Ali Hamdan

Abbas Chokor

Moustapha Reine Talj

M Doumiati

A centralized multilayer LPV /H ∞ control architecture for vehicle's global chassis control, and comparison with a decentralized architecture

Keywords: Centralized Multilayer Control, LPV /H ∞, Global Chassis Control, Active Suspensions, Direct Yaw Control, Active Front Steering, decentralized control

published or not. The documents may come     A centralized multilayer LPV/H-infinity control architecture for vehicle's global chassis control, and comparison with a decentralized architecture

INTRODUCTION

Active safety is an important issue considered in intelligent vehicles. According to the "National Highway Traffic Safety Administration (NHTSA)" statistics, human's faults cause almost 90% of road accidents as explained in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]. Advanced Driving Assistance Systems (ADAS) have been developed for several years in order to enhance the stability of road vehicles and to help the driver in maintaining the control of the vehicle under dangerous situations. ADAS systems are formed by several single-actuator approaches that have been proposed and marketed, such as: Electronic Stability Program (ESP) or Direct Yaw Control (DYC) to enhance the vehicle lateral stability; Active Front Steering (AFS) to mainly improve the vehicle maneuverability or lane keeping; and (Semi-) Active Suspensions (AS) to improve comfort, road holding and rollover avoidance [START_REF] Chen | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF]]. Many advanced studies are developed in literature to improve the global performance of the vehicle in different driving situations. These studies suggest coordination between several ADAS systems known as Global Chassis Control (GCC). The GCC system deals with the complexity of control problems for Multi-Input-Multi-Output (MIMO) systems. The main objective of the GCC is the coordination between several actuators to improve the vehicle global behavior in terms of maneuverability and lateral stability depending on the driving situation. Many advanced control approaches have been proposed for this issue. The authors in [START_REF] He | Coordination of active steering, driveline, and braking for integrated vehicle dynamics control[END_REF] applied a decentralized approach where they developed an AFS controller for maneuverability purpose and a DYC controller for lateral stability, This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF).

based on sliding mode technique, and then a monitor coordinates between the two controllers according to the driving situations. However, the overall stability of the system cannot be guaranteed in the decentralized approach, especially when the two controllers can be actuated concurrently. In [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF], the authors propose several robust and optimal centralized controllers for the MIMO system based on the LPV/H ∞ control technique, where the LPV /H ∞ controller promotes or reduces the steering and braking to enhance maneuverability and lateral stability. With this approach, the overall stability of the system is guaranteed and a polytopic approach is used to actuate the different controllers. However, these controllers were synthesized while disregarding the roll motion; the deduced rollover enhancement was a consequence of the lateral stability control. Authors in [START_REF] Chen | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF], [START_REF] Sename | Robust control and linear parameter varying approaches: application to vehicle dynamics[END_REF] have presented several centralized LPV /H ∞ controllers, where AFS, DYC and AS are used to control the lateral and vertical vehicle dynamics. From the other side, authors in [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF] and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF], have used the roll angle and roll rate to control the vehicle load transfer that leads to rollover avoidance. Furthermore, authors deduced lateral stability improvement as a consequence of roll control. All these interesting research have motivated us to study the control of the vehicle yaw rate, the side slip angle and the roll angle in order to improve the overall vehicle performance. Thus, in our present work, a new centralized multilayer control structure is developed to improve the maneuverability, lateral stability, and rollover avoidance using steering, braking actuators and active suspension system. The global centralized multilayer control architecture is shown in Fig. 1, and is developed later. The paper contributions are as follows:

δ d δ d V x δ c M z θ θ ref =0 - + + - ψ, β, β, θ, θ, V x .. . β Decision Layer Control Layer MIMO LPV / H ∞ β ref ψ ψref + - δ c a Tb rr Tb rl ρ 1 ρ 2 ( ρ 1 , ρ 2 ) SI ( β, β) LTR ( θ, θ)
Actuator Layer

Disturbances ( M d , ψ , F d , y , M d ,θ ) + + δ t AS M θ 4 * U ij

Centralized Controller

Fig. 1. Global chassis control architecture

• A new centralized control design, which merges the yaw rate control, the side-slip angle control, and the roll control, in one single centralized controller to maintain internal stability when switching between maneuverability, lateral stability and rollover avoidance objectives. • A comparison between the proposed controller, and a decentralized one, developed in the laboratory and based on sliding mode technique.

The paper structure is as follows: Section 2 exposes the extended bicycle model of the vehicle based on the combination of the coupled lateral (yaw and side-slip) and roll motions.

In Section 3, the proposed centralized control architecture is detailed, starting by a presentation of the MIMO LPV /H ∞ as a model-based controller. Then we pass to detail the control objectives represented as variable-weighted filters, to finally develop the LPV /H ∞ controller which guarantees H ∞ performances between the exogenous inputs and the controlled variables, based on offline Linear Matrix Inequalities LMI optimization, in the framework of the polytopic approach. A decentralized architecture developed in the laboratory is presented briefly in this section. Simulation validation of the proposed approach is reported in Section 4. Finally, the conclusions and the perspectives of this work are given in Section 5.

VEHICLE MODEL

The vehicle is a group of interconnected mechanical and electrical systems that make the vehicle behavior nonlinear. The ADAS systems such as AFS (Active Front Steering), active suspensions, differential braking, etc, improve the vehicle's performance (lateral motion, yaw motion, roll motion, etc.).

A complete nonlinear vehicle model has been developed in [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF]. However, this model is a nonlinear model that does not respond to the formulation of control problems. For this reason, a linear simplified LTI vehicle model is used to develop the GCC controller. This LTI model is a coupled yaw-lateral-roll linear vehicle model, inspired from literature [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF]], and is given by the following equations of "Plant P":

PlantP :            I z ψ = F y f l f + F yr l r + I xz θ + M z + M d, ψ , MV β + ψ = F y f + F yr + M s h θ θ + F d,y , I x + M s h 2 θ θ = M s h θ V β + ψ + (M s gh θ -K θ )θ -C θ θ + M d,θ , (1)
where the vehicle parameters and variables are given in Table 1. F y f represents the lateral force of the front left and right tires merged together at the center of the front axle. Similarly, F yr is noted for the rear axle. F y f and F yr are given as:

F y f = µC f α f , F yr = µC r α r , (2)
and the tires slip angles as:

α f = -β - l f ψ V + δ t , α r = -β + l r ψ V .
(3) By substituting (3) in (2), and then by substituting (2) in (1), the state space representation of the Plant P can be represented in (4) (given next page), where X = [ ψ, β , θ , θ ] T is the state vector, U = [δ c , Mz] T is the vector of control inputs, D = [M d, ψ , F d,y , M d,θ ] T is the vector of exogenous inputs. Noting that the matrix A ∈ IR 4×4 , and the input matrices B u ∈ IR 4×3 and B d ∈ IR 4×3 . In real time control, the output controlled variables ψ and θ are given at the center of gravity (CG) of the vehicle by a gyrometer; θ is estimated by a simple time integration from θ and could be directly delivered from the Inertial Measurement Unit (IMU) if available. The other states, side-slip angle β and its velocity β , could be calculated by an estimation. To do that, many observer approaches that deal with the real time implementation and vehicle dynamics have been presented in the literature, e.g. an observer based on Extended Kalman Filter EKF as proposed in [START_REF] Chen | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF]. It should be noticed that the "bicycle model" used in the control layer of Fig. 1 is presented in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] and is given in (5):

ψre f βre f =   -µ l f 2 c f +l r 2 c r I z V x µ l r c r -l f c f I z -1 + µ l r c r -l f c f MV x 2 -µ c f +c r MV x   ψre f β re f + µ l f c f I z µ c f MV x δ d , (5)
where δ d is the driver steer angle on the front wheels, ψre f is the desired reference yaw rate, β re f is the corresponding side slip angle, and V x is the vehicle longitudinal speed, considered as a varying parameter. For security reasons, the authors in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] propose to saturate β re f and ψre f below a threshold, as described in (6):

| ψre f |≤| 0.85µg V x | β re f = arctan(0.02µg) (6) Ẋ =     ψ β θ θ     =   
a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 0 0 0 1 a 41 a 42 a 43 a 44

   A    ψ β θ θ    X +    b u,11 b u,12 b u,13 b u,21 b u,22 b u,23 0 0 0 b u,41 b u,42 b u,43    B u δ d + δ c M z M θ U +    b d,11 0 0 0 b d,22 0 0 0 0 0 0 b d,43    B d M d, ψ F d,y M d,θ D ; y = X.
(4)

+ - + - + - W ψ (ρ 1 ) W β (ρ 1 ) W θ ( ρ 2 ) Wδ (ρ 1 ) W M z (ρ 1 ) δ c M z K LPV / H ∞ (ρ 1 , ρ 2 ) z 1 z 2 z 3 z 4 z 5 Vehicle LTI model (Plant P) ψ β θ ψ β θ ψ des β des θ des e ψ e β e θ M d , ψ F d , y M d ,θ δ c M z θ Σ g Mθ Mθ W M θ ( ρ 2 ) z 6
Fig. 2. Control layer architecture

GLOBAL CHASSIS CONTROL

Centralized Control Architecture:

In this subsection, we present a detailed synthesis of the centralized multi-layer global chassis control architecture of Fig. 1, based on the LPV /H ∞ theory. In the control layer, the output variables i.e the vehicle yaw rate ψ, the side-slip angle β , and the suspended mass roll θ are controlled and optimized together through an optimal MIMO LPV /H ∞ centralized controller, in order to enhance the vehicle maneuverability, the lateral stability and the rollover avoidance. θ is an exogenous output.

The desired states ψre f , and β re f are given in (5). In addition, ρ 1 and ρ 2 are two time-varying scheduling gains/parameters to organize the objectives of the MIMO LPV /H ∞ controller.

A decision layer is developed to control the situation of the vehicle; it sends the values of scheduling parameters, based on two criteria: lateral stability (SI) and load transfer ratio (LT R), discussed later. The actuator layer contains AFS, DYC and AS; it generates the physical inputs to vehicle system.

i) Control layer:

The architecture of the control layer is presented in Fig. 2. It contains the controller K LPV /H ∞ (ρ 1 , ρ 2 ) to be developed, the generalized plant ∑ g , where ρ 1 and ρ 2 are two endogenous weighted parameters determined by the decision-making monitor according to the driving situations and the LTI model (Plant P) used in the synthesis of this controller. The inputs of K LPV /H ∞ (ρ 1 , ρ 2 ) controller are the errors between the desired states and the actual ones of the yaw rate e ψ , the side-slip angle e β , and the roll angle e θ . Noting that the actual yaw rate ψ, side slip angle β , and roll angle θ are the outputs variables to be controlled and they are delivered from the LTI model (Plant P). The inputs of the Plant P are the AFS angle δ c , the moment M z around z axis (generated by the DYC) and the moment M θ around the roll axis (generated by the AS); M d, ψ , F d,y , and M d,θ are the disturbances related to the road status and weather conditions like wind (exogenous inputs). W ψ (ρ 1 ), W β (ρ 1 ), W θ (ρ 2 ), W δ (ρ 1 ), W M z (ρ 1 ) and W M θ (ρ 2 ) are the weighting functions de-termined in order to define the performance objectives Z 1 , Z 2 , and Z 3 and the actuator limitations Z 4 , Z 5 and Z 6 . The general form of these functions (see [START_REF] Doumiati | Robust lpv control for vehicle steerability and lateral stability[END_REF]]) depends on the simulated vehicle and integrated actuators:

-W ψ (ρ 1 ) weights the yaw rate signal:

W ψ (ρ 1 ) = ρ 1 s/M 1 + 2π f 1 s + 2π f 1 T 1 , (7)
where M 1 is the margin of robustness, and T 1 is the tolerated tracking error on e ψ . W ψ (ρ 1 ) is defined to diminish the yaw rate error in the range of frequencies lower than the roll-off frequency f 1 where the vehicle operates [START_REF] Heißing | Chassis handbook: fundamentals, driving dynamics, components, mechatronics, perspectives[END_REF]]. W ψ (ρ 1 ) is linearly parametrized by the varying parameter ρ 1 , where ρ 1 ∈ ρ 1 ≤ ρ ≤ ρ 1 ( with ρ 1 and ρ 1 are constants representing the lower and higher values of ρ 1 ). When ρ 1 = ρ 1 , maneuverability purpose is improved and the performance objective e ψ is penalized, on the contrary, when ρ 1 = ρ 1 , e ψ is relaxed and the lateral stability becomes a priority objective to be realized.

