Bernard Vau

Ioan Doré Landau

Adaptive Rejection of Narrow-band Disturbances in the Presence of Plant Uncertainties -A Dual Youla-Kucera Approach

Keywords: Adaptive disturbance rejection, Youla-Kucera parameterization, Adaptive control, Active noise control, Internal model principle

The stability of adaptive disturbance rejection schemes using Youla-Kucera (YK) parametrization and the internal model principle (IMP) in the presence of plant model uncertainties is investigated. The problem is approached by using the dual Youla Kucera parametrization for the description of the plant model uncertainties. The known disturbance case is discussed first, emphasizing the need of over parametrization of the Youla Kucera filter used for control in order to both solving the IMP and the stability problems. Then this solution is extended for the case of unknown disturbances leading to the use of a parameter adaptation algorithm with projection. A stability analysis of the adaptive scheme is provided. Simulation results on relevant examples and experimental evaluation on an active noise attenuation system illustrate the possibilities of this approach for handling significant plant-model mismatch.

Introduction

In the last twenty years, the issue of adaptive rejection of unknown disturbances has received a significant interest in the field of control. The basic assumption is that the disturbances are the result of a white noise or of a Dirac impulse passed through the "model of the disturbance" and therefore, using the "internal model principle"(IMP) they can be asymptotically rejected. However the parameters of these models are unknown and can be time-varying and therefore an adaptive approach has to be considered 1 . In this context however, it is assumed that the plant model is known (often obtained by system identification from experimental data) and remains almost constant. This type of adaptive problem has been termed "adaptive regulation". Most of the proposed algorithms are based on the Youla-Kucera (YK) parametrization (or Q-parametrization) [START_REF] Anderson | From Youla-Kucera to identification, adaptive and non-linear control[END_REF][START_REF] Tay | High Performance Control, Birkauser[END_REF], that al-Email addresses: bernard.vau@ixblue.com (Bernard Vau), ioan-dore.landau@gipsa-lab.grenoble-inp.fr (Ioan Doré Landau). 1 For known disturbances subject to small variations of their characteristics a robust approach can be considered [START_REF] Airimitoaie | Robust and adaptive active vibration control using an inertial actuator[END_REF], [START_REF] Landau | Robust and adaptive noise attenuation in ducts[END_REF].

lows for the tuning of a compensator within the class of all-stabilizing controllers. The basic diagram of such a system is shown in Fig 1 [START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF] [START_REF] Landau | Adaptive control[END_REF]. R 0 and S 0 define a polynomial central stabilizing controller with pre-specified fixed parts H R and H S (R 0 = R 0 H R , S 0 = S 0 H S ). An observer of the disturbance d is used. The output of the observer w is processed through the Youla-Kucera filter Q. The Q filter will be adapted in real time in order to cancel asymptotically the disturbance d. A successful adaptive rejection of disturbances resulting from an unstable exogenous system is mentioned in [START_REF] Valentinotti | Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite[END_REF]. In the field of active noise control, first references seem to be [START_REF] Ben Amara | Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems -Part I: Theory[END_REF], [START_REF] Ben Amara | Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems -Part II: Experiments[END_REF] and a more recent reference is [START_REF] Landau | Robust and adaptive noise attenuation in ducts[END_REF]. In the field of active vibration control a first reference seems to be [START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF]. In all these papers, the model of the system to be controlled is assumed to be perfectly known (models obtained by system identification). Under this assumption these algorithms do not require a specific stability condition, except that the closed-loop including the central controller must be stable. However in many situations, the plant model is subject to changes during operation and therefore the plant model uncertainties have to be taken into account. In order to address the issue of plant model uncertain- ties, Kinney and Callafon proposed an adaptive scheme called REACT [START_REF] Kinney | Robust estimation for automatic controller tuning with application to active noise control, in Model-based Control: Bridging rigorous theory and advanced technology[END_REF] that aims at rejecting unknown disturbances acting on an uncertain system. The uncertainties are represented by means of the dual Youla-Kucera parameterization [START_REF] Anderson | From Youla-Kucera to identification, adaptive and non-linear control[END_REF] that had been previously used in the context of identification (see for example [START_REF] Van Den Hof | Multivariable closed-loop identification: From indirect identification to dual Youla Parameterization[END_REF]). In the REACT scheme, conditions about stability of a robust controller are given. However no stability analysis is provided for the add-on adaptive scheme. In [START_REF] Jafari | Robustness and performance of adaptive suppression of unknown periodic disturbances[END_REF] the problem of adaptive rejection of unknown periodic disturbances in the presence of plant model uncertainties is discussed in the context of a different controller parametrization and the uncertainties are unstructured. Stability conditions are provided. The various applications reported in the literature, particularly in the fields of active vibration and noise control (see [START_REF] Landau | Benchmark on adaptive regulationrejection of unknown/time-varying multiple narrow band disturbances[END_REF], [START_REF] Landau | Adaptive and Robust Active Vibration Control[END_REF]), indicate that very reliable discrete linear models can be obtained by experimental system identification techniques (very small differences between simulations and real experiments) and that changes of the physical configuration and of various operational conditions lead to models of the same structure (with different orders and parameters). The work reported in this paper has been motivated by significant variations of the plant model which may occur in some active noise and vibration attenuation applications. There are various way to express the model uncertainties. However in this context it seems reasonable to use the dual Youla Kucera parametrization as a way to express the relationship between the nominal model used for design and the true model of the system. The main objectives of the paper are:

