is to restore the yaw rate as much as possible to the nominal motion expected by the driver
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 24 Active safety using coordinated steering/braking control Objective Problematic
Problem tackled: vehicle critical situations Lateral and yaw stability of ground vehicles & braking actuator limitations • Widely treated in literature [Ackermann, Falcone, Villagra, Bunte, Chou, Canale] (mainly • steering or braking, but a few use both)
Contributions Use Rear braking & Steering actuators to enhance vehicle stability properties • Extension of [Poussot-Vassal et al., CDC2008 & ECC2009] results • Propose a simple H tuning using [Bünte et al., IEEE TCST, 2004] results • ∞ LPV Controller structure exploiting system properties to handle braking constraints • Nonlinear frequency validations •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 25 Active safety using coordinated steering/braking control Objective Problematic
Problem tackled: vehicle critical situations Lateral and yaw stability of ground vehicles & braking actuator limitations • Widely treated in literature [Ackermann, Falcone, Villagra, Bunte, Chou, Canale] (mainly • steering or braking, but a few use both)
Contributions Use Rear braking & Steering actuators to enhance vehicle stability properties • Extension of [Poussot-Vassal et al., CDC2008 & ECC2009] results • Propose a simple H tuning using [Bünte et al., IEEE TCST, 2004] results • ∞ LPV Controller structure exploiting system properties to handle braking constraints • Nonlinear frequency validations •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 25 Active safety using coordinated steering/braking control Basics on vehicle dynamics Lateral motion of a vehicle
Motion of a vehicle is governed by • Side view tire forces Tire forces result from deformation • in contact patch Contact patch Lateral tire force, F , is function of: • y 1 Tire slip (α) Ground 2 Vertical load applied on the tire (Fz) 3 Friction coefficient (µ) Bottom view α
α (tire sideslip angle) V (tire velocity) Fy
Fy (lateral tire force)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 26 Active safety using coordinated steering/braking control Basics on vehicle dynamics
Maximum tire grip 6000 4 µFz 5000 3.5 3 4000
Linear Saturation Loss of control 2.5
3000 2
1.5 Lateral force (N) 2000 C α Lateral force (kN) 1 Measure 1 Linear model 1000 0.5 Pacejka model Dugoff model 0 0 5 10 15 20 0 5 10 15 20 Sideslip angle (°) Sideslip angle (°)
Vehicle response Normally, we operate in LINEAR region • • Predictable vehicle response During slick road conditions, emergency maneuvers, or aggressive driving • • Enter NONLINEAR tire region • Response unanticipated by driver
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 27 Active safety using coordinated steering/braking control Basics on vehicle dynamics
Maximum tire grip 6000 4 µFz 5000 3.5 3 4000
Linear Saturation Loss of control 2.5
3000 2
1.5 Lateral force (N) 2000 C α Lateral force (kN) 1 Measure 1 Linear model 1000 0.5 Pacejka model Dugoff model 0 0 5 10 15 20 0 5 10 15 20 Sideslip angle (°) Sideslip angle (°)
Vehicle response Normally, we operate in LINEAR region • • Predictable vehicle response During slick road conditions, emergency maneuvers, or aggressive driving • • Enter NONLINEAR tire region • Response unanticipated by driver
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 27 Active safety using coordinated steering/braking control Basics on vehicle dynamics Why we lose the vehicle control?
Imagine making an aggressive turn. . . If front tires lose grip first, plow out of turn • (limit understeer) • May go into oscillatory response • Driver loses ability to influence vehicle motion If rear tires saturate, rear end kicks out • (limit oversteer) Desired trajectory • May go into a unstable spin • Driver loses control Both can result in loss of control •
Desired trajectory
Unstable motion due to nonlinear tire characteristics
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 28 Active safety using coordinated steering/braking control Partial non linear Vehicle model Planar bicycle model (Dugoff et al.(1970))
Main dynamics under interest, toward control scheme . . . Equation of lateral motion: • ˙ mv β ψ˙ = Fy f + Fyr (1) − Equation of yaw motion: • Izψ¨ = l f Fy f lrFyr, (2) −
lf Fyf δ lr
Fyr . Ψ V vy
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 29 Active safety using coordinated steering/braking control Partial non linear Vehicle model Linear Synthesis model
The 2-DOF linear bicycle model described in Section 2 is used for the control synthesis. Although the bicycle model is relatively simple, it captures the important features of the lateral vehicle dynamics. Taking into account the controller structure and objectives, this model is extended to include: the direct yaw moment input M , • z∗ a lateral disturbance force F and a disturbance moment M . F affects directly the sideslip • dy dz dy motion, while Mdz influences directly the yaw motion.