-W β (ρ 1 ) weights the side slip angle:

W β (ρ 1 ) = 1 ρ 1 s/M 2 + 2π f 2 s + 2π f 2 T 2 . (8)
M 2 , T 2 and f 2 have similar definitions as M 1 , T 1 and f 1 . W β (ρ 1 ) is designed similarly to W ψ (ρ 1 ). W β (ρ 1 ) is inversely dependent on the varying parameter ρ 1 . This is because the lateral stability is more penalized than maneuverability in critical situations. This issue is detailed later in the decision layer.

-W θ (ρ 2 ) weights the roll angle according to a scheduling parameter ρ 2 :

W θ (ρ 2 ) = ρ 2 s/M 3 + 2π f 3 s + 2π f 3 T 3 . (9)
M 3 , T 3 and f 3 have similar meanings as M 1 , T 1 and f 1 . W θ (ρ 2 ) is linearly parametrized by the varying parameter ρ 2 , where

ρ 2 ∈ ρ 2 ≤ ρ 2 ≤ ρ 2 (
ρ 2 and ρ 2 are constants representing the lower and higher values of ρ 2 ). When ρ 2 = ρ 2 , the performance objective e θ is penalized and the rollover avoidance is a priority. On the contrary, when ρ 2 = ρ 2 , e θ is relaxed and rollover is not a risk.

-W δ (ρ 1 ) weights the steering control signal, δ c :

W δ (ρ 1 ) = ( 1 ρ 1 )G 0 δ (s/2π f 4 + 1)(s/2π f 5 + 1) (s/α2π f 5 + 1) 2 , G 0 δ = (∆ f /α2π f 5 + 1) 2 (∆ f /2π f 4 + 1)(∆ f /2π f 5 + 1) , ∆ f = 2π( f 4 + f 5 )/2, (10)
where f 4 and f 5 are the lower and upper limits of the filter bandwidth [ f 4 , f 5 ]. This filter is proposed to force the active steering system to act in this range [ f 4 , f 5 ]. Otherwise, this filter ensures the activation of steering system below the cutof frequency ( f 5 ) and above the driver ones ( f 4 ) (see [START_REF] Doumiati | Robust lpv control for vehicle steerability and lateral stability[END_REF]). Note that steering system is promoted to enhance the maneuverability when ρ 1 = ρ 1 and vice versa.

-W M z (ρ 1 ) weights the braking, M z :

W M z (ρ 1 ) = ρ 1 10 -6 s/(2π f 6 ) + 1 s/(κ2π f 6 ) + 1 , (11)
where f 6 is the braking actuator cut-off frequency and κ to treat the braking actuator limitations (see [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]).

When ρ 1 = ρ 1 , the braking input is penalized, on the contrary, the braking control signal is relaxed when ρ 1 = ρ 1 . This design depends on the vehicle lateral stability.

-W M θ (ρ 2 ) weights the suspensions M θ :

W M θ (ρ 2 ) = ( 1 ρ 2 )10 -4 s/(2π f 7 ) + 1 s/(κ2π f 7 ) + 1 , ( 12
)
where f 7 is the cut-off frequency and κ determines the limitation of suspension system. When ρ 2 = ρ 2 , the suspension system is penalized, however, the suspension system is relaxed when ρ 2 = ρ 2 (case of rollover risk is detected). Note that we didn't consider the actuators' constraints in this control layer. However, the control inputs are filtered by using the weights above and the actuators' models in the actuator layer. In addition, the tuning of the gains ρ 1 and ρ 2 respects the time response of the actuators.

After determining the subsystems of Fig. 2, H ∞ control technique is applied in order to minimize the controlled outputs Z 1 , Z 2 , Z 3 , Z 4 , Z 5 and Z 6 in presence of disturbances M d, ψ , F d,y , M d,θ and exogenous inputs ψdes , β des , θ des . More information about the optimal LPV /H ∞ theory is presented in [START_REF] Sename | Robust control and linear parameter varying approaches: application to vehicle dynamics[END_REF] and [START_REF] Gu | Robust control design with MATLAB R[END_REF].

A "sysic" Matlab function (Robust Control Toolbox) is used to make the interconnection between ∑ g subsystems. The generalized plant ∑ g is LPV [Apkarian et al. (1995)], given as following as:

Σ g (ρ) : ẋ z y = A(ρ) B 1 (ρ) B 2 (ρ) C 1 (ρ) D 11 (ρ) D 12 (ρ) C 2 D 21 0 x w u , (13)
= [Z 1 , Z 2 , Z 3 , Z 4 , Z 5 , Z 6 ]
T is the controlled output vector. Note that the matrices B 2 , and D 12 depend on ρ, which is not consistent with the requirements of H ∞ synthesis for polytopic systems. Some filters on the control input have been used to solve this problem [Apkarian and Gahinet (1995)].

Problem resolution:

LMI based LPV /H ∞ : The problem of LPV /H ∞ is to find the controller K LPV /H ∞ (ρ 1 , ρ 2 ),
scheduled by the parameters ρ 1 and ρ 2 , such that:

K LPV /H ∞ (ρ) : ẋc u = A c (ρ) B c (ρ) C c (ρ) 0 x c y , (14)
This controller aims to minimize the H ∞ norm of the closedloop LPV system established by the equations ( 13) and ( 14). Several approaches exist in the literature to solve this problem such as: polytopic, gridding and Linear Fractional Transformation LFT [START_REF] Zin | Sur la commande robuste de suspensions automobiles en vue du contrôle global de châssis[END_REF]]. In our work, a polytopic approach [see [START_REF] Scherer | Multiobjective output-feedback control via lmi optimization[END_REF]] has been used for controller synthesis.

Applying the Bounded Real Lemma (BRL) extended to LPV systems and after a change of basis presented in [START_REF] Scherer | Multiobjective output-feedback control via lmi optimization[END_REF]], a non conservative LMI is formulated in (15) and a Semi-Definite Program (SDP) has been applied to solve these inequalities equations (see [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]), while minimizing γ for ρ

∈ Ω = [ρ 1 , ρ 1 ]X[ρ 2 , ρ 2 ].
The aim of polytopic approach is to find the A(ρ), B(ρ) and C(ρ) by using a common Lyapunov function i.e X(ρ) > 0 and Y (ρ) > 0 at each vertex of the polytope function of ρ ∈ Ω. Noting that the number of vertex is 4 (2 n ) where n is the number of exogenous parameters. Thus, the solution is given by the resolution of system ( 16) at each vertex of the convex hull Ω

ω 1 = (ρ 1 , ρ 2 ), ω 2 = (ρ 1 , ρ 2 ), ω 3 = (ρ 1 , ρ 2 ), ω 4 = (ρ 1 , ρ 2 ) :        C c (ρ) = C(ρ)M(ρ) -T B c (ρ) = N(ρ) -1 B(ρ) A c (ρ) = N(ρ) -1 ( A(ρ) -Y (ρ)A(ρ)X(ρ) -N(ρ)B c (ρ). C 2 X(ρ) -Y (ρ)B 2 (ρ)C c (ρ)M(ρ) -T )M(ρ) -T , ( 16
) where M(ρ)N(ρ) T = I -X(ρ)Y (ρ) with M(ρ) and N(ρ) are given by the user. More details about the computation solution have been presented in [START_REF] Scherer | Multiobjective output-feedback control via lmi optimization[END_REF]]. Therefore, referring to the polytopic approach, the final controller K LPV /H ∞ (ρ 1 , ρ 2 ) is the summation of each convex controller calculated on each vertex of polytope [Apkarian et al. (1995)]:

K LPV /H ∞ (ρ 1 , ρ 2 ) = α 1 K H ∞ (ω 1 ) + α 2 K H ∞ (ω 2 ) +α 3 K H ∞ (ω 3 ) + α 4 K H ∞ (ω 4 ), (17)
where

∑ i=4 i=1 α i (ρ 1 , ρ 2 ) = 1; α i (ρ 1 , ρ 2 ) > 0.
Depending on the driving situation given in Fig. 3, the different polytopic coordinates α i (ρ 1 , ρ 2 ) weight the controller on each vertex in order to build the final controller of our system. They are calculated by using the Matlab function"polydec" (Robust Control Toolbox):

α 1 = ρ 1 -ρ 1 ρ 1 -ρ 1 . ρ 2 -ρ 2 ρ 2 -ρ 2 ; α 3 = ρ 1 -ρ 1 ρ 1 -ρ 1 . ρ 2 -ρ 2 ρ 2 -ρ 2 ; α 2 = ρ 1 -ρ 1 ρ 1 -ρ 1 . ρ 2 -ρ 2 ρ 2 -ρ 2 ; α 4 = ρ 1 -ρ 1 ρ 1 -ρ 1 . ρ 2 -ρ 2 ρ 2 -ρ 2 . (18)
ii) Decision Layer:

The decision layer is dedicated to adjust the controller achievements according to the driver situations. This layer delivers the two endogenous parameters ρ 1 and ρ 2 based on two criteria, lateral stability (SI) and load transfer ratio (LT R). Before the determination of these parameters, let us introduce the definition of these important criteria in the decision of the driver situation.

-"Lateral Stability Index" SI:

The lateral stability index SI determines the orientation of the vehicle depending on the speed vector at the CG, and its rate of change. SI is given as (see [START_REF] Chen | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF]]):

SI = c 1 β + c 2 β , (19)
where c 1 and c 2 are estimated w.r.t the vehicle parameters and the shape of the road. SI varies between 0 and 1. An analysis of the driver situation is done depending on SI. For example, when SI ≤ SI the vehicle is in normal driving situations. Therefore, the AFS is activated to enhance the maneuverability and the lateral stability in the moderate range of SI, and the DYC is penalized. In the contrary, when SI increases progressively and becomes closer to SI limit (SI ≥ SI), a lateral stability enhancement is needed and the DYC is activated. Referring to this analysis, the scheduled gain ρ 1 is designed to provide the LPV /H ∞ controller, the necessary information about the weights to be pushed or attenuated. The relation between ρ 1 and SI is given through a "sigmoid" function (20) (see Fig. 4.a) that guarantees a continuous and smooth variation of ρ 1 . The load transfer ratio LT R reflects vertical charge transfer from the inside to the outside wheels w.r.t the corner (turn).

ρ 1 = ρ 1 - ρ 1 -ρ 1 1 + e -8 SI-SI (SI-SI+SI 2 ) . ( 20
)     A(ρ)X + XA(ρ) T + B 2 C(ρ) + C(ρ) T B T 2 ( * ) T ( * ) T ( * ) T A(ρ) + A(ρ) T YA(ρ) + A(ρ) T Y + B(ρ)C 2 +C T 2 B(ρ) T ( * ) T ( * ) T B 1 (ρ) T B 1 (ρ) T Y + D T 21 B(ρ) T -γI ( * ) T C 1 (ρ)X + D 12 C(ρ) C 1 (ρ) D 11 (ρ) -γI     < 0 and X(ρ) I I Y (ρ) > 0. (15) ρ 1 ρ 1 ρ 1 ρ 2 ρ 2 ρ 2 k H ∞ (ω 2 ) k H ∞ (ω 1 ) k H ∞ (ω 3 ) k H ∞ (ω 4 ) k LPV / H ∞ Critical
Fig. 3. Controller -Polytopic approach SI ρ 1 SI SI ρ 1 ρ 1 SI ρ 1 ρ 1 ρ 1 |LTR| ρ 2 LTR LTR ρ 2 ρ 2 1 1 a) b) 0 0
R is function of the roll angle, its rate of change and the lateral acceleration and is given by an estimation of different parameters, as follows (see [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]]):

LT R = r 1 θ + r 2 θ + r 3 a y , (21) where r 1 , r 2 and r 3 are estimated depending on the vehicle parameters. LT R varies between -1 and 1. When, LT R ≤ LT R, no rollover risk is detected and the suspension system is deactivated, until that LT R increases and becomes LT R ≥ LT R, so a rollover should be prevented and the active suspension system is promoted. To do this issue, a "sigmoid" function ( 22

ρ 2 = ρ 2 + ρ 2 -ρ 2 1 + e - 8 LT R-LT R (|LT R|-LT R+LT R 2 ) . ( 22
)
iii) Actuator layer:

The actuator layer includes the different actuators used to generate the physical inputs of the system. In our work, AFS, DYC and AS have been used to provide these inputs. The AFS is an electrical motor which provides the added steering angle δ a c . In order to ensure that the AFS actuator is able to provide the added steering angle demanded by the controller δ c , the AFS is modeled as follows:

δ a c = 2π f 5 (δ c -δ a c ), (23)
where δ a c follows δ c , f 5 is the actuator cut-off frequency. This actuator is bounded between -δ a c,max , +δ a c,max , with δ a c,max the maximum amount of steering angle that can be added by the AFS actuator.