• to develop a Youla-Kucera controller parametrization for the case of plant uncertainties described by dual YK parametrization, • to develop adaptation algorithms for the case of plant model uncertainties described by the dual YK parametrization, • to provide conditions assuring the stability of the adaptive regulation scheme, • to illustrate the methodology by simulations on relevant examples and by experimental results (an active noise control system).

The main ingredient for solving this problem is to augment the size of the (finite impulse response) Q filter beyond the minimum value resulting from the application of the internal model principle (IMP) when there are no plant uncertainties. In this context, as a consequence of plant uncertainties, the closed loop poles are no more invariant with respect to the values of the (finite impulse response) Youla-Kucera filter parameters (as it will be shown in section 3.2) and they may become unstable. Therefore stability conditions related to the Q-filter parameters and dual YK filter parameters will have to be fulfilled. Furthermore in the adaptive operation since the size of the Q-filter is larger that the minimal one, persistent excitation arguments can no more be used for stability analysis and projection has to be included in the parameter adaptation algorithm. While the idea of augmenting the size of the Q filter to take into account plant-model mismatch has been probably first suggested in [START_REF] Valentinotti | Adaptive rejection of unstable disturbances: Application to a fed-batch fermentation process[END_REF], pp. 48-49, to our knowledge this approach has never been worked in detail to establish a clear procedure and to provide stability conditions. Preliminary results have been presented in [START_REF] Vau | Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties[END_REF]. The paper is organized as follows: Section 2 gives the description of the basic control structure. The development of the adaptive control strategy is presented in Section 3. Stability of the resulting scheme is analyzed in Section 4. The case of open loop stable plant models is discussed in Section 5. Simulation results on relevant examples are presented in Section 6. Experimental results on an active noise control system subject to important plant model variations are presented in Section 7.

Closed-loop Structure

The nominal plant model used for controller design (design model )2 is denoted G o (q -1 ) and is described by:

G o (q -1 ) = q -do B o (q -1 ) A o (q -1 ) (1)
with:

d 0 = the plant pure time delay in number of sampling periods;

A o = 1 + a 1 q -1 + • • • + a n A q -n A ; B o = b 1 q -1 + • • • + b n B q -n B = q -1 B * ; B * o = b 1 + • • • + b n B q -n B +1 ;
where A(q -1 ), B(q -1 ), B * (q -1 ) are polynomials in the delay operator q -1 and n A0 , n B0 and n B -1 represent their orders3 .

A stabilizing controller called "central controller"

C o (q -1
) is designed based on the nominal model:

C o (q -1 ) = R o (q -1 ) S o (q -1 ) = R o (q -1 )H R (q -1 ) S o (q -1 )H S (q -1 ) (2)
where H r (q -1 ) and H s (q -1 ) are some fixed parts which may be imposed during the controller synthesis 4 .

C o (q -1 ) is causal and S o (q -1 ) is a monic polynomial.

The closed loop poles of the nominal feedback system are defined by the polynomial:

P o (q -1 ) = A o (q -1 )S o (q -1 ) + q -do B o (q -1 )R o (q -1 ) (3)
which has (by design) all its roots strictly inside the unit circle. The real plant model denoted G(q -1 ) has the same structure as G 0 (q -1 ),

G(q -1 ) = q -d B(q -1 ) A(q -1 ) (4)
but the order of the various polynomials (n A , n B ), the delay d and the parameters are unknown. Remark: A system representation using coprime factorisation [START_REF] Anderson | From Youla-Kucera to identification, adaptive and non-linear control[END_REF][START_REF] Kinney | Robust estimation for automatic controller tuning with application to active noise control, in Model-based Control: Bridging rigorous theory and advanced technology[END_REF][START_REF] Kinney | Robust Estimation and Automatic Controller Tuning in vibration control of time varying harmonic disturbances[END_REF] can also be used. 5The following hypothesis is made throughout the paper: H1-The real plant model G is also stabilized by the central controller C 0 . Therefore the polynomial:

