H∞ Global Chassis Control through load transfer distribution and vehicle stability monitoring

5th IFAC Symposium on System Structure and Control Part of 2013 IFAC Joint Conference SSSC, FDA, TDS Grenoble, France, February 4-6, 2013

A new LPV/H∞ Global Chassis Control through load transfer distribution and vehicle stability monitoring S. Fergani, O. Sename, L. Dugard GIPSA-lab, Control Systems Dept, CNRS-Grenoble INP, ENSE3, BP 46, F-38402 St Martin d’H`eres cedex, France (e-mail: {soheib.fergani, olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr). Abstract: This paper proposes a new multivariable LP V /H∞ Global Chassis Control (GCC) strategy, using suspension, active steering and electro-mechanical braking actuators. This new approach allows, by allocating the load transfer in the four corners of the vehicle, scheduling the suspensions actuators and so to enhance vertical performances. Also, through a consistent stability monitor, based on a slip dynamics supervision, the braking and the steering controllers are scheduled. The good distribution of the load transfer aims at tuning the suspensions in the four corners (either soft or hard), to improve the car holding. The stability index schedules the action of the braking and the steering actuators, to ensure a good coordination between those controllers. This strategy improves the car dynamics behavior and the vehicle stability. Simulations performed on a complex nonlinear full vehicle model, subject to critical driving situations, show the reliability and the robustness of the proposed solution. Keywords: Vehicle dynamics, Braking, Suspension, Steering,load transfer distribution, LPV, H∞ control. 1. INTRODUCTION Automotive vehicles are complex systems involving the interaction of dynamic subsystems. Today, automotive systems employ more and more actuators and sensors to achieve the desired response of the vehicle. Thus, the 3 main actuators that influence vehicle dynamics are suspensions for the vertical displacements while lateral and longitudinal dynamics mainly depend on braking and steering systems. An important problem is the communication and coordination between those systems. In most design approaches, suspension, steering and braking control systems are synthesized independently to optimize local performances. Since the different dynamics are strongly coupled, it is difficult to decouple them. For instance, many studies have been recently dedicated to the control of braking, steering or suspensions systems (see Poussot-Vassal et al. (2011b) and references therein); the global communication and collaboration between each structure (sensors, controllers, and actuators) are achieved using empirical rules, based on the automotive engineers experience. This approach may lead to conflicting objectives. A trend in modern vehicles is the application of active safety systems to improve vehicle handling, stability and comfort. Nowadays, many advanced active chassis control systems have been developed and brought into the market: e.g., ABS (Anti-lock Braking System), and ESC (Electronic Stability Control). The development of chassis control systems is still the object of intense research activities from both industrial and academic sides. 1 This work was supported by the French National Research Agency, in the context of the project ANR BLAN 0308

978-3-902823-25-0/13/$20.00 © 2013 IFAC

809

Many of recent works have tried to treat the global chassis control involving several actuators. N´emeth and G´ asp´ ar (2011) shows a new design of actuator intervention for trajectory tracking. In Chou and d’Andr´ea Novel (2005), an interesting nonlinear control law using suspension and braking actuators for commercial cars has been proposed. More recently, in G´ asp´ ar et al. (2007) and Poussot-Vassal et al. (2011a) the authors have proposed a ”LPV” control structure, monitoring the lateral load transfer and involving active suspension and braking (EMB) control actions that improves the passenger comfort in normal situations and attenuates the lateral acceleration effect in critical ones. Very recently, the authors have developed various LP V /H∞ yaw control strategies using ElectroMechanical braking (EMB) and Active Steering (AS) actuators with smart scheduling policies (see Poussot-Vassal et al. (2011b)...), a step towards a full coordinated control. Following the previous authors’ works (Fergani et al. (2012a), Fergani et al. (2012b)), this paper proposes a new ”LPV/H∞ ” robust control strategy. It coordinates the work of the three main actuators (Suspensions, Active Steering, Electro-Mechanical Braking) by using two scheduling parameters giving by monitoring systems to overcome critical driving situations. This GCC (Global Chassis Control) strategy monitors the lateral transfer load, a scheduling parameter, to tune the suspension systems in the four corners, depending on the load distribution on those corners. This load transfer distribution approach aims at enhancing the vertical car’s performance, namely comfort and roadholding. Also, this strategy uses a stability index based on slip side dynamics monitoring (see in He et al. (2006)) to schedule the activation of the

