A Janot

P-O Vandanjon

M Gautier
email: maxime.gautier@irccyn.ec-nantes.fr

Refined Instrumental Variable method for non-linear dynamic identification of robots

Keywords: Identification algorithms, Least-squares methods, Robot dynamics

The identification of the dynamic parameters of robot is based on the use of the inverse dynamic identification model which is linear with respect to the parameters. This model is sampled while the robot is tracking "exciting" trajectories, in order to get an over determined linear system. The linear least squares solution of this system calculates the estimated parameters. The efficiency of this method has been proved through the experimental identification of a lot of prototypes and industrial robots. However, this method needs joint torque and position measurements and the estimation of the joint velocities and accelerations through the bandpass filtering of the joint position at high sample rate. So, the observation matrix is noisy. Moreover identification process takes place when the robot is controlled by feedback. These violations of assumption imply that the LS estimator is not consistent. This paper focuses on the Refined Instrumental Variable (RIV) approach to overcome this problem of noisy observation matrix. This technique is applied to a 2 degrees of freedom (DOF) prototype developed by the IRCCyN Robotic team.

Introduction

The usual identification method based on the inverse dynamic model (IDM) and LS technique has been successfully applied to identify inertial and friction parameters of a lot of prototypes, industrial robots and has been extended to cars, worksite engine, human being and haptic interfaces [START_REF] Atkeson | Estimation of Inertial Parameters of Manipulator Loads and Links[END_REF] [START_REF] Swevers | Optimal Robot Excitation and Identification[END_REF]) [START_REF] Khosla | Parameter Identification of Robot Dynamics[END_REF]) [START_REF] Kozłowski | Modelling and identification in robotics[END_REF]) [START_REF] Raucent | Identification of Barycentric Parameters of Robotic Manipulators from External Measurements[END_REF] [START_REF] Gautier | Identification of Robot Dynamics[END_REF]) [START_REF] Restrepo | Calibration of drive chain of robot joints[END_REF] (Gautier 1997) [START_REF] Venture | Modeling and identification of passenger car dynamics using robotics formalism[END_REF]) (C-E [START_REF] Lemaire | Dynamic identification of a vibratory asphalt compactor for contact efforts estimation[END_REF]) [START_REF] Janot | Modeling and Identification of a 3 DOF Haptic Interface[END_REF]) among others. At any case, a derivative bandpass data filtering is required to calculate the joint velocities and accelerations. Moreover identification process is carried out with a feedback controlled robot. These conditions may lead to a violation of statistical independence between the residual and the observation matrix which implies that the LS solution is not consistent. To overcome this problem of noisy observation matrix, several methods have been proposed in the past: Extended Kalman Filtering, total least-squares, Instrumental Variable method .

We show in [START_REF] Gautier | Extended Kalman Filtering and Weighted Least Squares Dynamic Identification of Robot[END_REF] that Extended Kalman Filtering is more complicated without improvements of results.

As far as total least squares are concerned, we used them in order to identify simultaneously dynamic and drive gain parameters [START_REF] Gautier | Identifi-cation of inertial and drive gain parameters of robots[END_REF]. However, we did not succeed in applying this method to take into account the feedback which correlates the noise.

Instrumental Variable method was already applied in robotics [START_REF] Puthenpura | Identifica-22 September 2010 tion of Continuous-Time Systems Using Instrumental Variables with Application to an Industrial Robot[END_REF]. This method was used in order to identify a SISO system linear with respect to the state in an open loop configuration for each axis of an industrial robot. In this paper, the IV is applied for a dynamic model of a robot non linear with respect to the state and in closed loop configuration.

Recently, the Instrumental Variable (IV) approach was renewed in the context of closed loop linear continuous system.

This method is particularly interesting because of its simplicity. Indeed, no noise model identification is needed and the IV estimator is consistent even if the noise is colored [START_REF] Young | Refined instrumental variable methods of time-series analysis: Part 1, SISO systems[END_REF], [START_REF] Söderström | System identification[END_REF]. However, this technique was generally applied to discrete system linear with respect to the state which is not the case in robotics. The choice of the instrument variable depends on the context. Moreover, the method was designed in open loop system. Progressively, algorithms suitable to our context, i.e. continuous time and closed loop system, have emerged. In particular, the so-called SRIVC algorithm (Simplified Refined Instrumental Variable Continuous-time) for open loop system, based on an auxiliary model as instrument variable, is a good candidate to our problem [START_REF] Young | An instrumental variable approach to ARMA model identification and estimation[END_REF]. Very recently, this last algorithm was modified in order to take into account closed loop system [START_REF] Gilson | A refined IV method of closed-loop system identification[END_REF] [START_REF] Young | Simple Refined IV Methods of Closed-Loop System Identification[END_REF] but still in the frame of system linear with respect to the state. This technique is implemented in the MATLAB CONTSID toolbox developed by the CRAN team [START_REF] Garnier | Latest developments for the matlab contsid toolbox[END_REF].

A derivation of this IV method was first successfully applied on a 1 DOF haptic device (P-O. [START_REF] Vandanjon | Comparison of two identification techniques: Theory and application[END_REF]). This derivation is based on the use of both the inverse dynamic model (IDM) and the direct dynamic model (DDM). The robustness to data filtering and to the initialization as the calculation of the optimal solution were presented in [START_REF] Janot | Identification of robots dynamics with the Instrumental Variable method[END_REF]. However, the consistence of the estimation (like statistical rules), the convergence of the purposed algorithm and the robustness to control laws were not introduced. This paper deals with these issues and the IV method is carried out on a 2 DOF prototype robot developed by the IRCCyN robotic team. This direct drive prototype is very well suited to our purpose because it emphasizes non linear coupling contrary to industrial robots with high gear ratio.

The paper is organized as follows: section 2 reviews the usual identification technique of the dynamic parameters of the robot. Section 3 presents the Instrumental Variable techniques. The experimental results are given in section 4. Finally, section 5 is the conclusion

IDIM

The inverse dynamic model (IDM) of a rigid robot composed of n moving links calculates the motor torque vector idm τ , as a function of the generalized coordinates and their derivatives. It can be obtained from the Newton-Euler or the Lagrangian equations, (W. [START_REF] Khalil | Modeling identification and control of robots[END_REF], [START_REF] Featherstone | [END_REF]. It is given by the following relation:

= ( ) + ( , )

idm τ M q q N q q && & (1)
Where, q , q & and q && are respectively the ( )

x n 1 vectors of generalized joint positions, velocities and accelerations, ( ) M q is the ( )

x n n robot inertia matrix, and ( , )

N q q & is the ( )

x n 1 vector of centrifugal, Coriolis, gravitational and friction forces/torques. The choice of the modified Denavit and Hartenberg frames attached to each link allows to obtain a dynamic model linear in relation to a set of standard dynamic parameters, st χ [START_REF] Gautier | Identification of Robot Dynamics[END_REF], [START_REF] Gautier | Direct calculation of minimum set of inertial parameters of serial robots[END_REF]:

( ) idm st st τ IDM q,q,q χ = & && (2)
Where ( ) st IDM q,q,q & && , is the ( )

x s n N jacobian matrix of idm τ , with respect to the ( )

x1 s N
vector st χ , of the standard parameters given by: T T T T ...

1 2 n st st st st χ χ χ χ   =   (3)
With: χ sj = [XX j XY j XZ j YY j YZ j ZZ j MX j MY j MZ j M j Ia j Fv j Fc j τ offj ] T , where:

o j j j j j j
XX , XY , XZ , YY , YZ , ZZ , are the six components of the inertia matrix, j j J , of link j at the origin of frame j, o The base parameters are the minimum number of dynamic parameters from which the dynamic model can be calculated. They are obtained from the standard inertial parameters by eliminating those which have no effect on the dynamic model, and by regrouping some others by means of linear relations. They can be determined using simple closed-form rules [START_REF] Gautier | Direct calculation of minimum set of inertial parameters of serial robots[END_REF] or using a numerical method based on the QR decomposition (Gautier 1991).

The minimal inverse dynamic model can be written as:

( ) idm τ IDM q,q,q χ = & && (4) Where:

( ) IDM q,q,q & && , is the ( )

x n b matrix of the minimal set of basis functions of the rigid body dynamics, (5) χ , is the ( )

x b 1 vector of the b base parameters. ( 6
)
Because of perturbations due to noise measurement and modeling errors, the actual force/torque τ differs from idm τ , by an error e , such that:

( ) idm τ e IDM q,q,q χ e τ =

+ = +

& && (7) Equation ( 7) gives the Inverse Dynamic Identification Model (IDIM).

We consider the off-line identification of the base dynamic parameters χ , given measured or estimated off-line data for τ and ( )

q, q, q
& && , collected while the robot is tracking some planned trajectories. Usually, the signals available from the robot controller are the joint position measurement and the ( )

x n 1 control signal vector v τ , calculated according to the control law.

Preprint submitted to Automatica

3
22 September 2010

Then ( )

q, q, q
& && in (7) are estimated with ( )

ˆq, q, q
& && respec- tively, obtained by bandpass filtering the measure of q (Gautier 1997). The derivatives are off-line calculated without phase shift, using a central difference algorithm of the lowpass filtered position q . The filtered position q is off-line calculated with a non causal zero-phase digital filter by processing the input data q , through a lowpass Butterworth filter in both the forward and reverse direction, using the filtfilt procedure from Matlab.

The control signal v τ , is connected to the input current reference of the current closed-loop of the amplifiers which supplies the motors. Assuming that the current closed-loop has a large bandwidth, greater than 500Hz, its transfer function is equal to its static gain, c K , in the frequency range (less than 10Hz) of the rigid robot dynamics.

Then, the actual force/torque τ , is calculated with the relation: [START_REF] Restrepo | Calibration of drive chain of robot joints[END_REF].

g v τ τ τ = (
The inverse dynamic identification model (IDIM) ( 7) is calculated at a frequency measurement m f , using samples of ( ) q ,q ,q & && , during the time length obs T , of the trajectory.