2 2 l f Cf +lr Cr lrCr l f Cf " l f Cf # 1 1 ψ¨ − ψ˙ Mdz Izv Iz Iz Iz Iz = − + C δ ∗ + Mz∗ + 1 (3) β˙ lrCr l f Cf Cf +Cr β f F 1 + − 0 mv dy mv2 − mv mv
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 30 Active safety using coordinated steering/braking control Lateral stability control Steering vs. Braking
Steering control:(Rajamani(2006), Guven et al.(2007)) Adds steering angle to improve the lateral vehicle dynamics • Regulates tire slip angles and thus, the lateral tire force • Drawback: • • Becomes less effective near saturation DYC (Direct Yaw Control) - Braking control:(Park(2001), Boada et al.(2005)) Regulates the tire longitudinal forces • Maintains the vehicle stability in all driving situations • Drawbacks: • • Wears out the tires • Causes the vehicle speed to slow down against the driver demand
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 31 Active safety using coordinated steering/braking control Lateral stability control
The idea is to design a controller that: Improves vehicle steerability and stability • • Makes the yaw rate tacking the desired value (response of a bicycle model with linear tires) • Makes the slip angle small Coordinates Steering/braking control • • Minimizes the influence of brake intervention on the longitudinal vehicle dynamics Rejects yaw moment disturbances •
Methodology: H∞ synthesis extended to LPV system: H synthesis: frequency based performance criteria • ∞ LPV: One type of a gain scheduled controller • See paper Doumiati et al (2013)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 32 Active safety using coordinated steering/braking control Lateral stability control
The idea is to design a controller that: Improves vehicle steerability and stability • • Makes the yaw rate tacking the desired value (response of a bicycle model with linear tires) • Makes the slip angle small Coordinates Steering/braking control • • Minimizes the influence of brake intervention on the longitudinal vehicle dynamics Rejects yaw moment disturbances •
Methodology: H∞ synthesis extended to LPV system: H synthesis: frequency based performance criteria • ∞ LPV: One type of a gain scheduled controller • See paper Doumiati et al (2013)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 32 Active safety using coordinated steering/braking control Lateral stability control Overall control scheme diagram
Vehicle velocity Steering angle (δd) Driver command
Sideslip Reference model dynamics (bicycle model) + Bounding limits
Tbr* Yaw rate target EMB + _ VDSC controller Vehicle simulation δ* model AS + + Monitor δd
External yaw Yaw rate (measure) disturbances
AS: Steer-by-wire system EMB: Brake-by-wire Electro Mechanical system
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 33 Active safety using coordinated steering/braking control Lateral stability control Overall control scheme diagram
Vehicle velocity Steering angle (δd) Driver command
Sideslip Reference model dynamics (bicycle model) + Bounding limits
Tbr* Yaw rate target EMB + _ VDSC controller Vehicle simulation δ* model AS + + MonitorMMiit δd
External yaw Yaw rate (measure) disturbances
AS: Steer-by-wire system EMB: Brake-by-wire Electro Mechanical system
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 34 Active safety using coordinated steering/braking control Lateral stability control Reference model
The basic idea is to assist the vehicle handling to be close to a linear vehicle handling characteristic that is familiar to the driver Bicycle linear model, F = C α (low sideslip angle) • y α ψ˙ µ g/Vx • ≤ × • Ensures small slip dynamics (β,β˙) • Attenuates the lateral acceleration
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 35 Active safety using coordinated steering/braking control Lateral stability control Reference model
The basic idea is to assist the vehicle handling to be close to a linear vehicle handling characteristic that is familiar to the driver Bicycle linear model, F = C α (low sideslip angle) • y α ψ˙ µ g/Vx • ≤ × • Ensures small slip dynamics (β,β˙) • Attenuates the lateral acceleration
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 35 Active safety using coordinated steering/braking control Lateral stability control Overall control scheme diagram
Vehicle velocity Steering angle (δd) Driver command
Sideslip Reference model dynamics (bicycle model) + Bounding limits
Tbr* Yaw rate target EMB + _ VDSC controller Vehicle simulation δ* model AS + + MonitorMMiit δd
External yaw Yaw rate (measure) disturbances
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 36 Active safety using coordinated steering/braking control Lateral stability control VDSC Controller architecture
Objective: Lateral stability Yaw rate control Steering angle SideSlip angle
Measurements/estimation Upper controller Level 1
and/or Commanded Desired yaw steering angle moment
Lower controller Level 2
Applying brake torque to the appropriate wheel
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 37 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control
∑ Vehicle model is LTI: Linear bicycle model • Synthesized considering a dry road z2 • W2
z3 ρ scheduling parameter: W3 (ρ) ρ(t) is time dependent and known • z4 W4 function h i ρ bounded: ρ ρ,ρ • . ∈ Ψd + S(ρ) * z1 M z Vehicle model W1 _ e . β Ψ LPV/H∞ δ*
. Ψ Fdy Generalized plant (tracking problem)
h i w(t) = ψ˙d ,Fdy exogenous input u(t) = δ ,Mz control input h ∗ i ∗ y(t) = eψ˙ measurement z(t) = W1z1,W2z2,W3z3,W4z4 controlled output
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 38 Active safety using coordinated steering/braking control Lateral stability control VDSC design (cont’d)
z : sideslip angle signal, β: W = 2. to reduce the body sideslip angle • 1 1 s/M+w0 z2 yaw rate error signal: W2 = , where M = 2 for a good robustness margin, A = 0.1 so • s+w0A that the tracking error is less than 10%, and the required bandwidth w0 = 70 rad/s. z braking control signal, M ,according to a scheduling parameter ρ: • 3 z∗
s/(2π f2) + 1 W3 = ρ , (4) s/(α2π f2) + 1
where f2 = 10 Hz is the braking actuator cut-off frequency and α = 100. n o ρ ρ ρ ρ (with ρ = 10 4 and ρ = 10 2). ∈ ≤ ≤ − − z , the steering control signal attenuation ( f = 1Hz, f = 10Hz): • 4 3 4 (s/2π f + 1)(s/2π f + 1) W = G 0 3 4 δ δ (s/α2π f + 1)2 4 (5) (∆ f /α2π f4 + 1)2 Gδ 0 = and ∆ f = 2π( f4 + f3)/2 (∆ f /2π f3 + 1)(∆ f /2π f4 + 1)
This filter is designed is order to allow the steering system to act only in [ f3, f4]Hz. At ∆ f /2, the filter gain is unitary [Bunte et al. 2004, TCST].
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 39 Active safety using coordinated steering/braking control Lateral stability control VDSC design (cont’d)
z : sideslip angle signal, β: W = 2. to reduce the body sideslip angle • 1 1 s/M+w0 z2 yaw rate error signal: W2 = , where M = 2 for a good robustness margin, A = 0.1 so • s+w0A that the tracking error is less than 10%, and the required bandwidth w0 = 70 rad/s. z braking control signal, M ,according to a scheduling parameter ρ: • 3 z∗
s/(2π f2) + 1 W3 = ρ , (4) s/(α2π f2) + 1
where f2 = 10 Hz is the braking actuator cut-off frequency and α = 100. n o ρ ρ ρ ρ (with ρ = 10 4 and ρ = 10 2). ∈ ≤ ≤ − − z , the steering control signal attenuation ( f = 1Hz, f = 10Hz): • 4 3 4 (s/2π f + 1)(s/2π f + 1) W = G 0 3 4 δ δ (s/α2π f + 1)2 4 (5) (∆ f /α2π f4 + 1)2 Gδ 0 = and ∆ f = 2π( f4 + f3)/2 (∆ f /2π f3 + 1)(∆ f /2π f4 + 1)
This filter is designed is order to allow the steering system to act only in [ f3, f4]Hz. At ∆ f /2, the filter gain is unitary [Bunte et al. 2004, TCST].