10.3182/20130204-3-FR-2033.00188

2013 IFAC SSSC Grenoble, France, February 4-6, 2013

Symbol

Value

Unit

ms musf j musrj Ix ; Iy ; Iz Iw tf ; tr lf ; lr R h

350 35 32.5 250; 1400; 2149 1 1.4; 1.4 1.4; 1 0.3 0.4

kg kg kg kg.m2 kg.m2 m m m m

Signification suspended mass front unsprung mass rear unsprung mass roll, pitch, yaw inertia wheel inertia front, rear axle COG-front, rear distance nominal wheel radius chassis height

Table 1. Renault M´egane Coup´e parameters steering and the braking actuators. The proposed strategy allows a hierarchical use of the different actuators, depending on the driving situation, to optimize their use. The solution of this problem is obtained within the LMI (Linear Matrix Inequalities) framework, while warranting the H∞ performances. The paper is structured as follows: Section 1 provides introductive elements and notations. Section 2 briefly introduces the mathematical models used for synthesis and validation purpose, together with their limitations. Section 3 is devoted to the main contribution of the paper, coordination of the three subsytems (steering, braking and suspension) with the specific scheduling parameters to enhance the vehicle performances. Performance analysis is performed in Section 4 using time domain simulations of a complex nonlinear full vehicle model. Conclusions and discussions are given in the last Section. Throughout the paper, the following notation will be adopted: indices i = {f, r} and j = {l, r} are used to identify vehicle front, rear and left, right positions respectively. Index are {s, t} define forces provided by suspensions and tires respectively. {x, y, z} define the forces and dynamics in the longitudinal, lateral and vertical axes respectively. q Then let v = vx2 + vy2 denote the vehicle speed, Rij = R−(zusij −zrij ) the effective tire radius, m = ms +musf l + musf r +musrl +musrr the total vehicle mass, δ = δd +δ + is the steering angle (δd , the driver steering input and δ + , the additional steering angle provided by steering actuator, see Section 3) and Tbij the braking torque provided by the braking actuator (see table.1). The model parameters are those of a Renault M´egane Coup´e (see Poussot-Vassal et al. (2011a)), obtained during a collaborative study with the MIPS laboratory in Mulhouse, through identification with real data. 2. VEHICLE MODELING Dynamical equations: In this paper, a nonlinear full vehicle model is developed for analysis. This model and the corresponding parameters are detailed in Poussot-Vassal et al. (2011b). It reproduces the vertical (zs ), longitudinal (x), lateral (y), roll (θ), pitch (φ) and yaw (ψ) dynamics of the chassis. It also models the vertical and rotational motions of the wheels (zusij and ωij respectively), slip vij −Rij ωij cos βij ratios (λij = max(v ) and center of gravity ij ,Rij ωij cos βij ) side slip angle (βcog ) dynamics as a function of the tires and suspensions forces.The full vehicle model in PoussotVassal et al. (2011b) will be used in simulation for val810

idation purpose (see Section 4). The main interest of the full vehicle model is that it takes into account the nonlinear load transfer, the slipping and side slip angles that are essential phenomena entering in the tire force, and consequently, in the global chassis dynamics, especially in dangerous driving situations. Suspensions model: Suspensions are usually modeled by a spring and a damping element. In real vehicles, their characteristics are nonlinear. Here, for control design purposes, without loss of generality, linear models are assumed for stiffness and damping as: ∞ Fszij = kij (zsij − zusij ) + cij (z˙sij − z˙usij ) + uH (1) ij where kij : the stiffness coefficient, cij : the damping coeffi∞ cient and uH ij : the suspension control. Actuators dynamic: The actuators are modeled as first order low-pass transfer functions in this paper: • The active suspension systems: 0 (2) − Fsuspij ) F˙ suspij = τ (Fsusp ij where τ = 200rad/s is the actuator cut-off frequency. 0 and Fsuspij are the suspension controller and Fsusp ij actuator outputs, respectively. • The EMB actuators, providing the braking torque: (3) T˙brj = ̟(Tb0rj − Tbrj )