ˆq, q, q & && to calculate ( ) ˆÎDM q,q,q & &&
The equations of each joint are regrouped together on all the trajectory to get an over-determined linear system such that:

( ) ( ) fm fm fm ˆŶ τ W q,q,q χ ρ = + & && (10)
With:

( )

m 1 fm j 1 j fm fm n fm j n Y ( t ) Y τ ... , Y ... Y ( t ) τ τ         = =             (11) ( ) ( ( ) ( ) ( )) ( ( ) ( ) ( ) m m m 1 j fm 1 1 1 j fm fm n j fm n n n
ˆŴ IDM q t ,q t ,q t ˆŴ q,q,q ... , W ... ˆŴ ÎDM q t ,q t ,q t

        = =               & && & && & && (12)
where: ( ( ) ( ) ( ))

j k k k ˆÎDM q t ,q t ,q t & &&
, is the jth row of the ( ) fm fm ˆˆˆŴ IDM q,q,q W q,q,q = & && & && will be used also to recall that fm W , is calculated with a sampling of ( ) ˆÎDM q,q,q & && .

x n b re- gressor matrix ( ( ) ( ) ( )) k k k ˆÎDM q t ,q t ,q t & && , (5).
In

m d f n × × .
After the data acquisition procedure and the parallel decimation of (10), we obtain the over determined linear system:

( ) ( ) ˆŶ τ W q,q,q χ ρ = + & && (13)
where:

o ( ) Y τ , is the x1 ( r ) vector of measurements, built from the actual force/torque τ , o ( ) ˆŴ q,q,q & && , is the x ( r b ) observation matrix, built from the estimated values ( )

ˆq,q,q & && of ( ) q, q, q & && . o ρ , is the x1 ( r ) vector of errors. o m d r n* n / n =
, is the number of rows in (13).

In Y and W , the equations of each joint are grouped together such that:

,

1 1 n n Y W Y ... W ... Y W         = =             (14)
where j Y and Using the base parameters and tracking "exciting" reference trajectories (Gautier et W. Khalil 1992) allow to get a full rank and well conditioned matrix W . The LS solution χ is given by: ( ) ( )

1 T T χ W W W Y W Y - + = = (15)
It is computed using the QR factorization of W . Standard deviations i χ σ , are estimated using classical results from statistics under the assumptions that W is a deterministic matrix, thanks to the data filtering procedure described above, and ρ , is a zero-mean additive independent Gaussian noise, with a covariance matrix ρρ C , such that:

T 2 ρρ ρ r ( ) σ C E ρρ I = = ( 16
)
where E is the expectation operator and r I , the ( )

x r r identity matrix.
An unbiased estimation of the standard deviation ρ σ is:

2 2 ρ σ (r b ) ˆŶ Wχ = - - (17)
The covariance matrix of the estimation error is given by:

T 2 T 1 χχ ρ [( )( ) ] σ ( ) ˆˆĈ E χ χ χ χ W W - = - - = (18)
i 2 χ χχ σ C ( ) ˆˆˆi ,i = is the i th diagonal coefficient of χχ ˆĈ . The relative standard deviation ri χ
%σ ˆ is given by: ri i

χ χ i %σ 100 σ χ ˆˆ= , for i χ ˆ≠ 0 (19)
The OLS can be improved by taking into account different standard deviations on joint j equations errors (Gautier 1997). Each equation of joint j in ( 13), ( 14), is weighted with the inverse of the standard deviation of the error calculated from OLS solution of the equations of joint j , given by:

( ) ( ) ( ) j j j j j ˆŶ τ W IDM q,q,q χ ρ = + & && (20)
This weighting operation normalizes the errors in (13) and gives the weighted LS (WLS) estimation of the parameters.

This identification method is illustrated in Fig. 1. The calculation of the velocities and accelerations are required using well tuned bandpass filtering of the joint position (Gautier 1997). One of the numerous validations of the identification is to simulate, a posteriori, the direct dynamic model (DDM) given by ( 10) and to compare the simulated trajectories with real trajectories when the torques are the same. These comparisons have to be done on trajectories which were not used for the identification process.

( )

1 q M ( q ) -N( q, q ) τ - = && & (21) Robot ( ) In v erse D yn a m ic Id e n tifica tio n M o d e l ID IM ˆÎD M q ,q ,q & && ˆ, , & && q q q ( ) ( ) fm ˆŴ IDM q ,q ,q & && Linear LS 2 ˆm in - Y W χ χ χ = ( ) ( ) ˆ( ), , , Y W IDM q q q τ & && ( ) q t ( ) t τ Control law χ ( ) r r r q ,q ,q & &&

Instrumental variable technique

Theoretical approach

From a theoretical point of view, the statistical assumptions for efficient LS estimation are violated in practical applications. In the equation ( 13), the observation matrix W is built from the measured joint positions q and from , which are numerically computed from q ,q ,q & && . Therefore the observation matrix is noisy. Moreover identification is carried out in closed-loop control. These violations of assumption imply that the LS estimator, χ , may be non consistent. Indeed, from (13) , it comes:

T T T T ev Ŵ Y W W W ρ W W χ χ = + = (22)
With ev ρ is the vector of errors (errors in variable) when

W is corrupted by noise nf W W W ∆ = - ev ρ W ρ ∆ χ = + (
23) Thanks to the Slutsky's theorem, it is obtained:

1 T T 1 1 plim plim plim m m m evm m m m χ χ W W W ρ m m - →∞ →∞ →∞     = +         (24)
With:

m plim →∞ is the convergence in probability, m is the number of repetition of W and ev ρ , m W (resp. evm ρ ) is the concatenation of W (resp. ev ρ ).
Under the classical assumptions:

( ) T plim E T m m m 1 W W W W m →∞   =     is positive definite (25) plim E T T m evm ev m 1 W ρ (W ρ ) m →∞   =     exists (26)
As ev ρ depends on the observation matrix W according to ( 23), E T (W ρ ) 0 ≠ . Therefore, the estimator is not consistent. 22 September 2010

Instrumental Variable method deals with this problem of noisy observation matrix (called error in variable in the statistical frame) and can be statistically optimal [START_REF] Davidson | Estimation and Inference in Econometrics[END_REF]) [START_REF] Young | Refined instrumental variable methods of time-series analysis: Part 1, SISO systems[END_REF]. The Instrumental Variable Method proposes a consistent estimator by building the instrument matrix V such as ( 22) becomes:

T T T T V ev V Y V Wχ V ρ V Wχ = + = (27) The instrumental variable solution, V
χ , is the solution of ( 27):

( ) T T V 1 χ V W V Y - = (28)
In the following V is calculated as a function of V χ . That defines an iterative procedure such as:

( ) T T Vk 1 k k 1 χ V W V Y - + = (29)
where :

( )

Vk k V V χ = This needs for ( ) T k
V W to be a regular matrix. Assuming:

T k,m plim m m 1 V W m →∞       is non singular and, ( 30
) T T k,m k plim E evm ev m 1 V ρ (V ρ ) 0 m →∞   = =     (31) With k ,m V is the concatenation of k V for any k, Vk χ
converges to χ with m. Indeed, with the Slutsky's theorem, we obtain:

1 T T Vk k,m k,m 1 1 plim plim plim m evm m m m χ χ V W V ρ m m - →∞ →∞ →∞     = +         (32)
And with ( 30) and (31), it comes:

Vk plim m χ χ →∞ = (33)
Then the IV estimator is consistent.

Calculation of the instrumental matrix

The main problem is to find an instrument matrix V. A usual solution is to build an observation matrix from simulated data instead of measured data. These simulated data (called also instruments) are the outputs of an auxiliary model [START_REF] Young | Refined instrumental variable methods of time-series analysis: Part 1, SISO systems[END_REF] which is an approximation of the noise-free model of the process to be identified. We chose the Direct Dynamic Model of the robot (DDM) given by ( 21) to be this auxiliary model.

The IV method adapted for dynamic identification of robots can be resumed by the following algorithm illustrated Fig.

2:

• The algorithm is initialized with any the values according to the subsection 3.4.

• At each step of the iterative algorithm, S S S q ,q ,q & && are calculated by simulation of the closed loop robot tracking exciting trajectories using the DDM with the parameters identified at the previous step. S W is obtained as a sam-pling of IDIM, ( )

S S S S ID q ,q ,q & &&
, and we choose the instrument matrix as:

( ) ( ) Vk S S S Vk k S ˆV χ W q ,q ,q , χ = & && (22) ( )
Y τ is calculated from the sampling and filtering of the measurements of τ , and ( ) W q,q,q & && is calculated through IDIM using the sampling and filtering of q .

• Vk+1 χ is given by ( 29) which is the LS solution of ( 27),

• The algorithm stops when the relative error decreases under a tolerance, ideally chosen to be a small number):

with the estimation error:

k S Vk ε Y W χ = -
Fig. 2 : IV identification procedure

Calculation of the solution

Suitable solutions consist in using orthogonal projection such as QR decomposition. In this case, we have:

W W W Q R = , V V V Q R =
.

With:

V Q and W Q are orthogonal matrices which are projectors on the vectorial subspace spanned by the columns of V and W. V R and W R are upper triangular matrices.

Considering only the b base parameters to be identified, we check we have at each iteration:

rank(R W ) = rank(Q W ) = rank(R V ) = rank(Q V ) = b.
This relation guarantees that the matrix V T W is invertible. Then, equation ( 27) becomes:

k 1 k k ε ε ε α + - ≤ robot S S S q , q , q & & & τ q Control Law Control Law S τ ( ) ( ) ( ) V Vk k ˆ DDM( ) S S S S S M q q τ N q ,q χ χ χ χ = - && & Band pass filter ˆq,q,q & && ( ) ˆÎDM q,q,q & && ( ) s a m p lin g + //f ilte rin g ˆÎD M W q ,q ,q → & && ( ) Vk IDIM τ =ID q ,q ,q χ S S S S S & && ( ) S S S S S sampling IDM W q ,q ,q =V k → & && obs T sampling+filtering τ Y → obs T T k k Vk+1 T V Y V Wχ = obs T r r r q q q           & && Actual closed loop robot Simulated closed loop robot T T T T V V V W W V ev V W W Q Y Q Q R χ Q ρ Q Q R χ = + = (34)
V χ is the LS solution of the last equations.

Compared with LS regressions, the IV method needs two QR decompositions.

Initialization of the algorithm

Another problem is to choose the initial values 0 χ . We can use CAD values, or identified values with the IDIM method, but we show that there is no need at all of a priori values. We propose an algorithm not sensitive to the initial conditions, which assumes that the condition ( ) ( )

ddm k ddm k ddm k ˆˆq ( χ ),q ( χ ),q ( χ ) q,q,q & && & && (35)
is satisfied at any iteration k , and especially for k =0. This is possible by taking the same control law structure for the actual robot and for the simulated one with the same performances given by the bandwidth, the stability margin or the closed-loop poles. Because the simulated robot parameters k χ , change at each iteration k , the gains of the simulated control law must be updated according to k χ .

For example, let us consider a PD control law for each joint j . The inverse dynamic model IDM (1) for the joint j , can be written as a decoupled double integrator perturbed by a coupling force/torque, such that:

= ( ) + ( , ) = ( ) ( ) + ( , )= ( ) j n j idm j ,i i j i 1 n j , j j j ,i i j j , j j j i j τ τ M q q N q q M q q M q q N q q M q q p = ≠ = + - ∑ ∑ && & && && & && (36)
where j p is considered as a perturbation given by: ( ) ( , )

n j j ,i i j i j p M q q N q q ≠ = - - ∑ && & (37) ( ) j ,i
M q , which depends on q , is approximated by a constant inertia moment j J , given by: ( )

( ) j j j j a j , j j a q J ZZ I max M q ZZ I = + + - - (38)
j J , is the maximum value, with respect to q , of the inertia moment around joint j z axis. This gives the smallest damping value and the smallest stability margin of the closed-loop second order transfer function (42), while q varies. It can be calculated from a priori CAD values of inertial parameters and must be taken at least as j j a ZZ I + .