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 39 Active safety using coordinated steering/braking control Lateral stability control VDSC design (cont’d)
z : sideslip angle signal, β: W = 2. to reduce the body sideslip angle • 1 1 s/M+w0 z2 yaw rate error signal: W2 = , where M = 2 for a good robustness margin, A = 0.1 so • s+w0A that the tracking error is less than 10%, and the required bandwidth w0 = 70 rad/s. z braking control signal, M ,according to a scheduling parameter ρ: • 3 z∗
s/(2π f2) + 1 W3 = ρ , (4) s/(α2π f2) + 1
where f2 = 10 Hz is the braking actuator cut-off frequency and α = 100. n o ρ ρ ρ ρ (with ρ = 10 4 and ρ = 10 2). ∈ ≤ ≤ − − z , the steering control signal attenuation ( f = 1Hz, f = 10Hz): • 4 3 4 (s/2π f + 1)(s/2π f + 1) W = G 0 3 4 δ δ (s/α2π f + 1)2 4 (5) (∆ f /α2π f4 + 1)2 Gδ 0 = and ∆ f = 2π( f4 + f3)/2 (∆ f /2π f3 + 1)(∆ f /2π f4 + 1)
This filter is designed is order to allow the steering system to act only in [ f3, f4]Hz. At ∆ f /2, the filter gain is unitary [Bunte et al. 2004, TCST].
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 39 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control
Controller solution: LPV/H∞ Mixed-Sensitivity problem Steering control • 10 ρ = ρ Minimizes the H∞ norm from w to z ρ = ρ • 5 γ∞ = 0.89 (Yalmip/Sedumi solver) • 0
Magnitude (dB) −5 10− 1 100 101 102 W3(ρ): Frequency (rad/sec) Brake control ρ = 0.1 braking is ON 100 • → ρ = 10 braking is OFF 50 • → 0
Magnitude (dB) −50 10−1 100 101 102 Frequency (rad/sec)
Figure: Bode diagrams of the controller outputs δ ∗ and Mz∗
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 40 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control
Controller solution: LPV/H∞ Mixed-Sensitivity problem Steering control • 10 ρ = ρ Minimizes the H∞ norm from w to z ρ = ρ • 5 γ∞ = 0.89 (Yalmip/Sedumi solver) • 0
Magnitude (dB) −5 10− 1 100 101 102 W3(ρ): Frequency (rad/sec) Brake control ρ = 0.1 braking is ON 100 • → ρ = 10 braking is OFF 50 • → 0
Magnitude (dB) −50 10−1 100 101 102 Frequency (rad/sec)
Figure: Bode diagrams of the controller outputs δ ∗ and Mz∗
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 40 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control
Sensitivity functions:
. β/ Ψ d β/F dy β/M dz 0 0 0
1/W1 −20 1/W1 1/W1 −20 −40 −50
−40 −60 −100 LPV −80 −60 −100 −150 Magnitude (dB) −80 Magnitude (dB) −120 Magnitude (dB) LPV
−140 LPV −200 −100 −160
−120 −180 −250 10−2 100 102 10− 2 100 102 10− 2 100 102 Frequency (Hz) Frequency (Hz) Frequency (Hz)
Figure: Closed loop transfer functions between β and exogenous inputs
Attenuation of the side slip angle • Rejection of the yaw disturbance •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 41 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control
Sensitivity functions:
. e . / F . e . / ψ ψ dy e / M ψ d ψ dz 10 50 20 1/W2 1/W2 0 5 1/W2 0 −20 0 −50 −40 −5 −100 −60 −10 −80 Magnitude (dB) Magnitude (dB) −150 Magnitude (dB) −15 LPV LPV −100 −200 −20 −120 LPV
−25 −250 −140 10−2 100 102 10− 2 100 102 10− 2 100 102 Frequency (Hz) Frequency (Hz) Frequency (Hz)
Figure: Closed loop transfer functions between eψ˙ and exogenous inputs
Attenuation of the yaw rate error • Rejection of the yaw disturbance •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 42 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control design
Sensitivity functions:
.
M* Fdy M* Ψ z / M*z / Mdz z / d 100 100 100 1/W3 (ρ) 1/W3 (ρ) 80 1/W3 (ρ) 50 50 60 0 1/W3 (ρ) 1/W3 (ρ) 40 1/W3 (ρ) 0 −50 20 ρ = ρ ρ = ρ −100 −50 0 ρ = ρ −150 Magnitude (dB) −20 Magnitude (dB) Magnitude (dB) −100 −200 −40 ρ = ρ ρ = ρ ρ = ρ −150 −60 −250
−80 −300 −200 10−2 100 102 10− 2 100 102 10− 2 100 102 Frequency (Hz) Frequency (Hz) Frequency (Hz)
Figure: Closed loop transfer functions between M∗ and exogenous inputs
ρ = 0.1 braking is activated, ρ = 10 braking is penalized → →
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 43 Active safety using coordinated steering/braking control Lateral stability control
VDSC-upper controller: LPV/H∞ control design
Sensitivity functions:
. * * * δ / Ψ d δ /F dy δ /Mdz 50 50 50
40 1/W4 0 1/W4 30 0 1/W4 20 −50 −50 10 −100 0 −100
ρ = ρ Magnitude (dB)
Magnitude (dB) −10 −150 Magnitude (dB) LPV LPV −20 −150 −200 −30 ρ = ρ
−40 −250 −200 10−2 100 102 10− 2 100 102 10− 2 100 102 Frequency (Hz) Frequency (Hz) Frequency (Hz)
Figure: Closed loop transfer functions between δ ∗ and exogenous inputs
Steering is activated on a specified range of frequency • W : Activates steering in a frequency domain where the driver cannot act (Guven et al.(2007)) • 4
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 44 Active safety using coordinated steering/braking control Lateral stability control Overall control scheme diagram
Vehicle velocity Steering angle (δd) Driver command
Sideslip Reference model dynamics (bicycle model) + Bounding limits Friction estimator
Tbr* Yaw rate target EMB + _ VDSC controller Vehicle simulation δ* model AS + + Monitor δd
External yaw Yaw rate (measure) disturbances
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 45 Active safety using coordinated steering/braking control Lateral stability control Coordination between Steering and braking
β β˙ phase plane is used as measure of the vehicle operating points • − Stability boundaries for controller design: χ = 1 β˙ + 4 β < 1 • 24 24 (Yang et al.(2009), He et al.(2006))
100 Stable region 80 60 AS control Control boundaries 40 DYC+AS 20 control Unstable region 0 −20 −40 DYC+AS −60 control Sideslip angular velocity (°/s) −80 Unstable region −100 −40 −30 −20 −10 0 10 20 30 40 Sideslip angle (°) This criterion, χ, allows accurate diagnosis of the vehicle stability.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 46 Active safety using coordinated steering/braking control Lateral stability control Coordination between Steering and braking