In the same way, the DYC moment M z can be realized by applying a braking torque on the rear wheels of radius r [START_REF] Doumiati | Robust lpv control for vehicle steerability and lateral stability[END_REF]]. The applied braking torque is given as follows:

               T b rr = -2 * M z * r t r , T b lr = 0, i f M z ≤ 0, T b lr = 2 * M z * r t r , T b rr = 0, i f M z > 0, (24)
where T b lr and T b rr are the left and right differential braking torque respectively. A simple model for the electro mechanical braking (EMB) actuator is used. The EMB actuator is modeled as: Ṫ a b,r j = 2π f 6 (T b,r j -T a b,r j ), (25) where T a b,r j tracks T b,r j , f 6 is the actuator cut-off frequency. This actuator control is bounded between [0, T a b,max ], where T a b,max is the saturation of the EMB actuator. Finally, the M θ moment is achievable by applying the active suspensions force-actuators on each wheel. These forces are given in the following form (see [START_REF] Chokor | Rollover prevention using active suspension system[END_REF]

]):              U f l = 0.5 l r l f +l r M θ t f , U f r = -0.5 l r l f +l r M θ t f , U rl = 0.5 l f l f +l r M θ t r , U rr = -0.5 l f l f +l r M θ t r .
(26)

Decentralized Control Architecture:

The global decentralized multilayer control architecture of Fig. 5 is presented briefly in this subsection. This architecture has been developed in the frame of global chassis control in the laboratory and is used to compare the results between the centralized and decentralized architecture [START_REF] Chen | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF]]. This decentralized sliding mode approach is chosen for the comparison purpose, because it represents the industrial state of the art and it is robust in case of system's uncertainty, disturbance and possible sensor faults. The main difference between the two architectures is in the control layer. Thus, the output variables i.e the vehicle yaw rate ψ, the side-slip angle β , and the suspended mass roll θ are controlled independently by using the single-input, single-output controller based on the Super-Twisting Sliding Mode (STSM) technique. Let us introduce an overview of the theory of Super-Twisting Sliding Mode. The STSM is a robust control technique that forces the states of the system to reach a sliding surface during a finite time (convergence phase) and to stay on this surface (sliding phase) in presence of perturbations. Consider the second order system given as: ẍ = f (X,t) + g(X,t)u(t) (27) where X = [x, ẋ] T ∈ ℜ 2 is the state vector, u is the control input, and f , g are continuous functions. X des is the desired state of X with X des = [x des , ẋdes ] T ∈ ℜ 2 . The error vector is given by

δ d δ d V x δ c M z θ θ ref - + ψ , β , β ,θ , θ , V x ...

Decision Layer

Control Layer

ψψ ref δ c a Tb rr a Tb rl a λ ψ λ β SI (β , β ) LTR (θ , θ )
Actuator Layer Therefore, a sliding variable s with relative degree r = 1 w.r.t the control input, is defined as:

Perturbations (M d , ψ , F d , y , M d ,θ ) + + δ t λ θ - + β ref β STSM SISO SISO STSM SISO STSM STSM AS M θ 4 * U ij
s = ė + k e, (28)
The second order derivative of s is: s(s,t) = Φ(s,t) + ξ (s,t) u(t) (29) where Φ(s,t) and ξ (s,t) are the unknown bounded signals.

The goal of the Super-Twisting algorithm is to enforce the sliding variable s to converge to zero (s = 0) in finite time. Assume that there exist positive constants S 0 , b min , b max , C 0 , U max verifying for all x ∈ ℜ n and |s(x,t)| < S 0 :

|u(t)| ≤ U max |Φ(s,t)| < C 0 0 < b min ≤ |ξ (s,t)| ≤ b max (30)
Thus, the control input based on the Super-Twisting Sliding Mode algorithm, is given as:

u(t) = u 1 + u 2 u 1 = -α 1 |s| τ sign(s), τ ∈]0, 0.5] u2 = -α 2 sign(s) (31)
α 1 and α 2 are positive gains. The following conditions guarantee the finite time convergence:

   α 1 ≥ 4C 0 (b max α 2 +C 0 ) b 2 min (b min α 2 -C 0 ) α 2 > C 0 b min (32)
The analysis of convergence is presented in [START_REF] Utkin | On convergence time and disturbance rejection of super-twisting control[END_REF]. An approximation function s |s|+ε is used to smooth the sign(s) function, where ε > 0. Let us define the three sliding variables for the three decentralized controllers as follows:

s ψ = e ψ = ψ -ψre f , s β = e β = β -β re f , s θ = ėθ + k θ e θ = ( θ -θre f ) + k θ (θ -θ re f ), (33)
The sliding variables s ψ , s β and s θ have a relative degree equal to one w.r.t δ c , M z and M θ respectively. Thus, in order to converge these variables to zero and the controlled states follow the desired ones, and based on the above discussion, the control inputs of AFS, DYC and AS applied to the system, are given by:

δ c = -α δ ,1 |s ψ | τ δ sign(s ψ ) -α δ ,2 t 0 sign(s ψ )dτ, M z = -α M z ,1 |s β | τ Mz sign(s β ) -α M z ,2 t 0 sign(s β )dτ M θ = -α M θ ,1 |s θ | τ M θ sign(s θ ) -α M θ ,2 t 0 sign(s θ )dτ, (34)
where α δ ,i , α M z ,i and α M θ ,i with i = [1, 2], are positive constants satisfying the conditions in (32). τ δ , τ M z and τ M θ are constants The decision layer is the same as before to monitor the driver situation based on SI and LT R criteria, then it delivers the different gains λ i in order to activate or deactivate the different actuators. These gains are given as follows (for more details see [START_REF] Chen | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF]]):

λ β = 1 1+e -8 SI-SI (SI- SI+SI 2 )
,

λ ψ = 1 -λ β . ( 35
)
λ θ = 1 1 + e - 8 LT R-LT R (LT R-LT R+LT R 2 ) , (36)
Concerning the actuator layer, it is the same as the one was developed in the centralized architecture.

SIMULATION RESULTS

In this section, the developed controller will be validated with a double lane change test at 110 km/h as initial speed. All simulations are done using Matlab/Simulink with a complete nonlinear model of the vehicle [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF]], validated on "SCANeR Studio" (OKtal) 1 [START_REF] Chokor | Rollover prevention using active suspension system[END_REF]]. Then, a

1 "SCANeR Studio" is a simulator dedicated to vehicle dynamics simulations. comparison is done between an uncontrolled vehicle, where no controller is used ("OL" as Open Loop) and controlled vehicle equipped with to different controllers, i.e, the centralized controller ("LPV /H ∞ ") and the decentralized one ("STSM" as Super-Twisting Sliding Mode). During this test, The driver's intention is to change the lane in a short time and then return to the same lane. Noting that in the two techniques of control, the active suspensions system AS aims to avoid rollover by decreasing the angle θ . But the validation of these controllers is done only on Matlab/Simulink because for this instant, the platform "SCANeR studio" simulator is not equipped with active suspensions system AS. The numerical values of the controller parameters used in the simulation are given in Table 2. Fig. 6, 7 and 8 show the different control variables such as the yaw rate, the side-slip angle and the roll angle respectively. Fig. 6 shows rate tracks the reference rate delivered the bicycle model, and both controllers have the same compared with the uncontrolled vehicle. Thus, the maneuverability objective is achieved. In order to improve the lateral stability and to prevent an undesirable driver situation, the side-slip angle should be reduced as shown in Fig. 7. Both control architectures have similar influence on this angle. On the other hand, the convergence of roll angle to zero allows

= M 2 = M 3 ; T 1 = T 2 = T 3 ; κ 2; 0.1 = 10%; 100 f 1 = f 2 = f 3 ; f 4 ; f 5 = f 6 = f 7
11.15 Hz; 1 Hz; 10 Hz c 1 ; c 2 ; r 1 ; r 2 ; r 3 9.55; 2.49; 2.5; 0.5; 0.1 SI; SI; LT R; LT R 0.6; 0.7; 0.6; 0. the avoidance of rollover risk, by reducing the load transfer ratio LT R. The Fig. 8 shows that the LPV /H ∞ controller is capable to more the roll angle to zero compared to the STSM controller that is less performant w.r.t to LPV /H ∞ controller. Noting that the choice and the tuning of parameters ρ 1 and ρ 2 (Fig. 11) is not obvious since LPV /H ∞ controller aims to compromise between the different control objectives in order to give good results of optimality. For this reason, some oscillations appear in the Lateral stability index (Fig. 9) and the load transfer ratio (Fig. 10). Therefore, ρ 1 is chosen as ρ 1 = ρ 1 when SI ≤ SI in order to promote the maneuverability objective, while ρ 1 = ρ 1 for a lateral stability improvement through the activation of differential braking actuators. Similarly, ρ 2 is chosen as ρ 2 = ρ 2 almost all the time, except 1 s and 3 s, where LT R is less than LT R = 0.6 and there is no risk of rollover. Around 1 s and 3 s, ρ 2 = ρ 2 in order to increase the use of the active suspensions that diminish the roll angle, when the LT R becomes higher then the maximal threshold (see Fig. 10). Fig. 12 shows the driver steering angle δ d , the AFS steering angle of both controllers δ c and the total steering angle applied to the vehicle δ t . The oscillations appear in δ t with the LPV /H ∞ because the controller forced the maneuverability objective. Fig. 13 shows the differential braking torque of rear wheels. The decentralized controller activates more the braking to ameliorate the lateral stability, while the LPV /H ∞ saves energy. Fig. 14 and 15 show the AS control inputs of each controller. The vehicle speed is less dropped in the centralized approach since less braking is applied as can be seen from Fig. 16.

CONCLUSION AND PERSPECTIVES

To conclude, in this paper a centralized multilayer LPV /H ∞ control architecture has been developed to improve the overall vehicle performance. A coordination of the Active Front Steering, Direct Yaw Control and Active Suspensions in one centralized controller has been proposed, to enhance the global behavior of the system. The proposed controller is validated in Matlab/Simulink and a comparison is done with another decentralized approach based on the Super-Twisting Sliding Mode (STSM) technique. Results confirm the importance of active suspensions in the centralized approach to prevent the rollover risk. In the Future, the LPV /H ∞ controller will be extended, in order to realize more objectives concerning the vertical displacement, control of pitch-angle...with the introduction of artificial intelligence (AI)-based techniques to improve the decision layer and the tuning of gains, and to make the controller more robust and optimal. We will consider also the variation of the road adherence, and the generalization of centralized approach especially for tuning gains.

  where ρ = {ρ 1 , ρ 2 }, x is the vector of states variables of Plant P and of the weighting functions, u = [δ c , M z , M θ ] T represents the control inputs, w = [ ψdes , β des , θ des , M d, ψ , F d,y , M d,θ ] T is the exogenous input vector, y = [ ψ, β , θ ] T is the measurement vector fed-back to the controller, y e = [ θ ] T is the exogenous output, and z

Fig. 4 .