where, ̟ = 70rd/s is the actuator cut-off frequency, Tb0rj and Tbrj are the rear braking controller and actuator outputs respectively. In this paper, only the rear braking system is used to avoid the coupling phenomena occurring with the steering system and because it affects more the vehicle yaw behavior than the front one does (j = r, l). • The AS actuator providing an additional steering angle: δ˙ + = κ(δ 0 − δ + ) (4) where, κ = 10rd/s is the actuator cut-off frequency, δ 0 and δ + are the steering controller and actuator outputs respectively. This actuator is constrained between [−5, +5] degrees. 3. THE NEW PROPOSED GCC STRATEGY: MONITORING AND SYNTHESIS This section is devoted to the description of the main result of this paper, namely, the multivariable Global Chassis Controller (GCC) involving front active steering, rear braking and active suspension actuators, scheduled by two monitoring parameters (see Fig.1). Indeed, two monitoring systems are used to provide the varying parameters in view of the GCC strategy. First, the suspension monitor which provides parameters tunes the suspension actuators in the four corners of the vehicle, based on an index of the load transfer. In this study, only the right-left transfer load is considered. Based on it, the suspension on each corner is tuned, either ”soft” to keep the driving comfort or ”hard” to not deteriorate the road holding of the vehicle. Another monitoring system, which supervises the sideslip dynamics, is used to generate the good braking torques and provides the accurate additive steering angles, to stabilize

2013 IFAC SSSC Grenoble, France, February 4-6, 2013

Road profil

zr +

Steer Input

δ

+

where χ = 2.49β˙ + 9.55β is the ”Stability Index”. Therefore, when the vehicle states move beyond the control boundaries and enter the unstable region, the braking actuators will be involved to generate an additive corrective yaw moment, pulling the vehicle back into the stable region. According to He et al. (2006), one of the significant benefits of this stability index is that the reference region defined in (6) is largely independent of the road surface conditions and hence, the accurate estimation of the road surface coefficient of friction is not required.

β ˙ β ˙ ψ ay

Σfull uij

zdef

Tbrj

v

+

Suspension controller

zdefij uij

−

˙ ref ψ

ρ1

v δ0

Steering controller

GCC

δ+

eψ˙

ρ2

Monitor 2

ρ1

Monitor 1

ρ2

Braking controller

v Tbrj

δ0 ˙ ψ ρ2

Remember that the control task is also supposed to provide a seamless application of the direct yaw moment control when it is required. Hence, the scheduling parameter ρ2 (χ) can be defined as:

ρ1 and ρ2 : scheduling parameters.

Fig. 1. Global chassis control Implementation scheme. the vehicle in dangerous driving situations. These progressive activation and use of those actuators, depending on the evaluation of the vehicle stability and load transfer bounce, provide a considerable help to the driver for overcoming critical situations.

 ρ2    χ−χ

if χ ≤ χ χ−χ ρ2 + ρ2 if χ < χ < χ ρ2 (χ) := χ−χ χ−χ   ρ if χ ≥ χ 2

(7)

3.1 Monitoring systems & Scheduling parameters generation where χ = 0.8 (user defined) and χ = 1. In the following, the two monitoring systems that provide the two varying parameters in view of the GCC are detailed. Suspension monitoring system: The suspension monitor is a system which evaluates the load transfer when the vehicle is running. In this study, the load transfer considered is the left right one. The main idea is to evaluate and compare the right left vertical forces in the four corners of the vehicle. The rate of the difference between the right and left forces is used to schedule the suspensions actuators. Based on the value of this parameter, the suspensions on the left and right sides of the vehicle are tuned either to ”soft” or ”hard” (resp. comfort or road holding performance objectives). This suspension monitor is obtained by the following equations:  Fzl = ms × g/2 + ms × h × ay /lf     Fzr = ms × g/2 − ms × h × ay /lr (5)     ρ1 = (Fzl − Fzr )/(Fzl + Fzr );