β β˙ phase plane is used as measure of the vehicle operating points • − Stability boundaries for controller design: χ = 1 β˙ + 4 β < 1 • 24 24 (Yang et al.(2009), He et al.(2006))
100 Stable region 80 60 AS control Control boundaries 40 DYC+AS 20 control Unstable region 0 −20 −40 DYC+AS −60 control Sideslip angular velocity (°/s) −80 Unstable region −100 −40 −30 −20 −10 0 10 20 30 40 Sideslip angle (°) This criterion, χ, allows accurate diagnosis of the vehicle stability.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 46 Active safety using coordinated steering/braking control Lateral stability control Monitor
_ Steering Steering + ρ full Braking
ρ_ _ Scheduling parameter λ _λ λ (Stability index)
Intermediate behavior
ρ if χ χ (steering control - Steerability control task) χ χ χ χ ≤ ρ(χ) := − ρ + − ρ if χ < χ < χ (steering+braking) (6) χ χ χ χ − − ρ if χ χ (steering+full braking - Stability control task) ≥ where χ = 0.8 and χ = 1 (χ is user defined)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 47 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
Available measurements (from ESC or reasonable cost sensors): Yaw rate, ψ˙ • Steering wheel angle, δ • Wheel speeds, w • i j Lateral acceleration, a • y β˙ can be evaluated through available sensors: • ay β˙ = ψ˙ , (7) vx − β?? Existing Methods: → Integration of β˙ • Kinematic equations (eq. a ,a ) • y x Model-based observer (Vehicle model + Estimation technique) •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 48 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
Available measurements (from ESC or reasonable cost sensors): Yaw rate, ψ˙ • Steering wheel angle, δ • Wheel speeds, w • i j Lateral acceleration, a • y β˙ can be evaluated through available sensors: • ay β˙ = ψ˙ , (7) vx − β?? Existing Methods: → Integration of β˙ • Kinematic equations (eq. a ,a ) • y x Model-based observer (Vehicle model + Estimation technique) •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 48 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
Available measurements (from ESC or reasonable cost sensors): Yaw rate, ψ˙ • Steering wheel angle, δ • Wheel speeds, w • i j Lateral acceleration, a • y β˙ can be evaluated through available sensors: • ay β˙ = ψ˙ , (7) vx − β?? Existing Methods: → Integration of β˙ • Kinematic equations (eq. a ,a ) • y x Model-based observer (Vehicle model + Estimation technique) •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 48 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
Available measurements (from ESC or reasonable cost sensors): Yaw rate, ψ˙ • Steering wheel angle, δ • Wheel speeds, w • i j Lateral acceleration, a • y β˙ can be evaluated through available sensors: • ay β˙ = ψ˙ , (7) vx − β?? Existing Methods: → Integration of β˙ • Kinematic equations (eq. a ,a ) • y x Model-based observer (Vehicle model + Estimation technique) •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 48 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
Available measurements (from ESC or reasonable cost sensors): Yaw rate, ψ˙ • Steering wheel angle, δ • Wheel speeds, w • i j Lateral acceleration, a • y β˙ can be evaluated through available sensors: • ay β˙ = ψ˙ , (7) vx − β?? Existing Methods: → Integration of β˙ • Kinematic equations (eq. a ,a ) • y x Model-based observer (Vehicle model + Estimation technique) •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 48 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
This study: Planar bicycle model (with constant velocity): • ˙ β = (Fy f + Fyr)/(mv) + ψ˙ (8) ψ¨ = l f Fy f lrFyr + M∗ /Iz − z Dugoff’s tire model: • Fy = C tan(α) f (α,Fz,C ), where f(.) is nonlinear (9) − α × × α Nonlinear filtering: Extended Kalman Filter • * State-space representation: M z . ψ T δ*+δd Vehicle X = [β, ψ˙ ] system • Fz T U = M , δ, F . • z∗ z • δ = δ ∗ + δd . Bicycle nonlinear Y = [ψ˙ ]T β • model EKF
Observer
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 49 Active safety using coordinated steering/braking control Lateral stability control Sideslip angle estimation
This study: Planar bicycle model (with constant velocity): • ˙ β = (Fy f + Fyr)/(mv) + ψ˙ (8) ψ¨ = l f Fy f lrFyr + M∗ /Iz − z Dugoff’s tire model: • Fy = C tan(α) f (α,Fz,C ), where f(.) is nonlinear (9) − α × × α Nonlinear filtering: Extended Kalman Filter • * State-space representation: M z . ψ T δ*+δd Vehicle X = [β, ψ˙ ] system • Fz T U = M , δ, F . • z∗ z • δ = δ ∗ + δd . Bicycle nonlinear Y = [ψ˙ ]T β • model EKF
Observer
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 49 Active safety using coordinated steering/braking control Lateral stability control VDSC Controller architecture
Yaw rate Objective: Yaw stability Steering angle control Sideslip angle
Measurements/estimation Upper controller Level 1
and/or Commanded Desired yaw steering angle moment
Lower controller Level 2
Applying brake torque to the appropriate wheel
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 50 Active safety using coordinated steering/braking control Lateral stability control VDSC-lower controller algorithm
The stabilizing moment Mz∗ provided by the controller is converted into braking torque and applied to the appropriate wheels
Rules Braking 1 wheel: from an optimal point of view, it is recommended to use only one wheel to • generate the control moment (Park(2001)) Only rear wheels are involved to avoid overlapping with the steering control • Decision rule:
Driving situations
Oversteer Understeer
Brake outer rear wheel Brake inner rear wheel
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 51 Active safety using coordinated steering/braking control Lateral stability control VDSC-lower controller algorithm
The stabilizing moment Mz∗ provided by the controller is converted into braking torque and applied to the appropriate wheels