 4 Fig. 4. Scheduling parameters -"Load Transfer Ratio" LT R:The load transfer ratio LT R reflects vertical charge transfer from the inside to the outside wheels w.r.t the corner (turn).R is function of the roll angle, its rate of change and the lateral acceleration and is given by an estimation of different parameters, as follows (see[START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]]):LT R = r 1 θ + r 2 θ + r 3 a y , (21) where r 1 , r 2 and r 3 are estimated depending on the vehicle parameters. LT R varies between -1 and 1. When, LT R ≤ LT R, no rollover risk is detected and the suspension system is deactivated, until that LT R increases and becomes LT R ≥ LT R, so a rollover should be prevented and the active suspension system is promoted. To do this issue, a "sigmoid" function (22) (see Fig. 4.b) is given to illustrate the relation between ρ 2 and |LT R|:

  ) (see Fig. 4.b) is given to illustrate the relation between ρ 2 and |LT R|:

Fig. 5 .

 5 Fig. 5. Decentralized global chassis control architecture E = X -X des = [e, ė] T ∈ ℜ 2 where e = xx des and ė = ẋẋdes .Therefore, a sliding variable s with relative degree r = 1 w.r.t the control input, is defined as:

  Fig. 6. Yaw rate comparison

Fig. 11 .

 11 Fig. 9. Lateral stability comparison

Fig. 14 .

 14 Fig. 12. angle comparison

  Fig. 15. AS control inputs LPV /H ∞ controller

Table 1 .

 1 Parameters Values for Simulation

	Symbols	Description	Parameters values
	ψ	Vehicle yaw rate	[rad/s]
	β	Vehicle side slip angle at CG	[rad]
	θ	Sprung mass roll angle	[rad]
	F y i	Lateral forces at the i axle	[N]
	δ d	Driver steering angle	[rad]
	V	Vehicle speed	[m/s]
	I x	Roll moment of inertia of sprung mass	534 [kg.m 2 ]
	I z	Vehicle yaw moment of inertia	1970 [kg.m 2 ]
	I xz	Vehicle yaw-roll product of inertia	743 [kg.m 2 ]
	t f	Half front track	0.773 [m]
	t r	Half rear track	0.773 [m]
	l f	Wheelbase to the front	1.0385 [m]
	l r	Wheelbase to the rear	1.6015 [m]
	h θ	Sprung mass roll arm	0.27 [m]
	M s	Sprung mass	1126.4 [kg]
	C f ,C r	Front, rear tire cornering stiffness	76776 [N/rad]
	K θ	Roll suspension angular stiffness	30000 [N.m/s]
	C θ	Roll suspension angular damper	10000 [N.m/s]
	g	Gravity constant	9.81 [m/s 2 ]
	µ	Road adherence coefficient	dry surface= 1 [-]

Table 2 .

 2 Controller Parameters for Simulation

	Parameters	Values
	M 1

ACKNOWLEDGEMENTS

The like to thank the Hauts-de-France Region and the European Regional Development Fund (ERDF) 2014/2020 for the funding of this work, through the SYSCOVI project. This work was also carried out in the framework of the Labex MS2T, (Reference ANR-11-IDEX-0004-02) and the Equipex ROBOTEX (Reference ANR-10-EQPX-44-01) which were funded by the French Government, through the program "Investments for the future" managed by the National Agency for Research.


Ali Hamdan

Abbas Chokor

Reine Talj
email: reine.talj@hds.utc.fr

Moustapha Doumiati

A decentralized multilayer sliding mode control architecture for vehicle's global chassis control, and comparison with a centralized architecture

Keywords: Decentralized Multilayer Control Architecture, Global Chassis Control, Active Suspensions, Direct Yaw Control, Active Front Steering, Sliding Mode Control

This paper presents a decentralized Global Chassis Control (GCC) architecture. The objective of this global chassis controller is to improve the overall vehicle performance i.e maneuverability, lateral stability and rollover avoidance, by coordinating the Active Front steering, Direct Yaw Control and Active Suspensions in a decentralized architecture. The developed architecture is multilayer, and based on higher order sliding-mode control, the super-twisting algorithm. The proposed GCC is validated by simulation using Matlab/Simulink, and a comparison is done with a centralized LPV /H ∞ architecture that has been developed in the laboratory, to show the difference in behavior and performance of both strategies of control.

INTRODUCTION

Active safety is an important feature into the intelligent vehicles. According to the "National Highway Traffic Safety Administration (NHTSA)" statistics, human's faults cause almost 90% of road accidents as explained in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]. Advanced Driving Assistance System (ADAS) influences on the behavior of vehicle on the road, and helps the driver in the driving process in order to avoid a dangerous situation. ADAS systems are formed by several single-actuator approaches that have been proposed and marketed, such as: Electronic Stability Program (ESP) or Direct Yaw Control (DYC) to enhance the vehicle lateral stability; Active Front Steering (AFS) to mainly improve the vehicle maneuverability or lane keeping; and (Semi-) Active Suspensions (AS) to improve comfort, road holding and rollover avoidance [START_REF] Chokor | A global chassis control system involving active suspensions, direct yaw control and active front steering[END_REF]. Many advanced studies are developed in literature to improve the global performance of the vehicle in different driving situations. These studies suggest coordination between several ADAS systems known as Global Chassis Control (GCC). The GCC system deals with the complexity of control problems for Multi-Input-Multi-Output (MIMO) systems. The main idea of the GCC is the coordination between the AFS and the DYC to improve the vehicle maneuverability and lateral stability depending on the driving situation. Many advanced control approaches have been proposed for this issue. The authors in [START_REF] He | Coordination of active steering, driveline, and braking for integrated vehicle dynamics control[END_REF] applied a decentralized approach where they developed a DYC controller for lateral stability purpose and an AFS controller for maneuverability purpose, based on sliding mode technique, and then a monitor switches between the two controllers according to the driving situations. However, the overall stability of the system is not guaranteed in the decentralized approach, but it is simple to develop, implement and tune. In [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF], [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF], the authors propose several robust and optimal centralized controllers for the MIMO system based on the LPV/H ∞ control technique, where the LPV /H ∞ controller penalizes or relaxes the steering and braking to enhance maneuverability and lateral stability. By using this method, the overall stability of the system is guaranteed and a polytopic approach is used to actuate the different controllers. However, these controllers were synthesized while disregarding the roll motion; the deduced rollover enhancement was a consequence of the lateral stability control. Authors in [START_REF] Sename | Robust control and linear parameter varying approaches: application to vehicle dynamics[END_REF], [START_REF] Chen | Integrated vehicle dynamics and control[END_REF] have presented several centralized LPV /H ∞ controllers, where AFS, DYC and AS are used to control the decoupled lateral and vertical vehicle dynamics. From the other side, authors in [START_REF] Van Tan | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF] and [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], have used the roll angle and its angular velocity to control the vehicle load transfer that leads to rollover avoidance. Moreover, authors deduced lateral stability improvement as a consequence of roll control. Centralized architectures are optimal in global performance, but are more complex to design and to implement, and could take an important amount of calculation. All these interesting research have motivated us to study the control of the vehicle yaw rate, the side slip angle and the roll angle in order to improve the overall vehicle performance. Thus, in our present work, a decentralized multilayer control structure, based on sliding mode super-twisting control approach, is developed to improve the maneuverability, lateral stability, and rollover avoidance using steering, braking actuators and active suspension system. A comparison between the proposed controller and a centralized architecture presented in [START_REF] Chokor | Design of a new gain-scheduled lpv/h ∞ controller for vehicle's global chassis control[END_REF] is done. The paper structure is as follows: Section 2 exposes the extended bicycle model of the vehicle based on the combination of the coupled lateral (yaw and side-slip) and roll motions. In Section 3, the proposed decentralized control architecture is detailed. Simulation validation of the proposed approach is reported in Section 4. Finally, the conclusions and the perspectives of this work are given in Section 5.

Vehicle model

The vehicle is a group of interconnected mechanical and electrical systems that make the vehicle behavior nonlinear. The ADAS systems such as AFS (Active Front Steering), active suspensions, differential braking, etc, improve the vehicle's performance (lateral motion, yaw motion, rolling motion, etc.). A complete nonlinear vehicle model has been developed in [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF]. However, this model is a nonlinear model that does not respond to the formulation of control problems. For this reason, a linear simplified LTI vehicle model is used to develop the GCC controller. It is an extended bicycle model, with coupled lateral/vertical dynamics. For vertical dynamics, the rolling motion is considered, for being the most critical for stabilization problems and rollover avoidance. Hence, this LTI model is a coupled yaw-lateral-roll linear vehicle model, inspired from literature [START_REF] Van Tan | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], and is given by the following equations of "Plant P":

PlantP :            I z ψ = F y f l f + F yr l r + I xz θ + M z + M d, ψ , MV β + ψ = F y f + F yr + M s h θ θ + F d,y , I x + M s h 2 θ θ = M s h θ V β + ψ + (M s gh θ -K θ )θ -C θ θ + M d,θ , (1)
where the vehicle parameters and variables are given in Table 1. F y f represents the lateral force of the front left and right tires merged together at the center of the front axle. Similarly, F yr is noted for the rear axle. F y f and F yr are given as:

F y f = µC f α f , F yr = µC r α r , (2)
and the tires slip angles as:

α f = -β - l f ψ V + δ t , α r = -β + l r ψ V . (3)
The reference "bicycle model" used in the control layer is presented in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] and is given in (4):

ψre f βre f =   -µ l f 2 c f +l r 2 c r I z V x µ l r c r -l f c f I z -1 + µ l r c r -l f c f MV x 2 -µ c f +c r MV x   ψre f β re f + µ l f c f I z µ c f MV x δ d , (4)
where δ d is the driver steer angle on the front wheels, ψre f is the desired reference yaw rate, β re f is the corresponding side slip angle, and V x is the vehicle longitudinal speed. For security reasons, the authors in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] propose to saturate β re f and ψre f below a threshold, as described in (5):

| ψre f |≤| 0.85µg V x | β re f = arctan(0.02µg) (5)

DECENTRALIZED GLOBAL CHASSIS CONTROL ARCHITECTURE

The global decentralized multilayer control architecture of Fig. 1 is presented in this section. The output variables i.e the vehicle yaw rate ψ, the side-slip angle β , and the suspended mass roll θ are controlled independently by using the single-input, singleoutput controller based on the Super-Twisting Sliding Mode (STSM) technique. Let us introduce an overview of the theory of Super-Twisting Sliding Mode. The STSM is a robust control technique that forces the states of the system to reach a sliding surface during a finite time (convergence phase) and to stay on this surface (sliding phase) in presence of perturbations. Consider the second order system given as:

ẍ = f (X,t) + g(X,t)u(t) (6)
δ d δ d V x δ c M z θ θ ref - + ψ , β , β ,θ , θ , V x ...

Decision Layer

Control Layer

ψψ ref δ c a Tb rr a Tb rl a λ ψ λ β SI (β , β ) LTR (θ , θ )
Actuator Layer where X = [x, ẋ] T ∈ ℜ 2 is the state vector, u is the control input, and f , g are continuous functions. X des is the desired state of X with X des = [x des , ẋdes ] T ∈ ℜ 2 . The error vector is given by E = X -X des = [e, ė] T ∈ ℜ 2 where e = xx des and ė = ẋẋdes . Therefore, a sliding variable s with relative degree r = 1 w.r.t the control input, is defined as:

Perturbations (M d , ψ , F d , y , M d ,θ ) + + δ t λ θ - + β ref β STSM SISO SISO STSM SISO STSM STSM AS M θ 4 * U ij
s = ė + k e, (7)
The second order derivative of s is:

s(s,t) = Φ(s,t) + ξ (s,t) u(t) (8)
where Φ(s,t) and (s,t) are the unknown bounded signals.