The joint j dynamic model is approximated by a double integrator, where j p , is a perturbation, as following:

( ) ( ) ( ) j j j j j j , j j 1 1 q τ p τ p M q J = + + && (39)
Let us consider the joint j PD control of the actual robot which is illustrated Fig. 3:

+ - + - j a g τ j r q j a v k 1 a j J 1 s 1 s + + j a p k j p j v τ j q & j q j τ j q &&
Fig. 3: Joint PD control of the actual robot.

The control input calculated by the robot controller is given by: ( )

j j j j j a a a p v r j v j v k k q q k q τ = - - & (40) j v τ ,
is the current reference of the current amplifiers which supplies the motor. The joint j , force/torque is given by:

j j a j g v τ τ τ = (41)
where: j a g τ , is the actual drive gain, calculated with the actual parameters in (9). a j J , is the actual value of j J .

•

In order to tune the tracking performances of the reference position j r q , the transfer function j r j q q is calculated with =0

j p : =0 =0 j j j j j j j j j j a 2 r j p a a a a v p p j j a 2 r j p a 2 a nj nj q 1 H q J s 1 s 1 g k k k q 1 H q 2 s s 1 τ ζ ω ω     = =     + +     = =     + + (42)
where:

a nj ω , is the actual natural frequency which characterizes the closed-loop bandwidth, a j

ζ , is the actual damping coefficient which characterizes the closed-loop stability margin, with:

j i i a a a a nj p v a j g k k J τ ω = , 1 j i i a a v a j a a p j g k 2 k J τ ζ = (43)
Then it comes: The variables ( )

, j j j j j ddm ddm ddm ddm ddm v , q , q , q τ τ & &&
, in Fig.

3, are computed by numerical integration of k DDM ( χ ) , according to (21).

The control law of the simulated robot has the same structure as the actual one, Fig. 3, where we take:

j a i g = j ap i
, the a priori value of

j a i g , a j J = k j Ĵ ,
ddm k ddm k ddm k ˆˆq ( χ ),q ( χ ),q ( χ ) q,q,q & && & && , at each iteration k.
We propose to take a regular inertia matrix 0 ( , ) ddm M q χ , in order to have a good initialization for the numerical integration of the DDM given by ( 21). This is named the "regular initialization".

It can be obtained with:

0 0 χ = , except for, 0 1, j Ia j 1,n = = (48)
The inertia of the rotor and gear of actuator j is generally taken into account in the IDM model (1) as: τ j r j j Ia q = && (49) Then, the initial inertia matrix becomes the identity matrix, which is the best regular matrix: 0 ( , ) = ddm n M q I χ (50) Another simple regular initialization is to take:

0 0 χ = , except for, 0 1, j ZZ j 1,n = = (51)
The initial inertia matrix, 0 ( , ) ddm M q χ , is no more the identity matrix, but remains regular. Another point is to choose the state initial condition of the state vector, ( )

(0) (0) ddm ddm q ,q &
, in order to integrate the DDM. The actual values ( )

(0) (0) q ,q &
, are supposed to be not perfectly known because of noises. Then, we choose, ( ) ( )

(0) (0) (0) (0) ddm ddm r r q ,q q ,q = & & , which is close to ( ) (0) (0) q ,q & . Because

Discussion on the assumptions

The IV method is based on two assumptions. The instruments matrix has to be not correlated with the noise (see ( 31)) and the matrices product between the instrument matrix and the noisy observation matrix has to be full rank (see ( 30)). These two assumptions imply that the IV estimator is consistent.

As seen in the previous section, the instrument matrix is built from a deterministic simulation. The only link between the instrument and the noise could be provided indirectly from the parameters identified at the previous step. This correlation is much lower than the noise on the system. Assuming that ev ρ is a zero-mean additive independent noise, we have:

T T k k E E E ev ev (V ρ ) (V ) ( ρ ) 0 =
Which guarantees the assumption (31).

In this paper, it is assumed that the trajectory is enough exciting in order to identify the base parameters. This means that :

( ) nf W q,q,q & && which is the noise free observation ma- trix built from the real trajectory, is full rank. According to the last section:

( ) ( ) ddm k ddm k ddm k ˆˆq ( χ ),q ( χ ),q ( χ ) q,q,q & && & && so k nf V W . As nf W W W ∆ - , it comes T T T k nf nf nf V W W W W W ∆ = -
It is not very probable that the noise on the observation matrix W

∆ gives the assumed full rank matrix T k V W singular. Indeed, we collect a very high number of samplings (at least 500 x b). So, the noises tend to be zero-mean additive independent noises. It means the columns of ∆W are independent. ∆W is also a full rank matrix. In addition, we check we obtain rank(R

W ) = rank(R V ) = rank(Q W ) = rank(Q V ) = b
at each step of the algorithm. Therefore, the assumption (30) is always true.

Experimental Validation

Case study: modeling of the SCARA robot

The identification method is carried out on a 2 degrees of freedom planar direct drive prototype robot without gravity effect, shown on Fig. 5. This direct drive prototype is very well suited to our purpose because it emphasizes non linear coupling when classical industrial robots with gear ratio above 50, divides this non-linear phenomenon by at least 2500. Moreover, the dynamic model of this robot includes eight parameters which allows us to present several conditions for the identification. At last, this robot and its real parameters, called the nominal parameters, are well known. Thus, we can check the physical meaning of the identified parameters.

The description of the geometry of the robot uses the modified Denavit and Hartenberg (DHM) notations (W. [START_REF] Khalil | A new geometric notation for open and closed loop robots[END_REF] which are illustrated on Fig. 6. The robot is direct driven by 2 DC permanent magnet motors supplied by PWM amplifiers. The dynamic model depends on 8 minimal dynamic parameters, considering 4 friction parameters:

[ ] T 1R 1 1 2 R 2 2 2 2 ZZ Fv Fc ZZ LMX LMY Fv Fc χ = (52) 2 1R 1 1 2 ZZ ZZ Ia M L = + + 2 R 2 2 ZZ ZZ Ia = + L =0.5m
, is the length of the first link.

In the case of the SCARA robot, the parameters, The 8 columns, , 1,8 7), are the following:

:,k IDM k = , of ( ) IDM q,q,q & && , in IDIM (
0 0 0 1 R 1 1 2 R 2 1 1 :,1 ZZ :,2 Fv 1 2 1 :,3 Fc :,4 ZZ 1 2 ) 1 2 2 2 1 2 2 :,5 LMX 2 1 2 1 q q IDM IDM , IDM IDM ,
q q sign( q ) IDM IDM , IDM IDM , q q ( 2q q ) cos q -q ( 2q q sin q IDM IDM q cos q q sin

+     = = = =         +     = = = =     +     + = = + 0 0 2 2 2 2 ) 1 2 2 2 1 2 2 :,6 LMY 2 1 2 1 2 :,7 Fv :,8 Fc 2 2
, q ( 2q q ) sin q q ( 2q q cos q IDM IDM , q cos q q sin q IDM IDM , IDM IDM q sign( q )

+       - + -   = =   -       = = = =        
(53) The closed-loop control is a PD control law (40) , according to Fig. 3,with: 2 . The new identification process is performed in different cases in order to compare the previous IDIM technique to the new IV technique and to investigate the robustness of IV with respect to the initialization, to the data filtering and to the closed-loop tuning. All the results are given in SI units, on the joint side.

1 1R 2 R 2 J ZZ ZZ LMX = + + ,

Comparison of IDIM and IV with good initial

values, 0

IV ˆˆ χ χ = .
At first, the algorithm is initialized with, IDIM χ , the vector of parameters identified with the IDIM LS estimator.

The IDIM LS off-line estimation is carried out with a filtered position q , calculated with a 20Hz cut-off frequency forward and reverse Butterworth filter, and with the velocities q & , and the accelerations, q && , calculated with a central difference algorithm of q . The parallel decima- Fv , have no significant estimations because of their large relative standard deviation (>30%). They have no significant contribution in the joint torques and they can be cancelled to keep a set of essential parameters of a simplified dynamic model, without loss of accuracy (W. [START_REF] Khalil | Identification of the payload inertial parameters of industrial manipulators[END_REF].

However, we prefer to keep all the parameters in the following, for a better comparison of IDIM and IV identification methods.

( , )= ddm M q I χ .
The robustness of IV with respect to a wrong initialization, such as the regular initialization (50), is investigated. The initial values of the dynamic parameters are given by (48), with:

[ ] T 1 0 0 1 0 0 0 0 0 ˆ χ =
The identified values given in Table 3, are very close to those given in Table 1. This result validates the regular initialization procedure. Moreover the algorithm converges in only 3 steps and is not time consuming. The relative norm errors on joint position, velocity and acceleration are plotted on Fig. 8 ,with the following legend:

• norm error relative to the actual filtered joint position, j ddm j j ˆq q / q -, velocity j ddm j j ˆq q / q -& & & , and accel- eration, j ddm j j ˆq q / q -&& && && , where ( )

ˆq,q,q
& && , are calculated as given in section 4.2. * norm error relative to the reference joint position, j j j ddm r r q q / q -, velocity,

j j j ddm r r q q / q - & & &
, and accel- eration, j j j ddm r r q q / q -&& && && .

The assumption (35), ( ) ( )

ddm k ddm k ddm k ˆq ( χ ),q ( χ ),q ( χ ) q,q,q & &&
& && , at each iteration k, is confirmed Fig. 8, with a constant relative norm error close to 0.5% for the position, 5%, for the velocity and 10%, for the acceleration. These results validate the updating procedure (46), of the simulated PD control law gains.

It can be seen also on Fig 8 that the simulated trajectory, ( )

ddm k ddm k ddm k ˆˆq ( χ ),q ( χ ),q ( χ ) & &&
, is 3 to 5 times closer to the actual one, ( ) ˆq,q,q & && , than to the reference one, ( ) r r r q ,q ,q & && , with a relative norm error close to 1.5% for the position, 15%, for the velocity and 30%, for the acceleration. Moreover, this error depends on the closed-loop bandwidth. It means that computing the observation matrix in (13) with the reference trajectory, ( ) r r r q ,q ,q & && , leads to a bad identification of the dynamic parameters. Then, the assumption , (

) ( ) The fast convergence of each parameter is shown in Table 4 , and is plotted on Fig 10.

ddm k ddm k ddm k ˆq ( χ ),q ( χ ),q ( χ ) q,q,q & && & && , is valid.
ddm k ddm k ddm k ˆq ( χ ),q ( χ ),q ( χ ) q,q,q & &&
& && , at each iteration k, with a constant small error. On the contrary, the relative torque norm error, given in All the actual and simulated data are sampled at m f = 200Hz. The IDIM LS estimation is carried out with the measured joint position q , and with ( ) ˆq,q & && , calculated by a central difference algorithm of q , without lowpass Butterworth filtering. There is no parallel decimation. IDIM Results are given in Table 5 IV starts with the regular initialization. IV Results are given in Table 6.