Rules Braking 1 wheel: from an optimal point of view, it is recommended to use only one wheel to • generate the control moment (Park(2001)) Only rear wheels are involved to avoid overlapping with the steering control • Decision rule:
Driving situations
Oversteer Understeer
Brake outer rear wheel Brake inner rear wheel
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 51 Active safety using coordinated steering/braking control Lateral stability control VDSC-lower controller algorithm
The stabilizing moment Mz∗ provided by the controller is converted into braking torque and applied to the appropriate wheels
Rules Braking 1 wheel: from an optimal point of view, it is recommended to use only one wheel to • generate the control moment (Park(2001)) Only rear wheels are involved to avoid overlapping with the steering control • Decision rule:
Driving situations
Oversteer Understeer
Brake outer rear wheel Brake inner rear wheel
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 51 Active safety using coordinated steering/braking control Simulations Simulation results and results
Matlab/Simulink software • Vehicle Automotive toolbox • • Full nonlinear vehicle model • Validated in a real car "Renault Mégane Coupé"
Two tests:
1 Double-lane-change maneuver at 100 km/h on a dry road (µ = 0.9) 2 Steering maneuver at 80 km/h on a slippery wet road (µ = 0.5)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 52 Active safety using coordinated steering/braking control Simulations Simulation results and results
Matlab/Simulink software • Vehicle Automotive toolbox • • Full nonlinear vehicle model • Validated in a real car "Renault Mégane Coupé"
Two tests:
1 Double-lane-change maneuver at 100 km/h on a dry road (µ = 0.9) 2 Steering maneuver at 80 km/h on a slippery wet road (µ = 0.5)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 52 Active safety using coordinated steering/braking control Simulations Test 1: Results [dry road µ = 0.9, V = 100 km/h]
Yaw rate [deg/s] β [deg]
30 4 Uncontrolled Uncontrolled 3 20 2
10 1
0 0 Reference Controlled −1 −10 −2 −20 −3 controlled −30 −4 0 0.5 1 1. 5 2 2.5 3 0 0.5 1 1. 5 2 2.5 3 t [s] t [s ]
Vehicle dynamic responses with and without controller
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 53 Active safety using coordinated steering/braking control Simulations Test 1: Results [dry road µ = 0.9, V = 100 km/h]
Top view of the vehicle Uncontrolled 30 3 Uncotrolled vehicle controlled 2. 5 20
2 10 1. 5
0
. [deg/s] Reference 1 Ψ −10 Controlled vehicle
y − Distance y − [m] 0. 5
−20 0
−0. 5 −30
−4 −3 −2 −1 0 1 2 3 4 0 10 20 30 40 50 60 70 80 δ [deg] x − Distance [m]
Figure: Response of the yaw rates versus steering Figure: Trajectories of the controlled and wheel angle uncontrolled vehicles
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 54 Active safety using coordinated steering/braking control Simulations Test 1: Results [dry road µ = 0.9, V = 100 km/h]
Stability index Additive steer angle
1 2 0.8 0
λ 0.6
0.4 [deg] δ −2 0.2 −4 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 3 ρ−parameter variations Brake torque
10 60
40 ρ 5 20 right [Nm] b
0 T 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Brake torque Corrective yaw moment 400 80 200 60
[Nm] 0 40 * z left [Nm] b
M 20 −200 T 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Time [s] Time [s]
Figure: Mz∗ and ρ variations according to χ for the Figure: Control signals generated by the controller double lane-change maneuver
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 55 Active safety using coordinated steering/braking control Simulations Test 2: Results [wet road µ = 0.5, V = 80 km/h]
Yaw rate Sideslip angle 25 3 20 Uncontrolled 15 2 Uncontrolled 10 1 5
0
[deg] 0 ’ [deg/s]
. β
Ψ −5 Reference
−10 −1
−15 −2 −20 Controlled controlled −25 −3 0 0. 5 1 1. 5 2 2. 5 3 0 0. 5 1 1. 5 2 2. 5 3 Time [s] Time [s]
Vehicle dynamic responses with and without controller
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 56 Active safety using coordinated steering/braking control Simulations Test 2: Results [wet road µ = 0.5, V = 80 km/h]
Top view of the vehicle 25 3 20
15 2. 5
10 Uncotrolled vehicle 2 5
0 1. 5 ’ [deg/s]
ψ −5 1 −10 y−Distance [m]
−15 0. 5 Controlled vehicle
−20 0 −25 −4 −3 −2 −1 0 1 2 3 4 0 10 20 30 40 50 60 δ [deg] x−Distance [m]
Figure: Response of the yaw rates versus steering Figure: Trajectories of the controlled and wheel angle uncontrolled vehicles
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 57 Active safety using coordinated steering/braking control Simulations Test 2: Results [wet road µ = 0.5, V = 80 km/h]
Stability index
0.8 0.6 λ 0.4 0.2 0 0.5 1 1.5 2 2.5 3 ρ−parameter variations 10
ρ 5
0 0.5 1 1.5 2 2.5 3 Corrective yaw moment
50 0 [Nm] * z −50 M −100 0 0.5 1 1.5 2 2.5 3 Time [s]
Figure: Mz∗ and ρ variations according to χ for the steering maneuver
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 58 Road profile estimation and road adaptive vehicle dynamics control Outline
1. Introduction 2. Models 3. Intro to Towards global chassis control 4. Active safety using coordinated steering/braking control Active safety Objective Basics on vehicle dynamics Partial non linear Vehicle model Lateral stability control Simulations 5. Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive controller synthesis Implementation & test validation on the INOVE test bench 6. LPV FTC for Vehicle Dynamics Control Towards global chassis control The LPV FTC VDC... approach Simulations on a full NL vehicle model 7. Conclusions and future work
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 59 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road profile vehicle control adaptation
Road Profile estimation strategies The H observer for road profile estimation. • ∞ The Algebraic flat observer for road profile estimation. • The Parametric Adaptive Observation for road profile estimation. • Guaranteed estimation based on interval analysis techniques. • Vehicle-cloud-vehicle, data clustering and and identification. •