The goal of the Super-Twisting algorithm is to enforce the sliding variable s to converge to zero (s = 0) in finite time. Assume that there exist positive constants S 0 , b min , b max , C 0 , U max verifying for all x ∈ ℜ n and |s(x,t)| < S 0 :

   |u(t)| ≤ U max |Φ(s,t)| < C 0 0 < b min ≤ |ξ (s,t)| ≤ b max (9)
Thus, the control input based on the Super-Twisting Sliding Mode algorithm, is given as:

u(t) = u 1 + u 2 u 1 = -α 1 |s| τ sign(s), τ ∈]0, 0.5] u2 = -α 2 sign(s) (10)
α 1 and α 2 are positive gains. The following conditions guarantee the finite time convergence:

   α 1 ≥ 4C 0 (b max α 2 +C 0 ) b 2 min (b min α 2 -C 0 ) α 2 > C 0 b min (11)
The analysis of convergence is presented in [START_REF] Utkin | On convergence time and disturbance rejection of super-twisting control[END_REF]. An approximation function s |s|+ε is used to smooth the sign(s) function, where ε > 0. Let us define the three sliding variables for the three decentralized controllers as follows:

s ψ = e ψ = ψ -ψre f , s β = e β = β -β re f , s θ = ėθ + k θ e θ = ( θ -θre f ) + k θ (θ -θ re f ), (12)
The sliding variables s ψ , s β and s θ have a relative degree equal to one w.r.t δ c , M z and M θ respectively. Thus, in order to converge these variables to zero and the controlled states follow the desired ones, and based on the above discussion, the control inputs of AFS, DYC and AS applied to the system, are given by:

δ c = -α δ ,1 |s ψ | τ δ sign(s ψ ) -α δ ,2 t 0 sign(s ψ )dτ, M z = -α M z ,1 |s β | τ Mz sign(s β ) -α M z ,2 t 0 sign(s β )dτ M θ = -α M θ ,1 |s θ | τ M θ sign(s θ ) -α M θ ,2 t 0 sign(s θ )dτ, (13)
where α δ ,i , α M z ,i and α M θ ,i with i = [1, 2], are positive constants satisfying the conditions in [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF]. τ δ , τ M z and τ M θ are constants between ]0, 0.5].

The decision layer monitors the driving situation based on SI (lateral stability index) and LT R (load transfer ratio) criteria, then it delivers the different gains λ i in order to activate or deactivate the different actuators. These gains are given as follows:

λ β = 1 1+e -8 SI-SI (SI- SI+SI 2 )
,

λ ψ = 1 -λ β . (14)
λ θ = 1 1 + e - 8 LT R-LT R (LT R-LT R+LT R 2 ) , (15)

SIMULATION RESULTS

In this section, the developed controller will be validated with a double lane change test at 110 km/h as initial speed. All simulations are done using Matlab/Simulink with a complete nonlinear model of the vehicle [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF], validated on "SCANeR Studio" (OKtal)3 [START_REF] Chokor | Rollover prevention using active suspension system[END_REF]. Then, a comparison is done between an uncontrolled vehicle, where no controller is used ("OL" as Open Loop) and controlled vehicle equipped with two different controllers, i.e, the decentralized controller ("STSM" as Super-Twisting Sliding Mode) and a centralized controller ("LPV /H ∞ ") developed in the laboratory Heudiasyc, and presented in [START_REF] Chokor | Design of a new gain-scheduled lpv/h ∞ controller for vehicle's global chassis control[END_REF]. During this test, The driver's intention is to change the lane in a short time and then return to the same lane. Noting that in the two techniques of control, the active suspensions system AS aims to avoid rollover by decreasing the angle θ . angle and the roll angle respectively. Fig. 2 shows that the yaw rate tracks the reference yaw rate delivered by the bicycle model, and both controllers have almost the same behavior compared with the uncontrolled vehicle. Thus, the maneuverability objective is achieved. In order to improve the lateral stability and to prevent an undesirable driver situation, the side-slip angle should be reduced as shown in Fig. 3. Both control architectures have similar influence on this angle. On the other hand, the convergence of roll angle to zero allows the avoidance of rollover risk, by reducing the load transfer ratio LT R. The Fig. 4 shows that the LPV /H ∞ controller is capable to diminish more the roll angle to zero compared to the STSM controller. Fig. 5 shows the lateral stability and Fig. 6 presents the lateral load transfer ratio (LTR). Both SI and LTR are improved with both GCC architectures. Hence, lateral stability and rollover avoidance are enhanced.

CONCLUSION AND PERSPECTIVES

To conclude, a decentralized multilayer sliding mode control architecture has been developed to improve the overall vehicle performance. This enhancement is done by coordination of the Active Front Steering, Direct Yaw Control and Active Suspensions in a decentralized controller. The proposed controller is validated by using Matlab/Simulink and a comparison is done with a centralized approach based on the LPV /H ∞ technique, presented in [START_REF] Chokor | Design of a new gain-scheduled lpv/h ∞ controller for vehicle's global chassis control[END_REF]. Results show an almost similar performance of the decentralized scheme with its centralized equivalent. However, decentralized architecture is simpler and easier to tune and implement than centralized controller. Hence, the decentralized architecture could be much more interesting. In future works, we will work on the proof of the global stability of the system with the decentralized global chassis controller, a Lyapunov-based analysis will be done to show the convergence and boundedness of the solution. Validation on the Scaner Studio simulator and on a real vehicle platform will also be investigated. In addition, other performance index will be also used to do the benchmark comparing against the other conventional control approaches.

Fig. 1 .

 1 Fig. 1. Decentralized global chassis control architecture

Fig. 2 ,Fig. 2 .

 22 Fig. 2. Yaw rate comparison

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 3456 Fig. 3. Side-slip angle comparison

Table 1 .

 1 Parameters Values for Simulation

	Symbols	Description		Parameters values
	ψ	Vehicle yaw rate		[rad/s]
	β	Vehicle side slip angle at CG		[rad]
	θ	Sprung mass roll angle		[rad]
	F y i δ d	Lateral forces at the i axle Driver steering angle		[N] [rad]
	V	Vehicle speed		[m/s]
	I x	Roll moment of inertia of sprung mass	534 [kg.m 2 ]
	I z	Vehicle yaw moment of inertia	1970 [kg.m 2 ]
	I xz	Vehicle yaw-roll product of inertia	743 [kg.m 2 ]
	t f	Half front track		0.773 [m]
	t r	Half rear track		0.773 [m]
	l f	Wheelbase to the front		1.0385 [m]
	l r	Wheelbase to the rear		1.6015 [m]
	h θ	Sprung mass roll arm		0.27 [m]
	M s	Sprung mass		1126.4 [kg]
	C f ,C r	Front, rear tire cornering stiffness	76776 [N/rad]
	K θ	Rolling suspension angular stiffness	30000 [N.m/s]
	C θ	Rolling suspension angular damper	10000 [N.m/s]
	g	Gravity constant		9.81 [m/s 2 ]
	µ	Road adherence coefficient		dry surface= 1 [-]
		Stability and rollover Monitor
	Bicycle Model
		AFS	DYC
	Driver	Vehicle (SCANeR)
		Pedals

"SCANeR Studio" is a simulator dedicated to vehicle dynamics simulations.

Acknowledgement The authors would like to thank the Hauts-de-France Region and the European Regional Development Fund (ERDF) 2014/2020 for the funding of this work, through the SYSCOVI project. This work was also carried out in the framework of the Labex MS2T, (Reference ANR-11-IDEX-0004-02) and the Equipex ROBO-TEX (Reference ANR-10-EQPX-44-01) which were funded by the French Government, through the program "Investments for the future" managed by the National Agency for Research.


Junmin Deng

Sungjun Bae

Sunho Yoon

Mathieu Pasturel

Remi Marsac

Khalil Hanna
email: khalil.hanna@ensc-rennes.fr

Rémi Marsac

Khalil Hanna

Adsorption capacity of the corrosion products of nanoscale zerovalent iron towards emerging contaminants

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Because nanoscale zerovalent iron (NZVI) is an environmentally-safe material and exhibits great particle reactivity, it has been widely used in treatment processes of various organic and inorganic contaminants [START_REF] Joo | Oxidative Degradation of the Carbothioate 479 Herbicide, Molinate, Using Nanoscale Zero-Valent Iron[END_REF][START_REF] Ma | The tortoise versus the hare -482 Possible advantages of microparticulate zerovalent iron (mZVI) over 483 nanoparticulate zerovalent iron (nZVI) in aerobic degradation of contaminants[END_REF][START_REF] Tsarev | The short-term 486 reduction of uranium by nanoscale zero-valent iron (nZVI): role of oxide shell, 487 reduction mechanism and the formation of U(V)-carbonate phases[END_REF] . As a result, NZVI has become one of the most extensively studied nanomaterials in wastewater treatment and remediation of soil and groundwater. [START_REF] He | Effect of Structural Transformation 490 of Nanoparticulate Zero-Valent Iron on Generation of Reactive Oxygen Species, 491[END_REF][START_REF] Liu | Depassivation of Aged Fe0 by Ferrous Ions: 493 Implications to Contaminant Degradation[END_REF][START_REF] Phenrat | Electromagnetic Induction of 496 Zerovalent Iron (ZVI) Powder and Nanoscale Zerovalent Iron (NZVI) Particles 497 Enhances Dechlorination of Trichloroethylene in Contaminated Groundwater and 498 Soil: Proof of Concept[END_REF][START_REF] Wei | 500 Influence of nanoscale zero-valent iron on geochemical properties of groundwater 501 and vinyl chloride degradation: A field case study[END_REF] For the remediation action, the NZVI slurry is directly introduced into soil and groundwater systems, and NZVI particles migrate from the injection points to affected zones. [START_REF] Su | Travel distance and transformation of injected emulsified zerovalent 504 iron nanoparticles in the subsurface during two and half years[END_REF] During this journey, NZVI could encounter many electron acceptors resulting in partial or complete oxidation of NZVI particles (also called surface passivation).

These electron acceptors may include oxygen as in oxic environments, nitrate, etc. and targeted compounds, i.e. contaminants. [START_REF] Zhang | Nanoscale Iron Particles for Environmental Remediation: An 507 Overview[END_REF][START_REF] Reinsch | Chemical 509 Transformations during Aging of Zerovalent Iron Nanoparticles in the Presence of 510 Common Groundwater Dissolved Constituents[END_REF][START_REF] Ahn | Effects of oxidants on 513 in situ treatment of a DNAPL source by nanoscale zero-valent iron: A field study[END_REF][START_REF] Chen | Effect of natural organic matter 516 on toxicity and reactivity of nano-scale zero-valent iron[END_REF] This oxidation can lead to either formation of Fe II -bearing phases on the NZVI surface or complete oxidation to ferric (oxyhydr)oxides, depending upon various factors including type and concentration of co-existing species, reaction time and oxic/anoxic environments. For instance, lepidocrocite, magnetite and maghemite appeared to be the main secondary iron minerals formed upon the oxic corrosion of NZVI. [START_REF] Pullin | The effect of common groundwater anions on the aqueous corrosion of zero-valent iron nanoparticles and associated removal of aqueous copper and zinc[END_REF] Although the ability of NZVI to reductively transform a wide variety of compounds has been extensively investigated, little is known about the fate of injected NZVI particles in natural systems. In addition, NZVI passivation byproducts have been R e v i s e d m a n u s c r i p t 4 identified under oxic and anoxic conditions, [START_REF] Liu | Evolution of nanoscale zero-valent iron (nZVI) in water: Microscopic and spectroscopic evidence on the formation of nano-and micro-structured iron oxides[END_REF] but no data exist on the reactivity of these byproducts in nature. Indeed, the passivation byproducts (i.e., secondary Fe minerals) would continue to migrate in environmental settings and potentially meet other types of contaminants. They could bind co-existing contaminants and then influence their aqueous or colloidal transport in soil and groundwater. Comprehensive examination of the reactivity of these "abandoned" particles and their mobility in natural settings is essential for ecological risk assessments.

Here, we examined the interactions between NZVI (fresh or passivated) and nalidixic acid (NA), a quinolone antibiotic widely used in human and veterinary medicine. NA was selected as a target emerging contaminant because it has been frequently detected in the environment (at concentration levels ranging from ng•L -1 to μg•L -1 ). [START_REF] Poppe | Trends in Antimicrobial Resistance of Salmonella Isolated from Animals, Foods of Animal Origin, and the Environment of Animal Production in Canada, 1994-1997[END_REF][START_REF] Campioni | Prevalence of gyrA Mutations in Nalidixic Acid-Resistant Strains of Salmonella Enteritidis Isolated from Humans, Food, Chickens, and the Farm Environment in Brazil[END_REF] To control the NZVI oxidation in aqueous suspension, hydrogen peroxide (H2O2) was used under anoxic conditions (N2 glove box). pH and oxidation-reduction potential (ORP) values and dissolved Fe(II) concentration were measured throughout the reaction, and transformation of NZVI particles were monitored by X-ray diffraction, X-ray photoelectron spectroscopy and high resolution-transmission electron microscopy (HR-TEM) equipped with the selected area electron diffraction (SAED).