Ŷ W / Y χ - =0.08
The identified values with IDIM are not good while the identified values with IV are still good.

IDIM fails because of the too large noise in the observation matrix, ( ) fm ˆŴ q,q,q & && , coming from the derivation of q , without lowpass filtering. Then the LS estimation is biased.

IV succeeds because the observation matrix, ( )

, k fm ddm ddm ddm Ŵ q ,q ,q δ χ & &&
, is calculated without noise with the simulated values ( )

ddm ddm ddm q ,q ,q & && .
This validation shows that IV cancels the bias of IDIM estimation, coming from a noisy estimation of ( ) ˆq,q,q & && , which gives a too noisy observation matrix ( ) fm ˆŴ q,q,q & && .

) ( )

ddm k ddm k ddm k ˆq ( χ ),q ( χ ),q ( χ ) q,q,q & &&
& && , at each iteration k, with a constant norm error larger but close to the value obtained with the full bandwidth, Fig. 11, close to, 0.5% for the position, 5%, for the velocity and 10%, for the acceleration.

Preprint submitted to Automatica The relative torque norm error, given in Table 9, and plotted on Fig 12, decreases in 6 steps, only twice more than with the full bandwidth (see Table 3). This shows that IV is not very sensitive to error in the simulated closedloop bandwidth, provided the control law structure is known. However, IV fails beyond 1/3 of the full bandwidth, with 3

d d f n n / ω ω ≤ .

Discussion and conclusion

One of the improvements of our algorithm is to avoid the acceleration calculation. It is one of the major difficult points of the LS identification technique. In the general case, this problem is solved by a suitable data filtering. But, the choice of the cut-off frequency is crucial. If the cut-off frequency is too low the system is ill-conditioned and the main parameters are badly identified. On the other hand, if the cut-off frequency is too large, the observation matrix is strongly noisy and the LS estimator is biased. It is the reason why some techniques have been developed to overcome this problem: by integrating the dynamic model [START_REF] Slotine | Adaptive manipulator control a case study[END_REF] [START_REF] Middleton | Adaptative computed torque control control for rigid link manipulator[END_REF] or by using the power (Gautier 1997). The drawback of the method integrating the dynamic model is the complex expression of the model. The drawback of the power model is the loss of information due to the mix of torques. Indeed, the dynamic effect of the wrist is negligible compared to the effect of the first three axes.

The IV method is not affected by these problems because we keep all dynamic equations. In addition, the IV is less sensitive to the choice of cut-off frequency compared with the LS technique. From our point of view, our algorithm acts implicitly as an adaptative filter. Indeed, the high frequency noises are eliminated thanks to the integration of the MDD while the frequency bandwidth of our interest is determined by the bandwidth of the closed loop. Finally, experimental results have proven that the prefiltering is not necessary.

Another major improvement of our approach is to ensure the bandwidth of the closed loop in the simulator scheme. By this way, we have always S S S q ,q ,q & && close to q,q ,q & && . The correlation between the instrument matrix and the observation matrix is still high because V is still close to W nf . That means we ensure the crucial assumptions T E(V ρ ) 0 = and T V W invertible, and this explains why our algorithm works very well.

Our approach can be seen as an extension of the socalled SRIVC algorithm (Simplified Refined Instrumental Variable Continuous-time) adapted recently for closed loop system [START_REF] Gilson | A refined IV method of closed-loop system identification[END_REF] [START_REF] Young | Simple Refined IV Methods of Closed-Loop System Identification[END_REF]. However, these algorithms are quite complicated and need prefiltering. They do not adapt the gain of the simulated feedback as it is proposed in this paper. Therefore, our method is not only an application of the IV to robotics but enrich the IV methodology by providing insights from robotics.

With our algorithm, the inverse and direct dynamic models are both validated at the same time. Up to now, the DDM was validated a posteriori in simulation. This is interesting for industrial applications because this algorithm saves time. In addition, if something goes wrong, that means the dynamic model is not valid since the IV method is robust to data filtering. This paper has presented an extension and an application of the IV method. This technique was successfully applied on a 2 DOF prototype robot. From these experiments, it comes that our IV algorithm is not sensitive to data filter-22 September 2010 ing, gives additional improvements and can be helpful for practice. In addition, the convergence of the purposed algorithm is granted. Indeed, the bandwidth of the closed loop implemented to control the robot is ensured in the simulation. This is done by adapting the gains. Finally, it is also robust to the initialization.

However, to apply our algorithm properly, the structure of the control law applied to control the robot must be known.

Future works concern the use of this technique to identify flexibilities.

  the Coulomb friction with respect to the sign of the velocity and tj Of is due to the current amplifier offset which supplies the motor. o 14 s N n = × , is the number of standard parameters.

jW

  represent the m d n / n equations of joint j . The ordinary LS (OLS) solution χ minimizes the 22 September 2010 squared 2-norm 2 ρ of the vector of errors.

Fig. 1 :

 1 Fig. 1: IDIM LS identification scheme.

Fig. 4 :

 4 Fig. 4: Joint PD control of the simulated robot.

  the closed-loop transient response due to different initial conditions differs between the actual and the simulated signals during a transient period of approximately, 5 d n / ω , the corresponding joint force/torque samples are eliminated from the identification data.

FigFig. 6 :

 6 Fig. 5: The scara robot prototype.

  are calculated with (45), taking a desired damping, d j ζ =1, for joint 1 and joint 2.The desired natural frequency, d nj ω , is chosen according to the driving capacity without saturation of the joint drive. For this robot we obtain a full bandwidth with, of the control and of the measurement are equal to, m f =200Hz. Torque data are obtained from (41), and from the current reference data v τ .The simulation of the robot is carried out with the same reference trajectory and with the same control law structure as the actual robot.The gains in the simulator are calculated with (46) and with the same values,

Fig

  Fig. 7.IV validation

Fig. 8 :Fig. 9 :

 89 Fig. 8: • norm error relative to the filtered actual position, velocity, acceleration. * norm error relative to the reference position, velocity, acceleration.

  Fig. 10: IV parameters convergence

4. 5 .ω

 5 IV robustness with respect to error in the simulated closed-loop tuning, d n This section investigates the effect of an error between the actual value, a n ω , and the simulated value d n ω , of the natural frequency which represents the closed-loop bandwidth.The IV identification is performed taking half the values of procedure used to obtain results shown in

  Fig. 12: • norm error relative to the filtered actual position, velocity, acceleration. * norm error relative to the reference position, velocity, acceleration.

  and samples of v τ

	to calculate τ with (8), at different times k t ,	m k 1,...,n =	,
	while the robot is tracking a reference trajectory ( ) r r r

Table 1 :

 1 IDIM identification

		Parameter 1R ZZ	IDIM 3.44 χ	χ 2 σ ˆ 0.034	χ %σ ˆ 0.50	r
		Fv 1 1 Fc		0.03 0.82	0.031 0.1	52. 0 6.0
		ZZ	2		0.062 0.0006 0.51
		LMX	2	0.121 0.0014 0.56
		2 LMY	0.007 0.0007 5.0
		2 Fv		0.013 0.006	23.0
		2 Fc -	W	IDIM Ŷ χ	0.137 0.006 / Y =0.024	2.30
							Table 2: IV identification
	Parameter 1R ZZ	3.44	2 3.45 χ	χ 2 σ ˆ 0.036	χ %σ ˆ 0.52	r
	Fv 1 1 Fc					0.03 0.82	0.04 0.82	0.032 0.05	40. 0 3.0
	ZZ	2					0.062 0.061 0.0006 0.49
	LMX	2			0.121 0.124 0.0013 0.52
	2 LMY			0.007 0.007 0.0005 3.5
	2 Fv					0.013 0.013 0.0084 30.0
	2 Fc -	W	0.137 0.137 0.008 / Y Ŷ IV χ =0.021	3.0
	4.3. IV, validation of the regular initialization,
							0
							2

Table 3 :

 3 IV identification with regular initialization

	Parameter 1R ZZ	0 1.0 3.45 χ 3 χ	χ 2 σ ˆ 0.036	χ %σ ˆ 0.52 r
	Fv 1 1 Fc	0.0 0.04 0.0 0.82	0.032 0.05	40. 0 3.0
	ZZ	2	1.0 0.061 0.0006 0.49

Table 4 :

 4 Parameters convergence with IV identification

	Parameter	χ	0	χ	1	χ	2	χ	3
	ZZ	1R		1.0 3.46	3.45	3.45
	Fv 1 1 Fc		0.0 0.04 0.0 0.82	0.02 0.85	0.02 0.85
	ZZ	2		1.0 0.06	0.061 0.061
	LMX	2	0.0 0.122 0.124 0.124
	2 LMY	0.0 0.05	0.07	0.07
	2 Fv		0.0 0.005 0.01	0.01
	2 Fc		0.0 0.130 0.132 0.132

  Table 3, and plotted on Fig 12, dramatically decreases in only 3 steps. This shows the fast algorithm convergence.