LPV/H∞ Road profile Adaptation control Road Adaptive Semi-Active Suspension for 1/4 vehicle using an LPV/H Controller. • ∞ A new LPV/H semi-active suspension control strategy for the full car with performance • ∞ adaptation to roll behavior based on a non linear algebraic road profile estimation
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 60 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road profile vehicle control adaptation
Road Adaptive Semi-Active Suspension for 1/4 vehicle using an LPV/H∞ Controller
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 60 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
One of the important investigation towards road safety On-line performance objectives adaptation (comfort vs roadholding). • Less expensive and very efficient. • Suspension control and adaptation: Camera based road monitoring selective control, very recently (2013) by Mercedes Benz.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 61 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
Road profile roughness estimation to identify the type of the road. • LPV/H semi-active suspension control adaptation to the type of the road profile. • ∞
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 62 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
Road profile roughness estimation to identify the type of the road. • LPV/H semi-active suspension control adaptation to the type of the road profile. • ∞
A shock absorber with magneto-rheological fluid that Vehicle Model with Measurement changes damping characteristics in the suspension sys- the semi-acive tem depending on electric current. MR dampers F = If tanh a z˙ + a z + b z˙ + b z Internal varying MR c 1 de f 2 de f 1 de f 2 de f Parameters
ρ1, ρ2 ρ1 = f (tanh(zde f ,z˙de f ),I) ρ2 = f (sat(tanh(zde f ,z˙de f ),I)) (dissipativity, saturation)
x˙ = A (ρ1,ρ2)x + B1uc + B2w ρ1 [ 1,1] Nonlinearities. lpv lpv lpv ∈ − −→ y = C x ρ2 [0,1] Saturation. lpv 1 lpv ∈ −→
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 62 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
Road profile roughness estimation to identify the type of the road. • LPV/H semi-active suspension control adaptation to the type of the road profile. • ∞
(H Observer) ∞
Vehicle Model with Measurement Road profile the semi-acive estimation MR dampers reconstruction
Internal varying Parameters ρ1, ρ2
(dissipativity, saturation)
1 zˆr = [musz¨us ks(zˆs zˆus) + kt zˆus FMR] k− − − − · t
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 62 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
Road profile roughness estimation to identify the type of the road. • LPV/H semi-active suspension control adaptation to the type of the road profile. • ∞
(H Observer) ∞
Vehicle Model with Measurement Road profile ˆ fzr = z˙r / 2π zr [Hz] the semi-acive estimation RMS · RMS MR dampers reconstruction Frequency estimation Internal varying Amplitude estimation and extraction Parameters ρ1, ρ2 Using ISO 8608
(dissipativity, saturation) Road roughness Estimation ˆ 2 Szr ( fzr ) = (Azr ) /(2∆ f ) q ρ3 ˆ 2 2 Azr = α1 + β1
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 62 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
Road profile roughness estimation to identify the type of the road. • LPV/H semi-active suspension control adaptation to the type of the road profile. • ∞
(H Observer) Type of Road Class ∞ Smooth runway A
Vehicle Model with Measurement Road profile Smooth highway B the semi-acive estimation Highway with gravel C MR dampers reconstruction Rough runway D Frequency estimation Pasture E Internal varying Amplitude estimation and extraction Plowed field F Parameters ρ1, ρ2 Using ISO 8608
(dissipativity, saturation) Road roughness Estimation PSD ρ3 ISO 8608
Road Classification
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 62 Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive control
Road profile roughness estimation to identify the type of the road. • LPV/H semi-active suspension control adaptation to the type of the road profile. • ∞
(H Observer) ∞
Vehicle Model with Measurement Road profile the semi-acive estimation MR dampers reconstruction Frequency estimation Internal varying Amplitude estimation and extraction Parameters ρ1, ρ2 Using ISO 8608
(dissipativity, saturation) Road roughness Estimation PSD ρ3 ISO 8608
Road Road adaptive controller Classification
K(ρ1, ρ2, ρ3)
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 62 Road profile estimation and road adaptive vehicle dynamics control Road Adaptive controller synthesis
LPV/H∞ control synthesis
Two scheduling parameters in the model: ρ1 = f (tanh(zde f ,z˙de f ),I) ρ2 = f (sat(tanh(zde f ,z˙de f ),I))
zs Wzs z1 zr z W z2 ρ1 [ 1,1] Nonlinearities. us zus • ∈ − −→ u Σ (ρ1,ρ2 ) ρ2 [0,1] Saturation. f u • ∈ −→ Wfilter zdef ˙zdef
ρ1, ρ2
uc K(ρ1, ρ2 )
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 63 Road profile estimation and road adaptive vehicle dynamics control Road Adaptive controller synthesis
LPV/H∞ control synthesis
One scheduling parameter ρ3 for online suspension adaptation to the road profile:
ρ3 = Kρ Sz ( fz ) [0,1] (10) 3 · r r ∈ where Kρ3 is used to bound ρ3, such that zs Wz z1 z3 W ( ρ ) z s r 3 r z zus Wzus 2 Σ (ρ1,ρ ,ρ ) I = Imax uf u 2 3 Wfilter z def i f ρ3 ρ3 ˙zdef I ≥I I min < < max I(ρ3) := (11) ρ1, ρ2 i f ρ3 < ρ3 < ρ3 Road I = Imin ρ3 Roughness uc K(ρ1, ρ2, ρ3) Estimation i f ρ3 ρ3 ≤
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 63 Road profile estimation and road adaptive vehicle dynamics control Road Adaptive controller synthesis
LPV/H∞ control synthesis
The general LPV/H∞ is obtained thanks to the polytopic appraoch, by solving the con- sidered set of LMIs on each one of the 23 = 8 vertices. The general LPV/H∞ is a convex combination of the 8 local controllers.