Adsorption tests were performed after total depletion of H2O2 in order to prevent any contribution from Fenton-like oxidation (mass balance was also checked) in NA removal. NA adsorption onto the resulting oxidized NZVI particles was evaluated as a function of pH and NA concentration. A surface complexation model was used to R e v i s e d m a n u s c r i p t 5 account for the impact of Fe(II) content on the NA adsorption into secondary Fe minerals.

Materials and methods

Chemicals and materials

Nalidixic acid (NA, ≥99.0%), sodium borohydride (NaBH4, ≥99.0%), ferric chloride hexahydrate (FeCl3•6H2O, ≥99.0%), hydrogen peroxide solution (H2O2, 30%), ferrous chloride tetrahydrate (FeCl2•4H2O, ≥99.0%), 1,10-phenanthroline (≥99.0%), acetic acid (≥99.5%), hydrochloric acid (HCl, 37%), sodium hydroxide (NaOH, ≥99.0%), glycerol (≥99.5%), tetracycline hydrochloride (TET, ≥99.0%), 4morpholineethanesulfonic acid (MES, ≥99.5%), 4-(2-hydroxyethyl)piperazine-1ethanesulfonic acid (HEPES, ≥99.5%), tris(hydroxymethyl)aminomethane (TRIZMA base, ≥99.9%) and Tris(hydroxymethyl)aminomethane hydrochloride (TRIZMA HCl, ≥99.5%) were all purchased from Sigma-Aldrich, France. Leonardite Humic Acid standard (LHA) was purchased from the International Humic Substances Society (IHSS). Maghemite (γ-Fe2O3) was purchased from Alfa Aesar, with a high purity (>99.0%). Magnetite (Fe3O4), hematite (α-Fe2O3) and lepidocrocite (γ-FeOOH) were synthesized as previously reported. [START_REF] Schwertmann | Iron Oxides in the Laboratory: Preparation and Characterization[END_REF] Acetonitrile (99.99%, Sigma) and acetic acid (99.7%, ACROS) were used for mobile phase of high-performance liquid chromatography (HPLC). NA stock solution (5 mM) and ferrous chloride stock solution (100 mM) were prepared with 0.1 M NaOH and 0.1M HCl, respectively. Glassware R e v i s e d m a n u s c r i p t 6 was soaked in a 5% (v/v) HCl container for at least 48 h and rinsed before use. Unless specifically stated, all solutions were prepared with deoxgenated deionized water (DDIW, 18.2 MΩ•cm) prepared by purging with nitrogen (N2, 99.99%) for 4 hours and stored in anaerobic chamber (JACOMEX).

Synthesis and characterization of NZVI

NZVI was synthesized following our previous work. [START_REF] Bae | Effect of NaBH4 on properties of nanoscale zero-valent iron and its catalytic activity for reduction of p -nitrophenol[END_REF] Briefly, 500 mL of sodium borohydride solution (0.9 M) was added dropwise into the 500 mL of ferric chloride hexahydrate solution (0.11 M) a fixed rate of 1 mL/min in anaerobic chamber. After finishing the synthesis, the precipitates in the suspension were separated by magnet, then washed 3 times with DDIW. The obtained NZVI was dried and stored inside the anaerobic chamber.

The oxidized particles were then analyzed by X-ray diffraction (XRD, D8, BRUKER). The oxidized NZVI suspensions were washed with DDIW for three times, and dried in a vacuum freeze drier (-52℃, 24 h). Then, the dried samples were transferred to sample holders and treated with 1:1 (v:v) glycerol solution to avoid the surface oxidation during the analysis of XRD. [START_REF] Bae | Influence of Riboflavin on Nanoscale Zero-Valent Iron Reactivity during the Degradation of Carbon Tetrachloride[END_REF] X-ray photoelectron spectroscopy (XPS, Sigma Probe system, Thermo) analysis was performed for four different samples (i.e., pristine NZVI, NZVI after reaction with H2O2 (3, 15, and 18 h). We used the power source (Al Kα X-ray, 1486.7 eV) of 75 W and the C 1s peak at 285 eV as a reference for correction of surface charging effects. The morphological characterization of R e v i s e d m a n u s c r i p t 7 different oxidized NZVIs were investigated by high resolution-transmission electron microscopy (HR-TEM, JEM-2100, JEOL) equipped with the selected area electron diffraction (SAED). The specific surface area of oxidized NZVIs was analyzed by multi-point N2 adsorption isotherm (Micromeritics, USA). The average particle size and zeta potential of the oxidized NZVI particles were measured by Zetasizer MAS (Matec Applied Sciences).

Analytical methods

Batch experiments were conducted in 500 mL flasks in anaerobic chamber to avoid the effect of dissolved oxygen during the reaction. 0.1 g NZVI was transferred to the flask containing 500 mL DDIW with stirring at 600 rpm to prepare an initial NZVI dosage of 200 mg/L. A portable pH-ORP meter (HANNA, HI991003) was used to monitor the variations in pH and ORP during the oxidation and adsorption processes.

After a steady state was reached for both pH and ORP, exact amounts (0.25, 0.5, 1, 2.5 or 5 mL) of H2O2 stock solution (1 M) were introduced into the suspensions to prepare different oxidized NZVIs by different H2O2 concentration at 0.5, 1, 2, 5 or 10 mM, respectively. After reaching the equilibrium of pH and ORP again, 1 mL of NA stock solution (5 mM) was transferred into the suspension to initiate the adsorption of NA (10 μM) by the oxidized NZVI. At the sampling times, 1 mL samples were taken from the suspension and filtered through a 0.2 μm filter (Whatman) for analysis of high-R e v i s e d m a n u s c r i p t 8 performance liquid chromatography (HPLC). After finishing 2-h adsorption, desorption tests were carried out at pH 12 to check the mass balance of NA (Table S1).

Aqueous concentration of NA was determined using HPLC (Waters 600 Controller) equipped with a photodiode array detector operating at 258 nm (Waters 996) and a reversed-phase C18 column (250 mm × 4.6 mm i.d., 5 μm). The mobile phase was a mixture of acetonitrile/water (60/40 v/v) containing 0.1% formic acid. The flow rate of the mobile phase was set at 1 mL/min in isocratic mode. [START_REF] Xu | Cobinding of Pharmaceutical Compounds at Mineral Surfaces: Mechanistic Modeling of Binding and Cobinding of Nalidixic Acid and Niflumic Acid at Goethite Surfaces[END_REF] The dissolved Fe(II) concentration was measured by a 1,10-phenanthroline method at a wavelength of 510 nm using an UV-vis spectrophotometer (U-3310, HITACHI).

The same procedure was used to investigate the oxidation of NZVI in buffered systems. A constant Good's buffer (MES, HEPES and TRIZMA) concentration of 10 mM was used to maintain the pH at 5.6, 7.0 and 9.0, respectively [START_REF] Buchholz | Effects of Zwitterionic Buffers on Sorption of Ferrous Iron at Goethite and Its Oxidation by CCl4[END_REF][START_REF] Marsac | Reduction Kinetics of Nitroaromatic Compounds by Titanium-Substituted Magnetite[END_REF] . These buffers were introduced into the reactor together with NZVI (200 mg/L).

All experiments were performed in triplicates, and the data reported here were the average of three replicated experiments and error bars represent the relative standard deviation.

Surface Complexation Modeling

The NA removal in the NZVI suspension at different pH values were described using surface complexation modeling. The geochemical speciation code PHREEQC and the "minteq" database were used. [START_REF] Parkhurst | User's guide to PHREEQC (Version 2): A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF] The pKa of NA is 6.19 and the logarithm of the R e v i s e d m a n u s c r i p t 9 formation constant of NA-Fe + (aq) is 3.99. [START_REF] Vincent | Prototropic and metal complexation equilibria of nalidixic acid in the physiological pH region[END_REF] The surface complexation models for magnetite are used, as previously reported, [START_REF] Jolsterå | Surface complexation modeling of Fe3O4-H + and Mg(II) sorption onto maghemite and magnetite[END_REF] and the protonation of Fe surface sites is formulated following a 2-pKa approach (Eqs. ( 1) and ( 2)).

≡ 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 2 + ⇋ ≡ 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 + 𝐹𝐹 + ; 𝑝𝑝𝑝𝑝𝑝𝑝 1 (1)
≡ 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ⇋ ≡ 𝐹𝐹𝐹𝐹𝐹𝐹 -+ 𝐹𝐹 + ; 𝑝𝑝𝑝𝑝𝑝𝑝 2 (2)
Charge-potential relationship was described according to the constant capacitance model (CCM), and the modeling parameters are presented in the supporting information (Table S2). Though the CCM is not available in PHREEQC (version 2), we have adapted parameters of the three plane model (TPM) implemented in PHREEQC in order to use the CCM, as previously reported. [START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] 3. Results and discussion

NZVI oxidation in aqueous solution and NA removal

Variations in pH, ORP and dissolved Fe(II) concentration were monitored during i) the addition of NZVI in reactor, ii) the oxidation of NZVI by H2O2, and iii) the removal of NA by the resulting secondary particles (Figure 1). When NZVI was added in water (i.e., the first 2-h period), we observed an obvious increase in pH (from 6.9 to 8.9) and a decrease in ORP (from 81 to -748 mV), which can be attributed to generation 3)). 27

𝐹𝐹𝐹𝐹 0 + 2𝐹𝐹 2 𝐹𝐹 → 𝐹𝐹𝐹𝐹 2+ + 2𝐹𝐹𝐹𝐹 -+ 𝐹𝐹 2 (3)
After adding H2O2 into the NZVI suspension, the ORP value increased rapidly up to 241 mV due to the standard potential of H2O2/ H2O (1.37 V) [START_REF] Bai | Choline biosensors based on a bielectrocatalytic property of MnO2 nanoparticles modified electrodes to H2O2[END_REF] , while pH dropped to 7.8 which is ascribed to the oxidation and hydrolysis of released iron ions. In addition, the release of H + from H2O2 dissociation (pKa of 11.6) presumably results in pH decrease. [START_REF] Kurniawan | Removal of refractory compounds from stabilized landfill leachate using an integrated H2O2 oxidation and granular activated carbon (GAC) adsorption treatment[END_REF] 6.5 After a long steady-state period for both ORP and pH values (around 15 h), ORP decreased sharply until -696 mV and the pH increased to 8.6, which can be attributed to the complete consumption of H2O2 (as it is also verified by the molybdate-catalyzed iodometric titration method [START_REF] Klassen | H2O2 Determination by the I3-Method and by KMnO4 Titration[END_REF] ). During the reaction between H2O2 and NZVI, protons are consumed (Eq. ( 4)), [START_REF] Segura | Zero valent iron (ZVI) mediated Fenton degradation of industrial wastewater: Treatment performance and characterization of final composites[END_REF][START_REF] Zhang | Removal of norfloxacin using coupled synthesized nanoscale zero-valent iron (nZVI) with H2O2 system: Optimization of operating conditions and degradation pathway[END_REF] which can balance the protons generated as a result of hydrolysis of Fe(III). The latter is generated from the rapid oxidation of ferrous species in the presence of H2O2, which has been experimentally checked by the no detection of dissolved Fe(II) during that period.

𝐹𝐹𝐹𝐹 0 + 𝐹𝐹 2 𝐹𝐹 2 + 2𝐹𝐹 + ⇋ 𝐹𝐹𝐹𝐹 2+ + 2𝐹𝐹 2 𝐹𝐹 (4)
Once H2O2 was totally consumed and ORP reached again negative values, release of dissolved Fe(II) into solution was observed. Then, the dissolved Fe(II) concentration decreased over reaction time, likely due to adsorption to oxide particles, particularly at high pH value (~8). It is worth noting that the color of suspension changed from black to yellow after the addition of H2O2, and gradually turned to black after the 15-h reaction.