	4.4. Comparison of IDIM and IV, without data
	filtering.

Table 5 :

 5 IDIM identification results without data filtering

	Parameter 1R ZZ	IDIM 1.5 χ	χ 2 σ ˆ 0.05	χ %σ ˆ 1.6	r
		Fv 1 1 Fc		0.095 0.15 0.55 0.26	80.0 23.3
		ZZ	2		0.14	0.018 6.7
		LMX	2	0.63	0.035 2.7
		2 LMY	0.1	0.023 11.8
		2 Fv		0.001 0.143 700.0
		2 Fc -	W	IDIM Ŷ χ	0.19 / Y	0.244 68.40 =0.8
	Table 6: IV identification results without data filtering
	Parameter 1R ZZ	0 1.0 3.45 χ 2 χ	χ 2 σ ˆ 0.007	χ %σ ˆ 0.1	r
	Fv 1 1 Fc				0.0 0.05 0.0 0.81	0.023 0.004	21.0 0.24
	ZZ	2				1.0 0.061 0.0004 0.3
	LMX	2			0.0 0.124 0.0015 0.3
	2 LMY			0.0 0.008 0.0009 5.6
	2 Fv				0.0 0.023 0.0022 48.0
	Fc 2				IDIM	0.0 0.13	0.0038 1.5

Table 2 ,

 2 that is to say a frequency measurement, =20, and a lowpass filter cut-off frequency equal to 4Hz . The parameters, given in Table7, converge in only 6 steps to values which are very close to those obtained in Table2, with a full closed-loop bandwidth.

m f =200Hz, and a parallel decimation with a factor, d n

Table 7 :

 7 IV with half full bandwidth

	Parameter 1R ZZ	0 1.0 3.44 χ 6 χ	χ 2 σ ˆ 0.014	χ %σ ˆ 0.2	r
	Fv 1 1 Fc		0.0 0.02 0.0 0.86	0.012 0.016	15.0 1.0
	ZZ	2		1.0 0.060 0.0001 0.1
	LMX	2	0.0 0.124 0.0002 0.1
	2 LMY	0.0 0.007 0.0003 2.0
	2 Fv		0.0 0.01	0.003	10.0
	2 Fc		0.0 0.13	0.0008 0.3
	The relative norm errors on joint position, velocity and
	acceleration are plotted on Fig 11, with the same legend as
	previously.
	It	can	be	seen	that,

September 2010

& && && &

& & &

& & & & && & &


Christophe Védrine

Silvia Fabiano

Canh Tran-Minh

Keywords: Conducting polymer, Tyrosinase, Phenolic compounds, Herbicides

published or not. The documents may come

Amperometric tyrosinase based biosensor using an electrogenerated polythiophene film as an entrapment support

I. Introduction

Biosensors are devices capable of recovering analytical information by utilising biological component as part of the sensor [1]. The use of an amperometric enzyme electrode provides a promising way of development of a wide range of biosensors. This approach combines specificity of the biocomponent (selective molecular recognition) with advantages of electrochemical detection [2]. The essential task in construction of an amperometric biosensor is to efficiently and effectively immobilise the bioactive moiety onto the electrode surface. Electrochemical polymerisation of conducting polymer is a simple one-step process to construct bioelectrodes. Moreover, this immobilisation method allows to easily control the thickness of enzyme film [1 and 3]. The ability to synthesise conductive electroactive polymers under mild conditions enables to perform the immobilisation of a range of biological moieties (enzymes, antibodies, even whole living cells…). Many conducting polymers can be electrochemically generated [4]. In most polymers such as polypyrrole [5, 6, 7 and 8], polyaniline [9, 10 and 11] and polythiophene [12 and 13], redox charges are delocalised over some polymer groups that could facilitate the oxidation-reduction processes. Polypyrroles can be formed under mildly oxidative conditions from aqueous media. Polyanilines are formed from similar conditions, although formation of the most highly conducting form requires the presence of acid. The monomers of simple polythiophenes are not water-soluble. Among the promising family of polythiophenes, poly 3,4ethylenedioxythiophene (PEDT) shows remarkable stability, provides homogeneous films [14] and can be synthesised electrochemically even in aqueous medium [15]. Unlike pyrrole, 3,4ethylenedioxythiophene monomer (EDT) does not require distillation before use. Previous works [16 and 17] showed the interest of using PEDT as a support for glucose oxidase (GOD) immobilisation. Tyrosinase is a binuclear copper containing metalloprotein and catalyses, in the presence of molecular oxygen, the hydroxylation and oxidation of mono-phenols to o-quinones (monophenolase activity) and the oxidation of o-diphenols to o-quinones (diphenolase activity) [18]. This enzyme, produced from mushrooms, has an isoelectric point of 4.5 [19] and carries a negative charge for pH >4.5 in aqueous solution. Attractive electrostatic interactions can occur with PEDT that is positively charged [15 and 20]. The PEDT/PPO biosensor is based on the detection of the electrochemical reduction at -0.2 V of o-quinone enzymatically produced. Thus o-diphenol electrochemically generated can undergo another enzymatic oxidation. It leads to a local increase of the concentration of odiphenol [21]. This amplification mechanism explains high sensitivities of mono-phenol or odiphenol detection with tyrosinase based bioelectrode. It was also reported that triazine and phenyl-urea herbicides could be determined from inhibition of tyrosinase response to a substrate [22, 23 and 24]. The present work describes a tyrosinase based biosensor. It attempts to demonstrate the potentialities of the PEDT immobilisation technique for analytical applications using tyrosinase (which has a more complex action mechanism than GOD). Some molecules of medical interest and pollutants potentially present in the environment were tested using this biosensor.

II. Experimental

I II I. .1 1. . R
Re ea ag ge en nt ts s EDT was kindly provided by Bayer AG (France). Polyethylene glycol (PEG) of 15 000 MW was purchased from Aldrich. Tyrosinase (polyphenol oxidase, PPO) (EC 1.14.18.1, 6680 U mg -1 lot 109H7037) from mushroom was procured from Sigma (France). Catechol, dopamine, epinephrine, L -dopa, p-cresol, 3-chlorophenol, 4-chlorophenol were purchased from Sigma. Phenol was obtained from Carlo Erba. The following herbicides (Pestanal ® ): atrazine [2-ethylamino-4-chloro-6-isopropyl amino-1,3,5 triazine], diuron [3(3,4-dichlorophenyl)1,1 dimethylurea], were purchased from Riedelde-Haen (France). They were prepared in anhydrous ethanol (HPLC grade, Carlo Erba) to get 10 g l -1 stock solutions which were stored in darkness at 4 °C for 1 month. All other chemicals were of analytical grade. Phosphate buffer was prepared using di-sodium hydrogen phosphate and sodium di-hydrogen phosphate (Prolabo, France). All solutions were prepared using milliQ ® pure water (Millipore, France). I II I. .2 2. . A Ap pp pa ar ra at tu us s Voltammetric and amperometric measurements were performed using a Tacussel PGP 201 potentiostat. The potentiostat output was recorded and processed by means of a VOLTA-MASTER 1 software. The electrochemical cell was a three-electrode cell where the PEDT/PPO modified glassy carbon disk electrode acted as the working electrode and a platinum wire as the counter electrode. All potentials were measured vs. SCE. The working electrodes were constructed using a BAS ® glassy carbon electrode with a disk-shaped active surface of 3 mm diameter. Diamond fluid kit was provided by BAS ® (England) to polish the electrode surface. I II I. .3 3. . I Im mm mo ob bi il li is sa at ti io on n p pr ro oc ce ed du ur re e Bare electrodes used for preparing the biosensors consisted of glassy carbon disks. The working electrode surface was polished before use with diamond solution of 15 μm, then 3 μm and finally 1 μm particle size. At last, it was carefully rinsed with distilled water. Two immobilisation procedures were used (Figure 1).

II.3.1. Method A, for direct determination of substrates

The electropolymerisation solution was prepared from 1 mg of tyrosinase dissolved in 200 μl of a 10 -2 M EDT aqueous solution. Five microlitres of this solution were deposited on a glassy carbon disk and dried at room temperature. The dry electrode was dipped in a PEG 10 -3 M phosphate buffer solution (0.02 M, pH 6.2) and the EDT electropolymerisation was carried out using a +1200 mV constant potential for 2 min.

II.3.2. Method B, for determination of inhibitors

The electrode was dipped in a 0.02 M pH 6.2 phosphate buffer solution containing 10 -2 M of EDT, 10 -3 M of PEG and 5 mg ml -1 of tyrosinase. Electrochemical growth of PEDT was carried out using a +1200 mV constant potential for 2 s. I II I. .4 4. . M Me ea as su ur re em me en nt ts s Amperometric measurements of substrates and inhibitors, with the PEDT/PPO biosensor were carried out in a 20 ml beaker containing 10 ml of phosphate buffer solution (0.1 M, pH 6.5). The electrochemical cell was completed with a SCE reference electrode and a platinum wire counter electrode. The solution was continuously stirred in the open air with a magnetic stirrer to maintain a constant oxygen concentration in the solution for the enzymatic reaction to operate properly. The temperature was controlled using a thermostat (Lauda-Thermostat, Germany). For substrates determination a potential of -200 mV was applied to the working electrode to detect o-quinone formation. When a baseline was stable, substrate was spiked. The current generated on the biosensor was measured when steady state was reached. For determination of inhibitors, dopamine 25 μM was used as a substrate, when the current was stable the inhibitor was spiked and the current decrease was measured. Since tyrosinase catalyses the oxidation of several mono-phenols and o-diphenols to oquinones in the presence of oxygen, its concentration should be kept constant because it is a co-substrate of the enzymatic reaction. Unless otherwise stated all experiments were carried out at 25 °C with an applied potential of -200 mV vs. SCE, in a phosphate buffer (0.1 M, pH 6.5) containing 0.1 M KCl.

III. Results and discussion

Several immobilisation methods have been used to construct PPO based biosensors (Table 1). Entrapment of PPO in a PEDT film is an easy and fast immobilisation method. There is no need to synthesise the monomer since it is commercially available. This polymer is directly electrogenerated on a glassy carbon electrode. Contrary to cryo-hydrogel or silica-gel immobilisation methods, it does not require any incubation step in a specific solution or in defined temperature conditions. PEDT/PPO electrodes were constructed according to two methods. Electrodes prepared with the method A were used to detect substrates. Biosensors constructed with method B were used for inhibitor determination. The main difference between these two methods lies in the film thickness achieved. I II II I. .1 1. . S Su ub bs st tr ra at te e d de et te er rm mi in na at ti io on n III.1.1. Optimisation of the enzyme immobilisation Method A (Figure 1) was used to achieve entrapment of tyrosinase for phenolic compound determination. The influence of enzyme loading in the polymer on the sensor response to 5 μM catechol was examined (Figure 2, solid line). Response increases when the amount of enzyme deposited on the electrode increases from 5 to 25 μg. At higher amount of deposited enzyme, response decreases. O-quinone production takes place mostly at the region closer to the film/solution interface. Therefore, most of o-quinone molecules produced in this way are diluted in the bulk solution hence their transfer to the electrode surface is decreased. Similar behaviour was reported for polypyrrole-GOD electrode [25].

The optimal amount of enzyme (25 μg) was used to assess the effect of electropolymerisation time. While 5 s of electropolymerisation time were found sufficient to ensure maximal response (Figure 3, solid line). It was observed that in this case the film was fragile, friable and could easily be detached from the electrode during handling. With 2 min electropolymerisation corresponding to complete polymerisation of the polymer, a more adherent film is obtained. Biosensor response decreases slightly. It is probably caused by the diffusional limitation of a polymeric layer.

III.1.2. Effects of pH and temperature on the biosensor response to catechol Appropriate pH ensures efficient entrapment of the enzyme while preventing loss of its activity under electropolymerisation conditions. An optimal pH of 6.2 was used: the same pH had previously been used for PEDT electropolymerisation [17]. Working pH, corresponding to the amperometric response of the PEDT/PPO electrode to catechol 5 μM was also investigated for pHs ranging from 5 to 8 in 0.1 M phosphate buffer solution (Figure 4). Maximal response is obtained for pH 6.5. This agrees with data reported by Cosnier and Innocent [START_REF] Cosnier | Innocent Bioelectrochem[END_REF] for a bioelectrode using a polypyrrole tyrosinase film. Effects of temperature on the enzyme electrode were studied with 5 μM catechol at temperature ranging from 15 to 40 °C (Figure 4). The biosensor response increases with temperature from 15 to 25 °C then a decrease is observed. The optimal temperature 25 °C also corresponds to the biosensor maximal enzyme activity.