3 2 A B S(ρ) = α (ρ) ck ck ∑ k C D k=1 ck ck where,
23 c ∏ j=1 ρ( j) C (Ωk) j αk(ρ) = | − | , ∏i (ρ( j) ρ( j)) j=1 −
23 ∑ αk(ρ) = 1 , αk(ρ) > 0 k=1
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 64 Road profile estimation and road adaptive vehicle dynamics control Implementation & test validation on the INOVE test bench Road adaptive control validation & implementation
The test bench is composed of: The process: 1/5 scaled real vehicle equipped with 4 Electro-Rheological semi-active • dampers and 4 DC motors to generate the desired road profiles. Matlab/Simulink environment + Xpc target environment for real time data acquisition and • control.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 65 Road profile estimation and road adaptive vehicle dynamics control Implementation & test validation on the INOVE test bench Road adaptive control validation & implementation
The test bench is composed of: The process: 1/5 scaled real vehicle equipped with 4 Electro-Rheological semi-active • dampers and 4 DC motors to generate the desired road profiles. Matlab/Simulink environment + Xpc target environment for real time data acquisition and • control.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 65 Road profile estimation and road adaptive vehicle dynamics control Implementation & test validation on the INOVE test bench Road adaptive control validation & implementation
The test bench is composed of: The process: 1/5 scaled real vehicle equipped with 4 Electro-Rheological semi-active • dampers and 4 DC motors to generate the desired road profiles. Matlab/Simulink environment + Xpc target environment for real time data acquisition and • control.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 65 Road profile estimation and road adaptive vehicle dynamics control Implementation & test validation on the INOVE test bench Road classification implementation results
(A) Road profile (H Observer) 0.03 Experimental data ∞ 0.02 Estimation 0.01 Vehicle Model with Measurement Road profile
[m] 0 the semi-acive estimation −0.01
MR dampers reconstruction −0.02
Frequency estimation −0.03 (B) PSD of the roughness Internal varying Amplitude estimation and extraction Parameters −3 −4 ρ1, ρ2 Using ISO 8608 ^ −5 . r r z z (dissipativity, saturation) −6 Road roughness log (S −7 f ) Estimated roughness Thresholds for ISO roads Estimation PSD −8 ρ ISO 8608 (C) Road identification 3 F
E Implemented Road D road Road adaptive controller Classification C
B K(ρ1, ρ2, ρ3) Road classification A 0 50 100 150 200 250 Time [s]
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 66 Road profile estimation and road adaptive vehicle dynamics control Implementation & test validation on the INOVE test bench Road classification implementation results
(A) Road profile 0.03 Experimental data 0.02 Estimation 0.01
[m] 0
−0.01
−0.02
Table: Road profiles Classification (ISO 8608). −0.03 (B) PSD of the roughness Type of Road Class −3 Smooth runway A −4
^ −5 . r r
Smooth highway B z z −6
Highway with gravel C log (S f ) −7 Rough runway D Thresholds for ISO roads −8 Estimated roughness Pasture E (C) Road identification Plowed field F F E Implemented D road C
B Road classification A 0 50 100 150 200 250 Time [s]
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 66 Road profile estimation and road adaptive vehicle dynamics control Implementation & test validation on the INOVE test bench Road adaptive control implementation results
100
2 80 Passive Suspension (PS) LPV controller a 18 60 16 2 14 40 12 20 10 0 8 −20 6
RMS [m/s ] 4 Sprung mass −40 2
acceleration [m/s ] −60 0 0.25 b 70 0.15 60 50 0.05 40 −0.05 30
RMS [mm] 20 −0.15 10 Unsprung mass
displacement [m] −0.25 0 0 1 2 3 4 5 6 7 8 9 10 PS
Time [s] LPV (a) plowed field (hard road F) at low velocity (comfort objective) (b) Raod type F, vx = 30 Km/h
3 1.4 2 Passive Suspension (PS) a 2 1.2 1 2 1 0.8 0 0.6 −1 0.4 RMS [m/s ]
Sprung mass −2 LPV controller 0.2 acceleration [m/s ] −3 0 2.5 0.01 Passive Suspension 0.008 LPV controller b 0.006 2 0.004 0.002 1.5 0 −0.002 1
−0.004 RMS [mm] −0.006 0.5 Unsprung mass −0.008 −0.01 displacement [m] 0 0 1 2 3 4 5 6 7 8 9 10 PS
Time [s] LPV (c) highway (smooth road ISO A) at low veloc- ity (road haolding objective) (d) Raod type A, vx = 100 Km/h
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 67 LPV FTC for Vehicle Dynamics Control Outline
1. Introduction 2. Models 3. Intro to Towards global chassis control 4. Active safety using coordinated steering/braking control Active safety Objective Basics on vehicle dynamics Partial non linear Vehicle model Lateral stability control Simulations 5. Road profile estimation and road adaptive vehicle dynamics control Road profile vehicle control adaptation Road Adaptive controller synthesis Implementation & test validation on the INOVE test bench 6. LPV FTC for Vehicle Dynamics Control Towards global chassis control The LPV FTC VDC... approach Simulations on a full NL vehicle model 7. Conclusions and future work
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 68 LPV FTC for Vehicle Dynamics Control Towards global chassis control Towards global chassis control approaches (GCC)
Some facts Vehicle-dynamics sub-systems control (suspension, steering, stability, traction ....) are • traditionally designed and implemented as independent (or weakly interleaved) systems. Global collaboration between these systems is done through empirical rules and may lead to • inappropriate or conflicting control objectives.
What is GCC ? combine several (at least 2) subsystems in order to improve the vehicle global behavior • Shibahata (2004) tends to make collaborate the different subsystems in view of the same objectives, according • to the situation (constraints, environment, ...) is develop to improve comfort and safety, according to the driving situation, accounting for • actuator constraints and to the eventual knowledge of the vehicle environment
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 69 LPV FTC for Vehicle Dynamics Control Towards global chassis control Active safety using LPV FTC VDC coordinated control
Key points Yaw is one of the most complex dynamics to handle on a ground vehicle. FTC LPV control: Undesired Prevents vehicle from skidding and spinning out • motion Improves lateral vehicle dynamics face to critical • situations Desired trajectory Handle Braking and suspension actuator • malfunctions and Steering activation
The LPV FTC strategy Control Issues Lateral coordinated steering/braking control: Monitoring Parameters • parameter dependent weighting functions for braking Braking efficiency : torque • torque limitation and activation of the steering action transmission Full car vertical suspension control: fixed control Steering activation during • • structure for suspension force distribution, parameter emergency situation (low slip) dependent weighting functions for roll attenuation in LTR: roll induced load transfer critical situations and comfort improvement in normal • by damper malfunctions ones.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 70 LPV FTC for Vehicle Dynamics Control Towards global chassis control Global chassis control implementation scheme
Steering Load Transfer + Braking Distribution Monitor 2 Monitor 1
ρs ρb ρlij Supervision strategy
ρ ρs ρlij b ρb
Steering Controller Braking Controller LPV/Hinf Suspension Controller uij + T Controllers δ brj
Steer input + δ uij Tbrj
δd Non Linear Full Vehicle Model
zr Road profil
Driving scenario O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 71 LPV FTC for Vehicle Dynamics Control The LPV FTC VDC... approach Coordinated steering/braking control
W z3 Tbrj (ρb)
0 Wδ (ρs) z4 Vehicle model : Single track model z1 We ˙ ψref (dry road).
Inputs/Ouputs: z2 ψ˙ref (v) + Wv˙y GCC(ρb, ρs) Bicycle e ˙ 0 w(t) = [ψ˙re f (v)(t),Mdz(t)] - ψref Tbrj , δ u(t) = [δ +(t),T + (t),T + (t)] ψ˙ brl brr y(t) = eψ˙ (t) z(t) = [z1(t),z2(t),z3(t)] Weighting functions for performance requirements
Weψ˙ and Wv˙y are 1st order systems.