To calculate the actual stability index χ defined previously, a side-slip dynamics observer is used to estimate β˙ and β (the sideslip) in real-time. β˙ can be reconstructed using available sensors but β is not available using standard sensors, and thus, it must be estimated (For instance see Doumiati et al. (2010, 2011b)). 3.2 Global chassis control design strategy In the following, the controllers synthesis is done in two steps in a hierarchical way. The first one is the synthesis of the suspension controllers, based on load transfer distribution. This is one of the main contributions of this study. The second step is the synthesis of the braking and steering controllers, based on the stability supervision of the vehicle, (see Doumiati et al. (2011a)). First step: the suspension control Problem formulation The control of the vertical dynamics is ensured by the suspension system, in order to achieve frequency specification performances, (see Savaresi et al. (2010)).

where Fzl and Fzr are the vertical forces, ay the lat✲ Wz s z4✛ eral acceleration and ρ1 the scheduling parameter (for ✛ Wu other parameters see table.1). The set of variation of this ✲ Wθ monitor is: ρ1 ∈ [−1 1]. The load transfer distribution Σvert ij is done as follow: when |ρ1 | → 0, the left suspensions zdef✲ ✲ Ksusp (ρ1 ) ∞ actuators are tuned to enhance road holding, conversely, uH ij when |ρ1 | → 1 the right suspensions are tuned to improve this performance objective. Fig. 2. Suspension system generalized plant. Braking and Steering monitoring system: This supervision strategy was introduced by the authors in Doumiati et al. (2011a). Since the vehicle stability is directly related to the sideslip motion of the vehicle, judging the vehicle stability region is derived from the ˙ method. A stability bound defined phase-plane (β − β) in He et al. (2006) is used here and is formulated as: χ < 1, (6) 811

2

2

z1 ✲ z2 ✲

11 Ω11 s+Ω11 is shaped in order to reduce where Wzs = ss2 +2ξ +2ξ12 Ω12 s+Ω12 2 the bounce amplification of the suspended mass (zs ) between [0, 12]Hz. 2 2 21 Ω21 s+Ω21 Wθ = ss2 +2ξ attenuates the roll bounce amplifi+2ξ22 Ω22 s+Ω22 2 cation in low frequencies. Wu = 3.10−2 shapes the control signal.

2013 IFAC SSSC Grenoble, France, February 4-6, 2013

Remark 1. The parameters of these weighting functions are obtained using genetic algorithm optimization as in Do et al. (2010).

connected to the ”LTI” generalized plant. The LPV framework brought by this matrix allows the system to cope with the design of a polytopic controller.

According to Fig. 2, the following parameter dependent suspension generalized plant (Σgv (ρ1 )) is obtained:

Second step: Braking/steering control Problem formulation The generalized plant described in Fig 3 is used for the synthesis of the gain scheduled controller K(ρ2 ). This synthesis is done, based on a bicycle model (a lateral linear model of the vehicle, see Poussot-Vassal et al. (2011b)).

  ξ˙ = A(ρ1 )ξ + B1 w ˜ + B2 u Σgv (ρ1 ) := z˜ = C1 ξ + D11 w ˜ + D12 u  ˜ + D22 u y = C2 ξ + D21 w

(8)

Weψ˙

T

˜ = where ξ = [χvert χw ] ; z˜ = [z1 z2 z3 ] ; w ∞ [zrij Fdx,y,z Mdx,y ]T ; y = zdefij ; u = uH ij ; and χw are the vertical weighting functions states.

˙ ref (v) ψ ˙ ψ

The main contribution is the use of the parameter ρ1 to schedule the load transfer on the four corners of the vehicle. This strategy allows a good distribution of the force on the left & right suspensions. The provided forces acting on the suspensions and tuned with the varying parameter ρ1 to handle the load transfer constraint, are given in the LPV framework by the following controller: x˙ c (t) = Ac (ρ1 )xc (t) + Bc (ρ1 )y(t)   1 − |ρ | 0  0 0 1  uf l (t) 0 0  u (t) 0 |ρ1 | K(ρ1 )  uf r(t)  =  0 (Cc (ρ1 )xc (t)) 0 1 − |ρ1 | 0 rl  urr (t)