III.1.3. Long-term stability

The main objective of enzyme immobilisation on a transducer, for analytical purposes, is to stabilise the enzyme for the biosensor to be used repeatedly over a long period of time. The long-term stability of the biosensor was monitored by measuring its response to 5 μM catechol solution everyday. The PEDT/PPO electrode was washed and stored, between measurements, at 4 °C in phosphate buffer solution. The enzyme electrode retained about 30 % of its initial activity after 12 days (Figure 5).

III.1.4. Response of the biosensor to different substrates

The two catalytic activities of tyrosinase (monophenolase and diphenolase) were tested using mono-phenolic and o-diphenolic compounds [27].

III.1.4.1. Detection of o-diphenols

Responses of the tyrosinase sensor to o-diphenols was first investigated. After each addition of aliquots of the catechol stock solution into air-saturated phosphate buffer solution the signal reaches a stable plateau, so that a calibration curve can be plotted (Figure 6). Doseresponse curves for dopamine, epinephrine, -dopa are also shown in this figure. Sensitivity corresponding to the linear range for catechol, dopamine, -dopa, epinephrine are about 1999, 133, 104, 56 mA M -1 cm -2 respectively. This sensitivity gradually decreases at higher substrate concentrations. The same sensitivity order was reported by Cosnier and Innocent [START_REF] Cosnier | Innocent Bioelectrochem[END_REF], and Besombes et al. [28]. The PEDT/PPO electrode sensitivity to dopamine is 2.2 times higher than that of polypyrrole/PPO electrode [29]. Tyrosinase exhibits a particular behaviour for L -dopa as a substrate. Sensitivity to L -dopa detection is higher than to epinephrine for low concentrations. At higher concentrations, sensitivity to epinephrine is better compared to L -dopa. Duckworth and Coleman [30] and Pomerantz and Warner [31] reported that two apparent values of Km for L -dopa have been observed (two order of magnitude of difference). These data could explain the particular behaviour of the PEDT/PPO electrode when L -dopa is used.

III.1.4.2. Detection of mono-phenols

Calibration curves obtained for mono-phenolic compounds vary in sensitivities depending on the analyte involved (Figure 7). Sensitivities (calculated in the linear range) decrease in this order: p-cresol>4-chlorophenol>phenol>3-chlorophenol. The main characteristics of the biosensor including sensitivity, linear range and detection limit are listed in Table 2.

The overall high sensitivity of the PEDT/PPO electrode compared to PPO biosensors using other matrices can be attributed to the biocompatible microenvironment for the enzyme. The difference in sensitivity between each mono-phenolic compound might depend on the hydrophobic characteristics of the immobilisation matrix [32] and molecular steric hindrance. In fact, 3-chlorophenol showed only a weak response. Transition state of this compound is difficult to form because of large steric restriction [33]. Polypyrrole/PPO bioelectrode showed similar detection profile towards chlorinated compounds. Moreover, sensitivities of PEDT/PPO electrodes towards phenol, 4-chlorophenol, 3-chlorophenol are 2.5, 3.8, 0.7 times of the polypyrrole/PPO electrode detection sensitivities respectively [34]. Compared to a solgel/PPO electrode described by Wang et al. [35], our electrode is 5.6 and 3.3 times more sensitive towards p-cresol and phenol respectively. No significant difference of response time has been observed for o-diphenolic and monophenolic compounds. While a time-lag is necessary for the sample solution to be homogeneous after substrate addition, a 20-40 s response of the PEDT/PPO biosensor is observed for any substrate. This response time is consistent with results reported by Wang et al. [35]. I II II I. .2 2. . D De et te er rm mi in na at ti io on n o of f i in nh hi ib bi it to or rs s Detection of atrazine by inhibition of a tyrosinase bioelectrode has already been reported [22]. Atrazine acts as a competitive inhibitor on the enzyme active site [28]. Similar inhibition with phenyl-urea herbicides was observed by McArdle and Persaud [22]. Since diuron is a phenylurea herbicide, both inhibitory effects of atrazine and diuron were determined with the PEDT/PPO electrode. Bioelectrodes prepared using the electropolymerisation method A did not show any inhibition when they were incubated with atrazine or diuron. Numbers of parameters act on the PEDT/PPO electrode behaviour such as inhibitor, substrate, and product diffusion, kinetic of immobilised tyrosinase, polymer film permeability [36]. For instance, Wang et al. [37] showed that the thicker the polymer film the lower the permeability. A new electropolymerisation method B was adopted to reduce the polymer film thickness while maintaining enough enzyme for a significant response (Figure 1). Since tyrosinase to catechol affinity is higher than to dopamine [38 and 39], this latter substrate was used for inhibitor determination. The influence of enzyme loading in the polymer on the sensor response to 25 μM dopamine was examined (Figure 2, dashed line). Similar results were observed with method A. Optimal response is achieved when the enzyme solution concentration is 5 μg μl -1 . Two seconds of electropolymerisation were found optimal to ensure maximal response (Figure 3, dashed line). It is the best compromise between thickness and amount of immobilised enzyme. The enzyme chemical environment is the same for both methods A and B. It was assumed pH and temperature optimisation performed on PEDT/PPO electrodes (method A) was still valid for bioelectrodes prepared according the method B. Inhibition tests were carried out using the following conditions: 25 μM dopamine, 0.1 M, pH 6.5 sodium phosphate buffer and 0.1 M KCl, 25 °C, -200 mV vs. SCE. Calibration curves for atrazine and diuron are reported in Figure 8. These results agree with those given by other authors [22, 28 and 40]. Diuron has a greater inhibitory action than atrazine on tyrosinase electrode, which is consistent with detection limits 0.5 and 1 mg l -1 respectively.

IV. Conclusion

In conclusion, tyrosinase can effectively be immobilised in PEDT electrogenerated film to produce sensitive biosensors. Optimisation of temperature and pH enables the biosensor to detect mono-phenolic and o-diphenolic compounds as substrates with high sensitivity and fast response. Compared to osmium hydrogel film, poly-pyrrole amphiphilic, cryo-hydrogel, silica sol-gel based biosensor, sensitivity of phenol detection of the PEDT/PPO electrode is higher than other unmediated immobilisation methods (Table 1).

: : I Im mm mo ob bi il li is sa at ti io on n m me et th ho od ds s f fo or r p pr re ep pa ar ra at ti io on n o of f P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e. . M Me et th ho od d ( (A A) ) f fo or r d di ir re ec ct t d de et te er rm mi in na at ti io on n o of f m mo on no o--p ph he en no ol li ic c a an nd d o o--d di ip ph he en no ol li ic c c co om mp po ou un nd d a an nd d m me et th ho od d ( (B B) ) f fo or r i in nh hi ib bi it to or r d de et te er rm mi in na at

Figures 7 F

 7 Figures

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  ti io on n. . F Fi ig gu ur re e 2 2: : E Ef ff fe ec ct t o of f e en nz zy ym me e l lo oa ad di in ng g o on n P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e r re es sp po on ns se e t to o 5 5 µ µM M c ca at te ec ch ho ol l ( (  ) ) u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho od d A A ( (2 2 m mi in n o of f e el le ec ct tr ro op po ol ly ym me er ri iz za at ti io on n) ) a an nd d t to o 2 25 5 m mM M d do op pa am mi in ne e ( (----------) ) u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho od d B B ct tr ro op po ol ly ym me er ri iz za at ti io on n) ). . C Co on nd di it ti io on ns s: so od di iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd ff fe ec ct t o of f e el le ec ct tr ro op po ol ly ym me er ri iz za at ti io on n t ti im me e o on n P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e r re es sp po on ns se e t to o 5 5 µ µM M c ca at te ec ch ho ol l ( (   / /) ) u us si in ng g p pr reep pa ar ra at ti io on n m me et th ho od d do op pa am mi in ne e ( (----------) ) u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho od d B B. . C Co on nd di it ti io on ns s: iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd Fi ig gu ur re e 4 4: : E Ef ff fe ec ct t o of f t te em mp pe er ra at tu ur re e ( (----------) ) a an nd d w wo or rk ki inng g p pH H ( (  ) ) o on n P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e r re es sp po on ns se e t to o 5 5 µ µM M c ca at te ec ch ho ol l u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho od d A A. . C Co on nd di it ti io on ns s: : 0 0. .1 1 M M s so od di iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd d 0 0. .1 1 M M K KC Cl l, , --/ /2 20 00 0 m mV V v vs s. . S SC CE E. .F Fi ig gu ur re e 5 5: : L Lo on ng g--t te er rm m s st ta ab bi il li it ty y o of f a a P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho od d A A. . C Co on nd di it ti io on ns s: od di iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd Fi ig gu ur re e 6 6: : D Do os se e--/ /r re es sp po on ns se e c cu ur rv ve es s o of f a a P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho od d A A f fo or r o o--d di ip ph he en no ol l d de er ri iv va at ti iv ve es s. . I In ns se et t: : T Ty yp pi ic ca al l r re es sp po on ns se e o of f a a P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e t to o c ca at te ec ch ho ol l i in n a an n a ai ir r--s sa at tu ur ra at te ed d b bu uf ff fe er r. . C Co on nd di it ti io on ns s: so od di iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd os se e--r re es sp po on ns se e c cu ur rv ve es s o of f a a P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e u us si in ng g p pr re ep pa ar ra at ti io on n m me et th ho odd A A f fo or r m mo on no o--p ph he en no ol l d de er ri iv va at ti iv ve es s. . C Co on nd di it ti io on ns s: od di iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd Fi ig gu ur re e 8 8: : I In nh hi ib bi it ti io on n e ef ff fe ec ct t o of f a at tr ra az zi in ne e a an nd d d di iu ur ro on n o on n t th he e P PE ED DT T/ /P PP PO O e el le ec ct tr ro od de e r re es sp po on ns se e t to o 2 25 5 µ µM M d do op pa am mi in ne e. . C Co on nd di it ti io on ns s: so od di iu um m p ph ho os sp ph ha at te e b bu uf ff fe er r a an nd Se en ns si it ti iv vi it ty y o of f p ph he en no ol l d de et te ec ct ti io on n o of f d di if ff fe er re en nt t u un nm me ed di ia at te ed d b bi io os se en ns so or rs s I Im mm mo ob bi il li is sa at ti io on n m me et th ho od ds s S Se en ns si it ti iv vi it ty y e r re eq qu ui ir re ed d f fo or r i im mm mo ob bi il li is sa at ti io on n p pr ro oc ce ed du ur re e ( (m mi in n) ) R Re ef fe er re en nc ce e

Detection of herbicides (atrazine, diuron) by enzyme inhibition has also been achieved at μM concentration levels. These results are in agreement with those reported by Besombes et al. [28] and Wang et al. [40]. Further investigations are required to achieve detection limits of 0.1 nM for catecholamine [41] and 0.1 μg l-1 for a single herbicide in drinking water, 0.5 μg l-1 for the phenol index in water required for medical and environmental applications respectively. The use of mediators would lower detection limits and reduce interferences [27]. Long-term stability could also be improved under dry storage conditions. Biosensors miniaturisation and incorporation in a flow-injection-analysis system are currently underway.