Once the ORP and pH values reached steady-state values, a desired concentration of NA was introduced into the reaction system, and residual NA concentration was monitored over time (Figure 1). A slight increase in pH can be mainly attributed to the alkalinity of the NA mother solution, but also to NA binding to oxide surfaces. Indeed, R e v i s e d m a n u s c r i p t 12 almost 60% of NA removal was observed after 2 h of reaction time at the working pH (~9). NA removal by, for instance, Fenton-like oxidation is excluded under our experimental conditions, since full mass balance was achieved at the end of reaction, i.e. desorbed amounts equivalent to adsorbed ones (Table S1). This great adsorption (~29 µmol per g of initial NZVI added) at an alkaline pH is quite unusual, and thus not comparable with the typical pH-dependence behavior of adsorption of monocarboxylates or polyfunctional compounds, as for example quinolones. [START_REF] Xu | Cobinding of Pharmaceutical Compounds at Mineral Surfaces: Mechanistic Modeling of Binding and Cobinding of Nalidixic Acid and Niflumic Acid at Goethite Surfaces[END_REF] Indeed, the sorption behavior of such compounds to metal oxides is generally attributed to a combination of pH-dependent speciation of compound (e.g. pKa of NA = 6.19) and surface charge characteristics of the mineral oxide (PZC of Fe-oxyhyrdoxides is generally between 8 and 9.5). [START_REF] Xu | Cobinding of Pharmaceutical Compounds at Mineral Surfaces: Mechanistic Modeling of Binding and Cobinding of Nalidixic Acid and Niflumic Acid at Goethite Surfaces[END_REF] As a result, adsorption is generally high at low pH value and then decreases when pH increases, and becomes negligible at pH higher than 10. [START_REF] Cheng | Adsorption of Quinolone Antibiotics to Goethite under Seawater Conditions: Application of a Surface Complexation Model[END_REF] Here, the NA adsorption is unusually high at pH around 9, and even increased from 29 to 40 µmol/g when the initial NA concentration increased from 10 to 20 µM, further confirming the high affinity of the NZVI oxidation products toward NA.

Secondary minerals formation and impacts on NA removal

NZVI can be oxidized and/or transformed into different iron oxides depending on the oxidant dose, which may exhibit contrasting affinities towards NA. For this reason, additional experiments of NZVI oxidation were performed with different H2O2 concentrations (Figure S1). Generally, higher H2O2 concentration led to a rapid increase concentrations (0 -10 mM) (Figure 2a). Interestingly, a negligible removal of NA was observed on the fresh NZVI, while the NA removal amount onto the resulting secondary minerals increased with increasing in H2O2 dose, yet no significant difference was observed for the two highest doses (5 and 10 mM). It is interesting to note that the NA removal amount by the corrosion particles of NZVI can be enhanced in the presence of humic acid (LHA was used here as model of natural organic matter) (see Figure S3).

Indeed, the presence of 5 mg/L of LHA increased the NA adsorbed amount from 22 to 30 µmol/g. This enhanced adsorption in the presence of humic acids can be ascribed to better dispersion of secondary mineral particles, thus increasing available surface area as previously reported. [START_REF] Du | High-dispersion zero-valent iron particles stabilized by artificial humic acid for lead ion removal[END_REF] R e v i s e d m a n u s c r i p t As the adsorption capacity is closely related to the properties of iron oxides and hydroxides, the resulting secondary minerals were firstly characterized by XRD (Figure 2b). The XRD pattern of fresh NZVI revealed the presence of a broad peak of α-Fe to outer iron oxide shell of NZVI particles. [START_REF] Bae | Effect of NaBH4 on properties of nanoscale zero-valent iron and its catalytic activity for reduction of p -nitrophenol[END_REF] At low H2O2 concentration (0.5 mM), peaks of α-Fe were still observed while new peaks corresponding to magnetite and/or maghemite appeared. At H2O2 concentration over 1 mM, magnetite/maghemite was detected as the major secondary iron minerals (Figure 2b).

To gain more insight about potential changes in surface properties upon NZVI oxidation, zeta potential and average particle size of the secondary mineral particles were measured. These results showed that H2O2 induced oxidation may influence the aggregation behavior in NZVI suspension (Figure S2). While Zeta potential negative value is within the reported values for bare NZVI at alkaline pH (9), [START_REF] Ibrahim | Stability and Dynamic Aggregation of Bare and Stabilized Zero-Valent Iron Nanoparticles under Variable Solution Chemistry[END_REF] H2O2 induced oxidation resulted in a significant reduction of the mean size of agglomerates from around 4000 nm to around 800 nm when the H2O2 concentration exceeded 2 mM.

However, the zeta potential of NZVI suspension did not change significantly over the entire H2O2 concentration range. Generally, increasing in negative surface charge of particles may indicate dispersion or lower aggregation. [START_REF] Dong | Influence of humic acid on the colloidal stability of surface-modified nano zero-valent iron[END_REF] Here, enhancement in the electrostatic repulsion effect and thus the dispersion of the particles is only observed at higher H2O2 dose, that could be associated with the formation of magnetite/maghemite particles (Fig. 2b). The high agglomeration observed for the fresh NZVI or slightly oxidized NZVI could be possibly due to electrostatic attractions between various kinds of particles: Fe 0 , iron oxides coating the Fe 0 core and other secondary minerals.

Furthermore, the van der Waals interactions between these particles may take place R e v i s e d m a n u s c r i p t 16 because of the limited electrostatic repulsion between particles. Accordingly, the BET surface area of the oxidized particles (using 5 mM of H2O2) (28.2 ± 1.5 m 2 /g) was found almost twice higher than the surface area of the fresh NZVI (14.9 ± 1 m 2 /g).

Collectively, these results suggest that fresh NZVI (or Fe 0 ) has negligible affinity for NA adsorption, and the secondary Fe minerals could be responsible of the NA removal in NZVI suspension.

Structural evolution of NZVI over reaction time

As the highest removal rate of NA was observed with a high dose of H2O2 (5 or 311), (400), (511), and (440) of magnetite/maghemite phase, respectively. [START_REF] Krystofiak | Multiple Morphologies of Gold-Magnetite Heterostructure Nanoparticles are Effectively Functionalized with Protein for Cell Targeting[END_REF] In addition, the XRD of 3-h sample revealed the presence of peaks of magnetite/maghemite, lepidocrocite, and hematite (Figure 3e). This is consistent with previous investigation, which showed that needle-shaped lepidocrocite was formed as a secondary product from NZVI oxidation in oxygenated water. [START_REF] Liu | Formation of lepidocrocite (γ-FeOOH) from oxidation of nanoscale zero-valent iron (nZVI) in oxygenated water[END_REF] TEM image of 18h oxidized NZVI (Figure 3c) shows the presence of nanoparticles aggregates without other distinct shaped particles. Single nanoparticles (20 nm as an average size) were connected to form chain-like magnetic nanoparticles (see Figure S4).

The SAED pattern of these aggregates revealed the reflections of (111, 4.87 Å), (220, 2.98 Å), (311, 2.53 Å), (400, 2.08 Å), (422, 1.70 Å), and (511, 1.59 Å), corresponding to magnetite or maghemite. [START_REF] Araújo-Neto | Monodisperse sodium oleate coated magnetite high susceptibility nanoparticles for hyperthermia applications[END_REF] Though these minerals both have indistinguishable diffraction patterns, the chain-like assembly of these nanoparticles may suggest strong ferromagnetic properties of particles at room temperature. Because the weak dipoledipole interactions between the maghemite particles are usually not sufficient to result in the chain formation, the chain assemblies observed here tend to support the formation of magnetite as the dominant phase. [START_REF] Lalatonne | Van der Waals versus dipolar forces controlling mesoscopic organizations of magnetic nanocrystals[END_REF][START_REF] Dar | Single crystalline magnetite, maghemite, and hematite nanoparticles with rich coercivity[END_REF] This falls in line with previous report, [START_REF] Bae | Advances in Surface Passivation of Nanoscale Zerovalent Iron: A Critical Review[END_REF] where magnetite has been detected as the major secondary iron mineral under anoxic conditions (i.e. equivalent to conditions here within the 15h-18h period of reaction). In addition, the oxidation of NZVI to magnetite (Fe3O4) seems to be more thermodynamically favorable at alkaline pH values. [START_REF] Parkhurst | User's guide to PHREEQC (Version 2): A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF][START_REF] Liu | Effect of particle age (Fe 0 content) and solution pH on NZVI reactivity: H2 evolution and TCE dechlorination[END_REF] R e v i s e d m a n u s c r i p t were composed of five different peaks at 707.0, 708.3-708.5 eV, 710.1-710.3, 711.1-711.6, and 713.2-713.7 eV, which are assigned to the binding energies for Fe(0) (706.5-707.0 eV), Fe(II)-O (708.2-710.9 eV), and Fe(III)-O (711.0-714.0 eV), respectively. [START_REF] Kumar | Reductive dechlorination of trichloroethylene by polyvinylpyrrolidone stabilized nanoscale zerovalent iron particles with Ni[END_REF] In the pristine NZVI, two distinct peaks were observed at 719.9 and 707 eV, corresponding to Fe2p1/2 and Fe2p3/2 of Fe(0), respectively (Figure 4(a)). [START_REF] Luo | Synthesis of nanoscale zero-valent iron immobilized in alginate microcapsules for removal of Pb(II) from aqueous solution[END_REF] After 3h reaction, we observed the disappearance of Fe(0) peaks and the formation of new Fe(III) satellite peak at 718.9 eV, indicating the presence of Fe(III) minerals (e.g. maghemite). [START_REF] Yamashita | Analysis of XPS spectra of Fe 2+ and Fe 3+ ions in oxide materials[END_REF][START_REF] Radu | X-Ray Photoelectron Spectroscopic Characterization of Iron Oxide Nanoparticles[END_REF][START_REF] Kraushofer | Atomic-Scale Structure of the Hematite α-Fe2O3(11̅ 02) "R-Cut" Surface[END_REF] The proportion of Fe(II) (55.4% → 24.2%) on the NZVI surface R e v i s e d m a n u s c r i p t 20 decreased after 3 h-reaction whereas that of Fe(III) increased from 41.2% to 75.8% (Figure 4(b)), underscoring the surface oxidation of NZVI by H2O2. However, the Fe(III) satellite peak gradually decreased over reaction time (3 to 18 h), whereas the peak of Fe2p3/2 shifted to lower binding energy (710.9 → 710.6 eV) (Figure 4(a)). The disappearance of Fe(III) satellite peak may result from mineral transformation of Fe IIIoxides (e.g. maghemite) into magnetite as previously reported. [START_REF] Kraushofer | Atomic-Scale Structure of the Hematite α-Fe2O3(11̅ 02) "R-Cut" Surface[END_REF] Indeed, the proportion of Fe(II) increased (34.7% at 15 h to 43.3% at 18 h), and Fe(III) decreased (65.3% at 15 h to 56.7% at 18 h) with increasing reaction time (Figure 4b).

Based on all experimental findings above, an oxidation pathway of NZVI by H2O2 can be proposed as two successive steps (Figure S5). In the early stage of NZVI oxidation, highly oxidizing condition caused by the addition of a high dose of H2O2 can form mixed valence oxides (i.e. magnetite), but also Fe III -oxyhydoxides (lepidocrocite, maghemite and hematite), resulting in change of NZVI suspension color from black to yellowish (Figure 1). After the remained H2O2 was completely depleted over 15h of reaction time, reducing conditions (ORP value reached the initial value of fresh NZVI suspension) and then release of ferrous ions into solution concurrently take place (Figure 1). Afterwards, the dissolved ferrous ions tend to re-sorb on the surface of Fe(III)-oxyhydroxides at alkaline pH value, leading to their transformation into magnetite as previously reported for lepidocrocite or hematite (Eqs. ( 5) and ( 6)). [START_REF] Usman | Fe II induced mineralogical transformations of ferric oxyhydroxides into magnetite of variable stoichiometry and morphology[END_REF][START_REF] Jolivet | Interfacial electron transfer in colloidal spinel iron oxide. Conversion of Fe3O4-γFe2O3 in aqueous medium[END_REF] 2γFeOOH

+ Fe 2+ → Fe 3 O 4 + 2H + (5)
R e v i s e d m a n u s c r i p t

21 𝛼𝛼Fe 2 O 3 + Fe 2+ + 𝐹𝐹 2 O → Fe 3 O 4 + 2𝐹𝐹 + (6)
Color change from yellowish to black of suspension further suggested such transformation into magnetite phase. Therefore, Fe(II)-release during the oxidation of NZVI suspension and its re-adsorption to secondary minerals may influence the surface reactivity of the resulting products.