0

z1

T

0

0

|ρ1 |

(9) where xc (t) is the controller state, Cc (ρ1 ) the calculated controller scheduled by the parameter ρ1 , u(t) = [uf l (t)uf r (t)url (t)urr (t)] and y(t) = zdef (t). The parameter ρ1 ∈ [−1; 1] is used to distribute the load on the four corners of the vehicle, ensuring a good tuning of the suspensions. When a load transfer is performed from the right to the left side, |ρ1 | → 0 and the suspensions on the left side of the vehicle are tuned to provide more force to handle this load. That allows to ensure a good road holding for the car. Conversely, when the load transfer is carried out on the right side, |ρ1 | → 1 and the suspensions on this side are tuned to handle the overweight, by providing the accurate suspension force to ensure more stability and handling for the vehicle. The LPV system (8) includes a single scheduling parameter and can be described as a polytopic system, i.e, a convex combination of the systems defined at each vertex of a polytope defined by the bounds of the varying parameter. The synthesis of the two sub-system controllers is made in the framework of the H∞ control of polytopic suspensions, (for more details, see Scherer (1996)). Remark 2. The main contribution in this synthesis is that the controller has a fixed structure, but a parameter dependency on the control output matrix is introduced. This allows the good load transfer distribution in a smooth way, depending on the situation. The LPV generalized plant is obtained, thanks to the matrix U (ρ1 ), which is   0 0 1 − |ρ1 | 0 |ρ1 | 0 0   0 (10) U (ρ1 ) =  0 0 1 − |ρ1 | 0  0 0 0 |ρ1 | 812

+ −

eψ ˙

K (ρ2 )

Mz

W Mz

z2

Wδ

z3

EMB Σ

δ

AS

Mdz

Fig. 3. Generalized plant model. where: • Σ, EMB and AS stand for the extended bicycle, electro-mechanical braking and active steering actuators models, respectively. • z1 , yaw rate error exogenous output signal, is the output of the tracking error performance, weighted by: 1 sGe /2πf1 + 1 Weψ˙ = (11) 2Ge s/2πf1 + 1 where f1 = 1Hz is the cut-off frequency of the high pass filter. Ge = 0.1 is the attenuation level for low frequencies (f < f1 ); in this case 0.1 means that the static tracking error should be lower than 10%. • z2 , the exogenous braking (or moment) control signal attenuation, is the output of the braking control, weighted by: s/(2πf2 ) + 1 WMz (ρ2 ) = ρ2 (12) s/(α2πf2 ) + 1 where f2 = 10Hz and α = 100 are the braking actuator bandwidth and the roll-off parameters, respectively. These parameters are chosen to handle the dynamical braking actuator limitations. WMz (ρ2 ) is linearly parametrized by the  considered varying parameter ρ2 (.), where ρ ∈ ρ2 ≤ ρ2 ≤ ρ2 (with ρ2 = 10−5 and ρ2 = 10−3 ). Then, when ρ2 = ρ2 , the braking input is penalized, on the contrary, when ρ2 = ρ2 , the braking control signal is relaxed. • z3 , the exogenous steering control signal attenuation, is the output of the steering control performance, weighted by: (s/2πf3 + 1)(s/2πf4 + 1) Wδ = G0δ (s/α2πf4 + 1)2 (∆f /α2πf4 + 1)2 (13) G0δ = Gδ (∆f /2πf3 + 1)(∆f /2πf4 + 1) ∆f = 2π(f4 + f3 )/2 where Gδ = 5.10−3 , f4 = 10Hz is the steering actuator bandwidth and f3 = 1Hz is the lower limit of the actuator intervention. For more details, see Doumiati et al. (2011a).