Christophe Védrine

Jean-Claude Leclerc

Claude Durrieu
email: durrieu@entpe.fr

Canh Tran-Minh

Optical whole-cell biosensor using Chlorella vulgaris designed for monitoring herbicides

Keywords: Biosensor, Algae, Chlorella, Fluorescence, Herbicide, Ecotoxicology

come

I. Introduction

Pesticides determination has been a growing concern of agriculture and health care professionals and regulatory agencies. High-performance liquid chromatography (HPLC) or gas chromatography coupled with mass spectrometry (GC-MS) have required a preconcentration method (liquid-liquid extraction, solid-phase extraction…) for analysing pesticides in drinking water ( [START_REF] Van Der Hoff | Trace analysis of pesticides by gas chromatography[END_REF][START_REF] Van Der Hoff | Trace analysis of pesticides by gas chromatography[END_REF][START_REF] Hogendoorn | Recent and future developments of liquid chromatography in pesticide trace analysis[END_REF][START_REF] Hogendoorn | Recent and future developments of liquid chromatography in pesticide trace analysis[END_REF]. They demand skilled technicians, expensive equipment and are inappropriate for continuous monitoring. On the other hand, early-warning systems are needed in order to react in case of accidental pollution. Biosensors for pollutants determination have proved to be sensitive, low cost and easily adapted for on-line monitoring [START_REF] Rogers | Biosensors for environmental applications[END_REF]. In addition, biosensors using whole cells are of ecotoxicity interest because these bioreceptors are the targets of numerous toxics.

Photosystem II (PSII)-based biosensors are reported to be able to detect herbicides in the environment [START_REF] Giardi | Photosystem II-based biosensors for the detection of pollutants[END_REF]. Photosynthesis inhibition is an interesting indicator that rapidly reflects the toxic effect of pollutants [START_REF] Overnell | Inhibition of marine algal photosynthesis by heavy metals[END_REF]. About 30% of herbicides are targeting the vegetal PSII [START_REF] Moreland | Mechanisms of action of herbicides[END_REF][START_REF] Draber | Herbicides in photosynthesis research[END_REF]. They include derivatives of phenylurea, triazine, and phenolic herbicides. These substances inhibit photosynthetic electron flow by blocking the PSII quinone binding site and thus modify chlorophyll fluorescence. Some biosensing systems for herbicides detection use isolated chloroplasts or intact cells of algae to measure changes in chlorophyll fluorescence [START_REF] Samson | Use of algal fluorescence for determination of phytotoxicity of heavy metals and pesticides as environmental pollutants[END_REF][START_REF] Arsalane | A new fluorometric device to measure the in vivo chlorophyll a fluorescence yield in microalgae and its use as a herbicide monitor[END_REF][START_REF] Conrad | Changes in yield of in vivo fluorescence of chlorophyll a as a tool for selective herbicide monitoring[END_REF][START_REF] Yoneyama | Simple and rapid screening method for photosystem II inhibitory herbicides using photoautotrophically cultured plant cells with chlorophyll fluorescence monitoring[END_REF][START_REF] Merz | Chlorophyll fluorescence biosensor for the detection of herbicides[END_REF][START_REF] El Jay | A high-sensitivity chlorophyll fluorescence assay for monitoring herbicide inhibition of photosystem II in the chlorophyte Selenastrum capricornutum: comparison with effect on cell growth[END_REF][START_REF] Van Der Heever | In vivo chlorophyll A fluorescence of Selenastrum capricornutum as a screening bioassay in toxicity studies[END_REF][START_REF] Van Der Heever | In vivo chlorophyll A fluorescence of Selenastrum capricornutum as a screening bioassay in toxicity studies[END_REF]. These reagentless biosensors are compatible for in-field use or on line monitoring [START_REF] Weston | Detection and quantification of triazine herbicides using algal cell fluorescence[END_REF][START_REF] Frense | Detection of environmental pollutants using optical biosensor with immobilised algae cells[END_REF][START_REF] Naessens | Fiber optic biosensor using Chlorella vulgaris for determination of toxic compounds[END_REF]. However, so far the limit of detection for atrazine reported with biosensors varied from 1 to 103 μg l -1 depending on the bioreceptor used [START_REF] Giardi | Photosystem II-based biosensors for the detection of pollutants[END_REF].

The objective of this study is to design a biosensor for on-line quality monitoring of groundwater and aquatic environment. Its performances should be close to European Community directive for herbicide detection (0.1 μg l -1 for a single herbicide in drinking water). The concept of algal biosensor developed by [START_REF] Naessens | Fiber optic biosensor using Chlorella vulgaris for determination of toxic compounds[END_REF] was adopted to design a new and reliable device for herbicides determination.

II. Experimental

I II I. .1 1. . S So ol lu ut ti io on ns s a an nd d r re ea ag ge en nt ts s Herbicides were chosen for their global or specific activity on PSII. They include atrazine [2ethylamino-4-chloro-6-isopropyl amino-1,3,5 triazine], simazine [2,4-bis(ethylamino)

-6- chloro-1,3,5-triazine], diuron [3(3,4-dichlorophenyl)1,1 dimethylurea], isoproturon [3-(4- isopropylphenyl)-1,1-dimethylurea],
and dinitro-o-cresol (DNOC) [4,6-dinitro-2hydroxytoluene]. All herbicides (Pestanal®) are purchased from Riedel-de-Haen (France). They are prepared in anhydrous ethanol (Carlo Erba) to get 10 -3 M stock solutions, which are stored in darkness at 4 °C for 1 month. All test solutions are diluted in Milli-Q® water (Millipore, France) immediately before use. Four buffer solutions were required to investigate across the 3-10 pH range. Citratephosphate (pH 3-5), phosphate (pH 6-8), boric acid-borax (pH 9), borax-NaOH (pH 10) buffer solutions were used at 10 mM concentration. All chemicals were of analytical-reagent grade. I II I. .2 2. . M Me et th ho od ds s o of f i in nv ve es st ti ig ga at ti io on n The Chlorella vulgaris strain (CCAP 211/12, Culture Collection of algae and protozoa, Cumbria, UK) was grown in the culture medium Lefebvre-Czarda described in the Guidance of International Organisation for Standardisation (ISO 8692). Cells were grown in a 300 ml bioreactor that enables continuous culture (1500 lx, 12 h photo-period). During illumination, the reactor was supplied with medium while culture was removed at a same flow rate (15 ml h -1 ). Before each experiment using the biosensor, 15 ml of fresh culture was harvested 5 h after the beginning of illumination. The active membrane was constructed by physical entrapment of the algal cells onto a porous matrix. Immobilisation was achieved by simple filtration of an algal suspension on a quartz microfibre filter QMA Whatman®. Concentration of algae in suspension was previously determined by optical density (OD) with a spectrophotometer Cary 300 (Varian, France) and counted under a microscope using a Thoma numeration cell (Polylabo, France). Typically, 20 ml of a suspension of OD=0.25 at 760 nm (about 7×10 6 cells per ml) was used for a 11.3 cm 2 membrane (3.8 cm diameter). This membrane was punched to smaller discs (8 mm in diameter, about 6×10 6 immobilised cells) that fit the five seatings of the rotating support. I II I. .3 3. . C Co on ns st tr ru uc ct ti io on n o of f t th he e a al lg ga al l o op pt ti ic ca al l b bi io os se en ns so or r A fibre-optic biosensor (Figure 1) was constructed with five removable algal membranes placed on a rotating support of a 10 ml homemade flow cell. An electronically controlled motor rotated the support to position the membranes alternately in front of the tip of an optical fibre bundle. The incident light hits the upper part of the membrane and the resulting fluorescence radiation is collected up to the Spex Fluorolog 2 fluorometer (from Jobin-Yvon) equipped with a microcomputer for data recording. The flow running through the biosensor is temperature controlled using a thermostat (Lauda, Germany). Flow temperature inside the biosensor is monitored using a temperature probe (Checktemp2, Hanna instruments). I II I. .4 4. . O Op pe er ra at ti in ng g c co on nd di it ti io on ns s Algal chlorophyll fluorescence measurement was carried out in two steps: 1 min to measure fluorescence, 4 min of darkness for the membrane to recover. While one membrane was in measurement position, the other four membranes were in stand-by position until the support rotates again. The excitation wavelength was set to 482 nm and the emission was measured at 683 nm: these wavelenghts are found optimal for fluorescence determination with C. vulgaris (CCAP 211/12). An Ismastec peristaltic pump (Switzerland) was used to send a continuous flow of solution through the measurement device (Figure 1) between the five algal membranes and the optical fibre bundle. The sensor was first fed with a toxic-free solution (reference solution) for 14 h to get a stable fluorescence signal. Then a herbicide was introduced to measure the biosensor response. Reversibility of the biosensor response was tested after the reference solution ran through the biosensor again for 2 h. Data were processed to obtain the mean fluorescence value (corresponding to 60 s of measurement) for each membrane. Unless otherwise stated, all experiments were performed at 20 °C in phosphate buffer solution (pH 7, 10 mM) with a 2 ml min -1 flow rate. The biosensor long-term stability under on-line working conditions was carried out over 4 weeks. A 1 μg l -1 flow solution of atrazine was tested everyday for 1 h to determine the biosensor response, then a natural water flow (Volvic, France) was performed for 23 h.