Additional experiments of NA removal by fresh NZVI or oxidized products (Figure S6) using Good's buffers showed that NA adsorption decreased with pH increasing.

However, the NA adsorption at pH 9 was much lower in buffered systems as compared to the un-buffered NZVI suspension (Figure 1). This discrepancy is probably due to the interactions of Good's buffers with the Fe oxide surfaces, which may cause the rapid Fe(0) corrosion and Fe(II) release. [START_REF] He | Effects of Good's Buffers and pH on the Structural Transformation of Zero Valent Iron and the Oxidative Degradation of Contaminants[END_REF] It was reported that such Fe(II) release may lead to lepidocrocite formation through Fe(II)-catalyzed transformation of poorly crystallized Fe-oxides (e.g. ferrihydrite) and/or oxidation of Fe(II) at acidic-neutral pH. [START_REF] He | Effects of Good's Buffers and pH on the Structural Transformation of Zero Valent Iron and the Oxidative Degradation of Contaminants[END_REF] Accordingly, lepidocrocite was identified here as the major phase in buffered NZVI suspension at pH 5.6 and 7 (Figure S7). However, the oxidation products in TRIZMA buffered system (pH 9) were mostly highly amorphous, which makes difficult an accurate identification of secondary iron minerals (Figure S7). It is worth noting that oxidation in TRIZMA buffered system led to dispersion of NZVI particles in suspension and enhancement in zeta potential (Figure S8) compared to that without TRIZMA (Figure S2), thus confirming interactions of TRIZMA molecules with Fe-oxides.

Therefore, interactions of organic buffer's molecules with mineral surfaces may affect R e v i s e d m a n u s c r i p t 22 the Fe(II) binding. In the absence of Good's buffers, no elution of Fe(II) is expected and thus the surface bound Fe(II) can be preserved. This is consistent with previous works which showed that organic buffers increased the Fe(II) apparent solubility in goethite and magnetite suspensions even in the alkaline pH range. [START_REF] Buchholz | Effects of Zwitterionic Buffers on Sorption of Ferrous Iron at Goethite and Its Oxidation by CCl4[END_REF][START_REF] Marsac | Reduction Kinetics of Nitroaromatic Compounds by Titanium-Substituted Magnetite[END_REF] Collectively, these results further suggest that the Fe(II) bound to secondary minerals (i.e. magnetite) could control on the surface reactivity and then the binding capacity toward negatively charged contaminants.

NA adsorption mechanisms on secondary minerals

To check the pH dependence of Fe(II) release and NA sorption onto the NZVI oxidation products, residual concentrations of NA and dissolved Fe(II) in oxidized NZVI suspension were monitored over a wide range of pH (6-11) (Figure 5). NA adsorption was found the greatest between pH 6 and 9, and the lowest between pH 10 and 11. This pH adsorption edges differs from the previously reported data of NA adsorption to Fe-oxyhydroxides [START_REF] Xu | Cobinding of Pharmaceutical Compounds at Mineral Surfaces: Mechanistic Modeling of Binding and Cobinding of Nalidixic Acid and Niflumic Acid at Goethite Surfaces[END_REF][START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] or the NA adsorption data obtained here with three synthetic Fe-oxyhydroxides (See Figure S9). Indeed, NA adsorption to nonstoichiometric magnetite (Fe3O4) [START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] , goethite (α-FeOOH) [START_REF] Xu | Cobinding of Pharmaceutical Compounds at Mineral Surfaces: Mechanistic Modeling of Binding and Cobinding of Nalidixic Acid and Niflumic Acid at Goethite Surfaces[END_REF] at that pH range. [START_REF] Bae | Reactivity of Nanoscale Zero-Valent Iron in Unbuffered Systems: Effect of pH and Fe(II) Dissolution[END_REF] This observation falls in line with a previous investigation on the reactivity assessment of magnetite in presence of variable dissolved Fe(II) amounts [START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] .

Indeed, it was shown that Fe(II) recharge of magnetite enhanced its binding capacity towards organic and inorganic compounds, shifting the maximum sorption to alkaline pH values. [START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] Furthermore, Fe(II)-amendment of non-stoichiometric magnetite (Fe(II)/Fe(III) = 0.40) led to similar sorption capacity as compared to the stoichiometric magnetite (i.e. Fe(II)/Fe(III) = 0.50). [START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] In the present work, the Fe(II)/Fe(III) ratio of NZVI oxidized products determined by acid digestion was found very high (1.03) and much more than the expected ratio for a magnetite phase, probably because of the presence of residual traces of Fe 0 . In order to confirm the role of surface bound Fe(II) in the enhanced NA binding, we washed the final NZVI products with DDIW for 3 times and then monitored the NA uptake (Figure S10). Sharp decrease of Fe(II)/Fe(III) ratio from 1.03 to 0.61 upon washing of NZVI products indicated strong loss of Fe(II) during the washing process.

For NA adsorption at pH 9 (Figure S10), almost 2-fold decrease in adsorbed amount was observed after the washing process, confirming the crucial role of the surface bound Fe(II) in the enhanced NA adsorption.

As an attempt to explain the enhanced NA adsorption at high pH with respect to the presence of Fe(II), we used a surface complexation model, previously developed for the stoichiometric magnetite. [START_REF] Cheng | Influence of Magnetite Stoichiometry on the Binding of Emerging Organic Contaminants[END_REF] We assumed that NA binds to two surface hydroxo groups [START_REF] Xu | Cobinding of Pharmaceutical Compounds at Mineral Surfaces: Mechanistic Modeling of Binding and Cobinding of Nalidixic Acid and Niflumic Acid at Goethite Surfaces[END_REF]52 by involving its carboxylate and its keto-group as following:

2 ≡FeOH + 2 H + + NA -⇌ (≡Fe)2NA + + 2 H2O S K (7)
As presented in Figure 5, accurate description of experimental results of NA adsorption by the oxidized NZVI particles was obtained at a wide pH range (6-11). We used the measured dissolved Fe(II) concentration at the end of each adsorption experiment as input parameters to account for NA-Fe(II) aqueous complex formation.

The good accuracy with the experimental data using the modeling parameters of the stoichiometric magnetite (see Table S2) suggests that magnetite controls NA binding to oxidized NZVI, and further confirms the key role of surface bound Fe(II).

R e v i s e d m a n u s c r i p t 10 of

 10 OH -, Fe 2+ , and H2 during the anaerobic corrosion of NZVI (Eq.(

Figure 1 .

 1 Figure 1. Variations in pH, ORP, color of suspension, dissolved Fe(II) concentration and NA concentration during the NZVI oxidation and NA adsorption. Experimental conditions: [NZVI] = 0.2 g•L -1 , [H2O2] initial = 5 mM, [NA]initial = 10 μM, 20 ±1 °C.

  R e v i s e d m a n u s c r i p t 11

R e v i s e d m a n u s c r i p t 13 in

 13 ORP value in NZVI suspension, and then decrease to reach the initial value, except for the highest H2O2 dose. For the sake of clarity, only the last stage, i.e. NA adsorption, was shown and the adsorbed amount of NA was plotted versus time for different H2O2

14

 14

Figure 2 .

 2 Figure 2. (a) NA removal by the oxidation NZVI samples (b) XRD patterns of secondary minerals at different H2O2 concentrations (0 -10mM); unbuffered systems (pH= 9 ±0.2 for the adsorption stage); [NZVI]=0.2 g•L -1 , [NA]initial=10 μM, 20 ±1 °C.

u s c r i p t 15 ( 44 .

 1544 5° 2θ) with weak peaks of magnetite and/or maghemite (marked as M) due probably

  10 mM), we have investigated the morphological changes of oxidized NZVI particles over reaction time when 5 mM of H2O2 was used for oxidation. Two key stages of NZVI oxidation kinetics were investigated (as shown in Figure1) : (i) 3h, after H2O2 addition and when ORP and pH values have reached a plateau (oxidizing conditions), and (ii) 18h just before NA addition and when ORP and pH values have reached constant values after complete H2O2 depletion.

Figure 3 .

 3 TEM images and SEAD pattern of the oxidized NZVI with 5 mM H2O2 at 297 two oxidation times (a and b) 3 hours and (c and d) 18 hours, and (e) corresponding 298 XRD patterns. 299 300 In the 3-h sample, we observed the presence of chain-like aggregates of nanoparticles 301 and needle-like shaped individual nanoparticles (Figure 3). The SAED pattern of chain-R e v i s e d m a n u s c r i p t 18 like aggregates (Figure 3b) showed the d-spacing of 4.87, 2.53, 2.09, 1.60 and 1.49 Å, which are assigned to the (111), (

Figure 4 .

 4 Figure 4. XPS spectra for (a) Fe2p of NZVI before and after reaction with H2O2 and (b) and the deconvolution results of Fe2p3/2 (706-716 eV). Conditions: [H2O2] = 5 mM, [NZVI]=0.2 g•L -1

Figure 5 .

 5 Figure 5. pH-dependency of (a) NA adsorption and (b) dissolved Fe(II) concentration in NZVI suspension after oxidation (5mM H2O2). Lines are modeling results. Experimental conditions: [NZVI]= 0.2 g•L -1 ,[NA]= 10 μM, 20 ±1 °C.The BET surface area used here is that measured for the oxidized particles (using 5 mM of H2O2) (28.2 ± 1.5 m 2 /g).

R e v i s e d m a n u s c r i p t 25 It

 25 is interesting to note that the great binding capacity of the corrosion particles of NZVI at alkaline pH values also concerns other antibiotics of contrasting structure and properties. Indeed, great adsorption of TET (i.e. 70% removal of 10µM) onto the oxidized NZVI particles was observed at pH 9.0 ± 0.2 (FigureS11). Taken together, these results highlight the key role of Fe(II) generated along the NZVI oxidation process in promoting greater binding abilities of the secondary minerals.

R e v i s e d m a n u s c r i p t 26 (

 26 passivation in ambient environments can lead to either formation of Fe II -bearing phases on the NZVI surface or complete oxidation to ferric (oxyhydr)oxides. Under the experimental conditions of this study, NZVI oxidation led to formation of Fe II -bearing secondary minerals, with magnetite as the major phase.The latter exhibited higher adsorption ability for organic contaminants, in contrast to the fresh NZVI. In addition, an unexpected great adsorption at alkaline pH values was observed with the formed secondary Fe minerals. This behavior is due to the gradual increase in Fe(II) content at the surface of magnetite phase over the reaction time. A surface complexation model confirmed that NA adsorption onto the secondary magnetite is due to the formation of surface bound Fe(II). If Fe(II) is released into solution, the surface bound Fe(II) decreased together with the NA adsorbed amount at alkaline pH values. As iron (oxyhydr)oxide-coated NZVI particles or Fe(II)-Fe(III) oxyhydr)oxides may exhibit different adsorption affinities toward negatively charged molecules (e.g. antibiotics) or positively charged compounds, more attention should be paid to the reactivity assessment of passivated NZVI particles or corrosion products.Therefore, the modeling of contaminant fate and transport should consider the impact of these secondary Fe minerals on the mobility of emerging contaminants in soil and groundwater. .Marsac, S. Martin, J.-F. Boily and K. Hanna, Oxolinic Acid Binding at Goethite and Akaganéite Surfaces: Experimental Study and Modeling, Environ. Sci. Technol., 2016, 50, 660-668.

  Because of H + promoted dissolution of magnetite, Fe(II) dissolution takes place at low pH, which can explain the high amount of dissolved Fe(II)

	decreased as pH increasing.
	m a n u s c r i p t
	e v i s e d	or other ferric
	oxyhydroxides (maghemite, hematite or lepidocrocite) decreased as increasing pH and became negligible for pH higher than 9. Here, the pH-adsorption curve of NA onto R
	23

NZVI oxidized products shifts to larger pH values, probably because of the presence of dissolved Fe(II). The concentration of dissolved Fe(II) (no dissolved Fe(III) was found)

Acknowledgements

We acknowledge support from the National Research Foundation of Korea (project no.

NRF-NRF-2019R1C1C1003316

). We gratefully acknowledge to Isabelle Soutrel (LC/UV) and Vincent Dorcet (THEMIS platform) for the assistance.

Conflicts of interest

There are no conflicts to declare.

Supplementary information: Additional information