2013 IFAC SSSC Grenoble, France, February 4-6, 2013

Fig. 4. ρ1 : load transfer in- Fig. 5. ρ2 : stability index. dex. The generalized plant obtained is the following:  ˙  ξ(t) = Aξ(t) + B1 w(t) + B2 (ρ)u(t) Σ : z(t) = C1 (ρ2 )ξ(t) + D11 w(t) + D12 (ρ2 )u(t) (14)  y(t) = C2 ξ(t) + D21 w(t) where w(t) u(t) y(t) z(t)

[ψ˙ ref (v)(t), Mdz (t)] [δ ∗ (t), Mz∗ (t)] eψ˙ (t) [z1 (t), z2 (t), z3 (t)]

exogenous input signals control input signals Fig. 7. Roll motion. signal measurement controlled outputs signals (15) ξ(t) is the concatenation of the linearized vehicle model, actuators and parameter dependent weighting function state variables. The LPV controller is given by : x˙ c (t) = Ac (ρ2 )xc (t) + Bc (ρ2 )eψ˙ (t) = = = =

are are are are

Fig. 6. Chassis displacement.

the the the the



 δ ∗ (t) = Cc0 (ρ2 ) xc (t) (16) Mz∗ where xc (t) is the controller state, y(t) = eψ˙ , u(t) = [δ ∗ (t) Mz∗ ], with δ ∗ (t), Mz∗ are the steering control input and the braking control moment respectively. Remark 3. The authors stress that all the controller presented in this study was designed thanks to the LPV/H∞ framework, based on LMI’s resolution (for more detail see Fergani et al. (2012a)). K(ρ2 )

Fig. 8. Yaw rate.

Fig.

4. SIMULATION RESULTS In this section, simulations are performed on a full vehicle non linear model, see Section 2. The following results are those obtained by the controllers previously described in Section 3.2. To test the efficiency of the proposed LPV/H∞ GCC, a ”hard” driving scenario has been chosen: the vehicle runs at 100km/h in straight line on wet road (µ = 0.5, where µ is a coefficient representing the adherence to the road). It meets a 5cm bump on the left wheels (t = 1.5s), and another one on the right wheels,(t = 2.5s). During this scenario, a line change manoeuvre is performed by the driver. In this study, the new LPV/H∞ GCC strategy is compared to the uncontrolled vehicle, to show the improvements on the different dynamics. Fig 4 and 5 represent the two scheduling parameters used in the proposed LPV/H∞ . It can also be noticed that the load transfer and the stability of the vehicle in the LPV (in red) case are improved. Fig 6 and 7 show the chassis displacement and the roll motion respectively. These two figures, representative of the 813

10. gle.

Sideslip

!!

"#$

Fig. 9. Yaw rate error.

an- Fig. 11. Evolution of the vehicle in the β-ψ˙ plane.

vertical dynamics of the vehicle, show that the proposed strategy enhances very well the vertical behavior of the car. The new LPV suspensions control based on the load transfer distribution through an LPV technic using ρ1 as a scheduling parameter reduces considerably the roll motion θ(t), which is the right-left load bounce. Also, the chassis displacement is well attenuated. Then, the passengers comfort (represented by the chassis displacement) and the road holding of the vehicle (represented by the roll motion) are both improved. In Fig 8 and 9, the LPV/H∞ strategy enhances the lateral stability. It minimizes the yaw rate error to ensure a good trajectory tracking. In Fig 8, a ”reference vehicle” yaw rate is given to emphasize on the good results in term of vehicle lateral dynamics improvement brought by the proposed approach. Fig 10 and 11 show the efficiency of the introduced LPV/H∞ control in term of stability enhancement of the vehicle. In Fig 10, the sideslip dynamics are attenuated in the LPV case, which allows to maintain the handling of the vehicle. The evolution of the vehicle in the β-ψ˙ plane,

2013 IFAC SSSC Grenoble, France, February 4-6, 2013

Fig. 12. Corrective yaw mo- Fig. 13. Additive steer angle ment. δ+ .