III. Results and discussion

I II II I. .1 1. . C
Co on nt ti in nu uo ou us s c cu ul lt ti iv va at ti io on n o of f a al lg ga al l c ce el ll ls s A 300 ml bioreactor was designed to have a continuous culture over 5 weeks. The medium flow rate had been adjusted so that the optical density (OD) at 760 nm remained at 0.5 (ca. 14×10 6 cells per ml). A stable physiological activity is reached 4 days after the beginning of cultivation. This system provides fresh culture for everyday consumption. Harvested cells are in a same and optimal physiological state to improve reproducibility and sensitivity of herbicides detection. Moreover, the C. vulgaris continuous cultivation is very easy to set up and less time consuming compare with batch cultures. Studies conducted on life cycles of a continuous and synchronous culture of Chlorella ellipsoidea [START_REF] Tamiya | Growth and cell division of Chlorella[END_REF] showed that cells harvested 5 h after the beginning of illumination are most photosynthetically active since they are derived from nascent cells. Similar results demonstrated that maximal quantum efficiency of photosynthesis was achieved between 2 and 8 h after the beginning of illumination for continuous cultures of Scenedesmus obliquus [START_REF] Senger | Changes in fluorescence and absorbance during synchronous growth of Scenedesmus[END_REF] and Chlamydomonas reinhardii [START_REF] Senger | The regulation of electron flow in synchronized cultures of green algae[END_REF]. [START_REF] Samuelsson | A method for studying photosynthetic capacities of unicellular algae based on in vivo chlorophyll fluorescence[END_REF] have studied the DCMU-induced fluorescence at various stages of a Chlorella pyrenoidesa culture. They showed that maximal DCMU-induced fluorescence corresponded to a maximal photosynthesis activity. Considering these reported results, we have decided to harvest C. vulgaris cells 5 h after the beginning of illumination to ensure optimal physiological activity and biosensor parameters optimisation (pH, temperature…). Additionally, the use of a continuous culture is a very convenient way to overcome problems link to culture of C. vulgaris. I II II I. .2 2. . D De et te ec ct ti io on n p pr ri in nc ci ip pl le e Response of the algal biosensor was obtained from the chlorophyll fluorescence emission at 683 under 482 nm excitation light. These wavelengths were experimentally determined. Excitation maximum corresponds to the Soret band maximum absorption of chlorophyll b [START_REF] Hipkins | Spectroscopy[END_REF] present in large amounts in green algae. Emission maximum corresponds to the main emission peak (fluorescent PSII band) for C. vulgaris [START_REF] Govindjee | Fluorescence properties of chlorophyll b-and chlorophyll ccontaining algae[END_REF] and Scenedesmus subspicatus [START_REF] Frense | Detection of environmental pollutants using optical biosensor with immobilised algae cells[END_REF].

This biosensor has been designed from practical considerations. This five membranes configuration enables to achieve a full time use of source and detector. Membranes are under the same conditions of light and toxic exposure. It results in good repeatability in membrane fluorescence measurement (2.5% of standard deviation among five membranes using algae from the same continuous culture). I II II I. .3 3. . R Re es sp po on ns se e o of f t th he e b bi io os se en ns so or r The biosensor was tested in the absence of toxic compounds and in the presence of herbicides to compare their effects on fluorescence induction kinetics. The various steps characterising the algal biosensor response to herbicides have been described by [START_REF] Naessens | Fiber optic biosensor using Chlorella vulgaris for determination of toxic compounds[END_REF]. The presence of anti PSII herbicides (diuron, atrazine, simazine and isoproturon) increases the fluorescence emission. Reproducibility was assessed with three different continuous cultures. Five membranes of each were tested to obtain the standard deviation of the response to pollutant (6.5%). Fourteen hours were needed to reach a stable fluorescence level. This fluorescence stability is required to detect any slight modification of the signal. Figure 2 illustrates typical fluorescence signal change following an increase in atrazine concentration in the flow stream. The signal reaches a stable plateau for each addition of atrazine, so that a calibration curve can be plotted. The biosensor response time necessary to attain 95% maximal response was measured for flow rates comprise between 2 ml min -1 and 10 ml min -1 for 50 μg l -1 atrazine concentration. Since a time lag is required to bring the herbicide to the bioreceptor, response times decrease with increasing carrier flow rates (data not shown). At high flow rate, the overall response time tends to approach the effective biosensor response time, which is about 10 min. This agrees with data reported by [START_REF] Frense | Detection of environmental pollutants using optical biosensor with immobilised algae cells[END_REF]. I II II I. .4 4. . E Ef ff fe ec ct t o of f a al lg ga al l d de en ns si it ty y o on n t th he e b bi io os se en ns so or r b be eh ha av vi io ou ur r The effect of algal loading in the membrane on the fluorescence signal (Figure 3) was assessed in good conditions since no leaching of algae was observed. When immobilised cells on the membrane increases, fluorescence increases and reaches a maximum corresponding to 15×10 6 cells. Then fluorescence decreases very slightly from 15×10 6 to 30×10 6 cells. This is attributed to part of the fluorescence reabsorbed by neighbouring algae. To optimise biosensor response to atrazine in the range of 0.25-10 μg l -1 , various concentrations of immobilised cells were tested (Figure 4). A maximal response corresponding to 6×10 6 immobilised cells on the membrane was observed for any atrazine concentrations and also for higher concentrations (up to 1 mg l -1 , data not shown). The detection limit (a signal-to-noise of 3) corresponds to 0.4% of fluorescence increase. It can be conclude that the atrazine detection limit of this biosensor is 0.25 μg l -1 (inset Figure 4). I II II I. .5 5. . E Ef ff fe ec ct t o of f t te em mp pe er ra at tu ur re e a an nd d p pH H o on n a al lg ga al l r re es sp po on ns se e t to o a at tr ra az zi in ne e Effects of temperature and pH on the algal response were tested with two different concentrations of atrazine (50 and 1000 μg l -1 ). The biosensor response to atrazine investigated from 10 to 30 °C (Figure 5) shows a maximum at 20 °C. This also corresponds to the temperature used for algae cultivation conditions. Good response between 10 and 25 °C still allow sensitive determination of atrazine. However, the sensor response is very affected beyond 25 °C for any atrazine concentrations and measurement in this region should be avoided. The pHs tested ranges from 3 to 10 (Figure 6). Considering the various buffers involved, low buffer solution concentrations were used to minimise the effect of buffer composition on algae metabolism. Maximum response is achieved at pH 7, which corresponds to the culture medium pH. Between pH 5 and 9 the biosensor response is high enough to ensure sensitive determination of atrazine. Maximal response is reduced by half for pH 3 and 10. To monitor atrazine in water, the C. vulgaris biosensor should operate as close to the optimal conditions as possible (pH 7 and 20 °C) to achieve best results. I II II I. .6 6. . L Lo on ng g--t te er rm m s st ta ab bi il li it ty y u un nd de er r o on n--l li in ne e w wo or rk ki in ng g c co on nd di it ti io on ns s The main objective of algae immobilisation is to stabilise the bioreceptor for the biosensor to be used repeatedly over a long period of time under on-line monitoring conditions. No loss of activity participating to the biosensor response had been observed. The response of the biosensor to 1 μg l -1 of atrazine remains stable over 4 weeks (data not shown). I II II I. .7 7. . D De et te ec ct ti io on n l li im mi it t a an nd d E EC C 5 50 0

One of our objectives was to improve the detection limit with a C. vulgaris based biosensor. Atrazine was first tested to determine optimal operating conditions, which were later applied for other herbicides. Dose response curves corresponding to atrazine, simazine, diuron and isoproturon are presented in Figure 7. Successive addition method is not appropriate to construct DNOC response curve due to its dual mode of action. The detection limit, the toxic concentration EC50 that affects 50% of the response and reversibility of action of these pollutants are listed in Table 1.

Triazines and phenylurea are well-known herbicides that specifically fix to the Q B binding site of PSII with high affinity. This blocks the photosynthetic electron flow and causes an increase in chlorophyll fluorescence intensity. Experiments performed with atrazine, simazine, isoproturon and diuron (classical PSII inhibitors) showed that the biosensor was very sensitive to all four herbicides at sub ppb level. The EC 50 obtained is consistent with the detection limit (the lower the EC 50 , the lower the limit of detection). Those herbicides can be considered as reversible since most activity is recovered after exposition to herbicides and flushing the biosensor with a reference solution.

Phenolic herbicides have two modes of action: they are inhibitors of PSII electron transport, and also uncouplers of oxidative phosphorylation and photophosphorylation, due to their protonophoric properties [START_REF] Oettmeier | Phenolic herbicides and their methyl-ethers: binding characteristics and inhibition of photosynthetic electron transport and photophosphorylation[END_REF]. This could explain the specific behaviour of the biosensor towards the phenolic herbicide, DNOC. The fluorescence intensity increases until 300 μg l -1 . It could be attributed to the inhibition of PSII electron transport while the uncoupling effect is comparably negligible. Although the PSII inhibition still increases at higher concentrations, the uncoupling effect of DNOC tends to become the major parameter, which decreases fluorescence signal. Although DNOC is a poor inhibitor of PSII electron transport compared with triazine, phenyl-urea and others from the same family (dinoseb, dinoterb, ioxynil) [START_REF] Scalla | Mécanismes d'action phytotoxique des autres familles d'herbicides[END_REF], it can be detected down to 5 μg l -1 (Table 1). It should be noted that the phytotoxicity of DNOC is mainly due to its uncoupling effect rather than inhibition effect on PSII electron transport [START_REF] Scalla | Mécanismes d'action phytotoxique des autres familles d'herbicides[END_REF]. Since its mode of action, modification of fluorescence signal is irreversible. Rinsing the biosensor with a DNOC free solution results in a decrease of the fluorescence signal far below the reference level suggesting that the membrane has been damaged due to the uncoupling effect while PSII inhibition is no longer effective. In case of herbicides monitoring, precaution should be taken in interpretation of the response particularly if DNOC concentration exceeds 300 μg l -1 .

Conclusion

The fluorescence-based biosensor using C. vulgaris is particularly suitable for detection of PSII-inhibiting herbicides. It can also be used for determination of other herbicides such as DNOC, which is a poor inhibitor of PSII electron transport. Two strategies have been adopted to improve the performance of this biosensor. First, optimisation of the bioreceptor is achieved with a continuous cultivation technique, which provides harvested cells in a same optimal physiological state that increases reproducibility.

Thus it facilitates the determination of optimal operating conditions (algal density on the membrane, pH, temperature) and results in an improvement of pollutant detection. This strategy has never been reported (to our knowledge) for biosensors using C. Vulgaris. Second, reliability of the sensor to detect pollutants is improved as the number of assays performed is multiplied by five compared with a single membrane based biosensor. This design enables an easier monitoring of the evolution of the flow toxicity because of the 1 min lag difference between the measurement of each membrane.

Response time and detection limit of this biosensor are compatible for groundwater and aquatic environment quality monitoring and its use as an early warning system. In fact, the level of atrazine in river water varies seasonally with the highest concentrations found in the spring and summer months [START_REF] Solomon | Ecological risk assessment of atrazine in North American surface waters[END_REF]. For example, [START_REF] Hall | Enzyme immunoassay based survey of precipitation and surface water for the presence of atrazine, metolachlor and 2,4-D[END_REF] reported detectable levels of atrazine rapidly rose to 43 μg l -1 during May and then dropped sharply to 1.8 μg l -1 by the end of June. The biosensor would be an appropriate tool to monitor seasonal variation of atrazine in aquatic media and be used as an alarm system. Further investigations with several micro-organisms tested simultaneously in this multi-membrane device would give a better understanding of the impact of pollutants on aqueous ecosystems.

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