Weighting functions for actuator coordination
Wδ (ρs) = (1 ρs) 4th order braking (and steering) penalized if ρ = ρ • − × → WT (ρb) = (1 ρb) 1st order braking (and steering) allowed if ρ = ρ • br j − × → When a high slip ratio is detected (critical situation) , the tire may lock, so ρb 0 and the gain of the weighting function is set to be high. → This allows to release the braking action leading to a natural stabilisation of the slip dynamic.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 72 LPV FTC for Vehicle Dynamics Control The LPV FTC VDC... approach The suspension control configuration
Wzs(ρs) z1
z3 Wu Wθ(1 ρs) z2 Σgv −
zdefij Ks(ρl) uijH∞
A new partly fixed control structure: manage the suspension control distribution in case of damper malfunction
x˙c(t) = Ac(ρs,ρl )xc(t) + Bc(ρs,ρl )y(t) H∞ u f l (t) 1 ρl 0 0 0 Ks(ρs,ρl ) := H∞ − u f r (t) 0 ρl 0 0 0 = Cc (ρs)xc(t) uH∞ (t) 0 0 1 ρl 0 rl − H∞ 0 0 0 ρl urr (t)
ρl allows to generate the adequate suspension forces in the 4 corners of the vehicle depending on the load transfer (left right) caused by the performed driving scenario.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 73 LPV FTC for Vehicle Dynamics Control Simulations on a full NL vehicle model Simulations on a full NL vehicle model Simulation results
Vehicle Automotive ’GIPSA-lab’ toolbox • • Full nonlinear vehicle model • Validated in a real car "Renault Mégane Coupé" coll. MIAM lab [Basset, Pouly and Lamy] see C. Poussot-Vassal PhD. thesis
The stabilizing torques Tb∗ provided by the controller is then handled by a local ABS strategy Tanelli et al. (2008)
Simulation scenario
Double lane-change maneuver at 100 km/h Faulty left rear braking actuator: on a WET road (from t = 2s to t = 6s) • saturation = 75N Driver Steering Angle 20 5cm Road bump from t = 0.5s to • 15 t = 1.5s and from t = 4s to t = 5s) 10
5 Faulty front left damper: force limitation • 0 [Deg] of 70% d δ −5 Lateral wind occurs at vehicle’s front −10 • −15 generating an undesirable yaw moment
−20 0 1 2 3 4 5 6 (from t = 2.5s to t = 3s). t [s]
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 74 LPV FTC for Vehicle Dynamics Control Simulations on a full NL vehicle model Monitoring parameters
Braking scheduling parameter Suspension scheduling parameter 1 0,6
0,5 0.8 0,4
0.6 0,3
ρ l ρ b b l ρ ρ 0,2 0.4
0,1 0.2 0
0 −0,1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t [s] t [s]
Performance scheduling parameter 1
0.9 ρ handles the braking efficiency • b 0.8 ρs: activation of the steering actuator 0.7 • 0.6 ρl (LTR): Coordination of suspension
s 0.5 • ρ ρs control and on-line modification of the 0.4 suspension performances 0.3
0.2
0.1
0 0 1 2 3 4 5 6 t [s]
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 75 LPV FTC for Vehicle Dynamics Control Simulations on a full NL vehicle model Braking/Steering actuators - stability analysis
Rear Left Braking Torque Rear right Braking Torque 800 800
600 600
400 400 left [Nm] 200 right [Nm] 200 b b T 0 T 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t [s] t [s] Additive Steering Angle Stability Region 4 40 Stability boundries Uncontrolled 2 20 0 0 −2 FTC LPV
δ [deg] −20
−4 β’[deg/s] −40 −6 0 1 2 3 4 5 6 −6 −4 −2 0 2 4 6 Fault Tolerant Yaw controlt [s] through an efficient coordination of braking/steeringβ [deg] actuators.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 76 LPV FTC for Vehicle Dynamics Control Simulations on a full NL vehicle model Braking/Steering actuators - stability analysis
Rear Left Braking Torque Rear right Braking Torque 800 800
600 600
400 400 left [Nm] 200 right [Nm] 200 b b T 0 T 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t [s] t [s] Additive Steering Angle Stability Region 4 40 Stability boundries Uncontrolled 2 20 0 0 −2 FTC LPV
δ [deg] −20
−4 β’[deg/s] −40 −6 0 1 2 3 4 5 6 −6 −4 −2 0 2 4 6 Fault Tolerant Yaw controlt [s] through an efficient coordination of braking/steeringβ [deg] actuators.
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 76 LPV FTC for Vehicle Dynamics Control Simulations on a full NL vehicle model Suspension control distribution
Suspension Forces Roll displacement 500 1 rr 0 Fs −500 0.5 0 1 2 3 4 5 6 200 Faulty damper 0 fl 0 Faulty dampers Fs −200 0 1 2 3 4 5 6 −0.5 500 θ [deg] fr 0
Fs −1 −500 0 1 2 3 4 5 6 500 −1.5 rl 0 Fs −500 −2 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t [S] t [s]
9000 Rear left left damper With Damper Fault Without Damper Fault 8000
7000 Rear right damper
6000 Rear right damper Rear left left damper
5000 Front right damper
4000 Front right damper Front left damper
3000
2000
Front left damper 1000
0 Fixed structure LPV control for suspension force coordination in case of damper malfunction 1 2
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 77 Conclusions and future work Conclusions
About today’s presentation:
An approach to the vehicle yaw stabilizing problem. . . Objective: Enhance vehicle steerability and stability • • Steerability is enhanced in normal driving condition. • Braking is involved only when the vehicle tends to instability. Flexible design: Integration of different scheduled sub-controllers • Scheduling parameters: Estimation of the sideslip angle • Real-time implementation: General structure does not involve online optimization •
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 78 Conclusions and future work Future work
Implementation of the controller in a real car • Integration of the suspension system in the control scheme • Design of an LPV vehicle system • • Variation of the cornering stiffness with respect to road conditions (dry, wet, icy,. . . )
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 79 Conclusions and future work
Thank you for your attention
O.Sename-S.Fergani (GIPSA-lab - LAAS) Intelligent Vehicles Summer School July 2-7, 2017 80 Bibliography References
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