Fig. 14. Rear left braking Fig. 15. Rear right braking torque. torque. clearly demonstrates that the LPV strategy prevents the car to go beyond the stability region limits. The actuators contribution for improving the stability and the performances of the vehicle is illustrated via Fig 12, 13, 14 and 15. The braking control is activated for ρ = ρ and limited for ρ = ρ (see Doumiati et al. (2011a)). The braking controller provides a corrective yaw moment: tr ∆Fx (17) Mz∗ = 2 where tr is the vehicle’s rear axle length, ∆Fx is the longitudinal force between the left and right driving wheels of the same axle. The braking torques can be deduced thanks to the following equation: (18) Tb,ij = Rw F xij , where Rw is the effective tire radius and F xi,j , the longitudinal tire force. 5. CONCLUSION This paper addressed the problem of vehicle dynamical stability and performances improvement. It introduced a new LPV/H∞ global chassis control strategy involving different actuators, namely, suspensions, electro-mechanical rear braking and active steering ones. The main contribution is the innovative way of using the load transfer monitoring as a varying parameter to distribute the charge and to tune the suspensions on the four corners of the vehicle to enhance the vertical performances. Another novelty is the use of a stability index, based on the sideslip dynamics supervision, to coordinate the actuators actions and keep the manoeuvrability and the stability of the vehicle. The next step will be to develop the same strategy for high performance actuators and semi-active suspensions. REFERENCES Chou, H. and d’Andr´ea Novel, B. (2005). Global vehicle control using differential braking torques and active suspension forces. Vehicle System Dynamics, 43(4), 261–284. 814

Do, A.L., Sename, O., and Dugard, L. (2010). An LPV control approach for semi-active suspension control with actuator constraints. In Proceedings of the IEEE American Control Conference (ACC), 4653 – 4658. Baltimore, Maryland, USA. Doumiati, M., Sename, O., Dugard, L., Martinez-Molina, J., Gspr, P., and Szabo, Z. (2011a). Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent riccati equation technique. Proc.Vehicle Sys. Dyn. Doumiati, M., Victorino, A., Charara, A., and Lechner, D. (2011b). On board real-time estimation of vehicle lateral tire-forces and sideslip angle. IEEE Transactions on Mechatronics. Doumiati, M., Victorino, A., Lechner, D., Baffet, G., and Charara, A. (2010). Observers for vehicle tyre/road forces estimations: experimental validation. Vehicle Sys. Dyn, 48, 1345–1378. Fergani, S., Sename, O., and Dugard, L. (2012a). A lpv/H∞ global chassis controller for performances improvement involving braking, suspension and steering systems. In Proceedings of the 7th IFAC Symposium on Robust Control Design. Aalborg, Denmark. Fergani, S., Sename, O., and Dugard, L. (2012b). Performances improvement through an lpv/h∞ control coordination strategy involving braking, semi-active suspension and steering systems. In Proceedings of the 51th IEEE Conference on Decision and Control (CDC). Maui, Hawaii, Denmark. G´ asp´ ar, P., Szab´ o, Z., Bokor, J., Poussot-Vassal, C., Sename, O., and Dugard, L. (2007). Toward global chassis control by integrating the brake and suspension systems. In Proceedings of the 5th IFAC Symposium on Advances in Automotive Control (AAC). Aptos, California, USA. He, J., Crolla, D., Levesley, M., and Manning, W. (2006). Coordination of active steering, driveline, and braking for integrated vehicle dynamics control. Proc. Inst. Mech Engineers, PartD: Automobile Engineering. N´emeth, B. and G´ asp´ ar, P. (2011). Design of actuator interventions in the trajectory tracking for road vehicles. In Proceedings of the 51th IEEE Conference on Decision and Control (CDC). Orlando, Florida, USA. Poussot-Vassal, C., Sename, O., Dugard, L., G´ asp´ ar, P., Szab´ o, Z., and Bokor, J. (2011a). Attitude and handling improvements through gain-scheduled suspensions and brakes control. Control Engineering Practice, 19(3), 252 – 263. Poussot-Vassal, C., Sename, O., Dugard, L., and Savaresi, S.M. (2011b). Vehicle dynamic stability improvements through gain-scheduled steering and braking control. Vehicle System Dynamics, 49:10, 1597–1621. Savaresi, S., Poussot-Vassal, C., Spelta, C., Sename, O., and Dugard, L. (2010). Semi-Active Suspension Control for Vehicles. Elsevier - Butterworth Heinemann. Scherer, C. (1996). Mixed H2 /H∞ control for time-varying and linear parametrically-varying systems. International Journal of Robust and Nonlinear Control, 6(9-10), 929–952.