P (q -1 ) = A(q -1 )S o (q -1 ) + q -d B(q -1 )R o (q -1 ) (5)
which defines the poles of the closed loop when G 0 is replaced by G has its roots strictly inside the unit circle. In other terms we will consider the class of system G satisfying the hypothesis H1. 6A class of systems satisfying this hypothesis can be defined by using the Vinnicombe distance (sufficient condition). One has the following result [START_REF] Vinnicombe | Uncertainty and feedback -H∞ loop-shaping and the v-gap metric[END_REF], [START_REF] Landau | Digital Control Systems[END_REF]:

Lemma 1 : The controller C o which stabilizes the model G o will also stabilize the model G if:

δ ν (G o , G) b(C o , G o ) (6)
where δ ν (.) is the Vinnicombe distance and b(.) is the generalized Vinnicombe stability margin.

Development of the algorithm

As already indicated in the Introduction, applications in the fields of active vibration and noise control (see [START_REF] Landau | Benchmark on adaptive regulationrejection of unknown/time-varying multiple narrow band disturbances[END_REF], [START_REF] Landau | Adaptive and Robust Active Vibration Control[END_REF]) clearly emphasize that model representation of the form (1) and ( 4) are very reliable and the changes of physical configurations and operation conditions lead to models of the same structure (with different orders and parameters). In this context it seems reasonable to use the dual Youla Kucera parametrization as a way to express the relationship between G(q -1 ) and G o (q -1 ). Such an approach for describing model uncertainty has been already used. See for example [START_REF] Kinney | Robust Estimation and Automatic Controller Tuning in vibration control of time varying harmonic disturbances[END_REF] and [START_REF] Anderson | From Youla-Kucera to identification, adaptive and non-linear control[END_REF].

In order to develop the adaptive scheme for handling both unknown disturbances and plant model uncertainties, we will consider first the "nominal" case without plant model uncertainties and assuming that the model of the disturbance is known. This will allow to set up the structure of the control law. Then the model uncertainty (assumed temporarily to be known) will be added. This will emphasize the need for an overparametrized Q filter in order to simultaneously fulfill the IMP conditions and the stability conditions related to the size of the uncertainty. In the next step the adaptive control algorithm will be set up and analyzed.

The Nominal Case

Let {u(t)} and {y(t)} be the input and output sequences of the controlled plant, and {d(t)} the sequence of an output disturbance such that |d(t)| < C ∀t, with 0 < C < ∞. In the nominal case, one has

y(t) = G o (q -1 )u(t) + d(t) (7)
Moreover, one assumes that the output disturbance d(t) results from the filtering of a Dirac impulse δ(t)

d(t) = N d (q -1 ) D d (q -1 ) δ(t) (8)
where D d (q -1 ) has all its roots on the unit circle and is known 7 .

For the purpose of this paper, Q(q -1 ) is considered to be a polynomial of the form:

Q(q -1 ) = q Q 0 + q Q 1 q -1 + . . . + q Q n Q q -n Q . ( 9
)
which is fed by the signal w(t) (see Fig 1).

w(t) = -q -do B o (q -1 )u(t) + A o (q -1
)y(t) (10) Remark: Other Q-filter structures may also be considered like linear combination of orthogonal transfer functions (Laguerre, Kautz or Generalized basis of orthonormal transfer functions) [START_REF] Heuberger | Modelling and identification with rational Orthogonal Basis Functions[END_REF]. Note that for the nominal case

w(t) = A 0 (q -1 )d(t) (11)
which can be interpreted as a stable observation of the disturbance [START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF]. In the presence of the Youla-Kucera parametrization, the controller becomes:

u(t) = -C(q -1 )y(t) = - R(q -1 ) S(q -1 ) y(t) (12)
where8

R(q -1 ) = R o + A o H R H S Q S(q -1 ) = S o -q -do B o H R H S Q (13)
To compute Q(q -1 ) in order that S in ( 13) contains the internal model of the disturbance (i.e.: S = S D d ) required by the Internal Model Principle for asymptotic rejection of the disturbance, one has to solve:

S D d + H R H S q -do B o Q = S o (14)
where Q and S are unknown 9 . For Q(q -1 ) = 14) has a solution if D d and H R H S q -do B o are coprime, and a minimal solution is obtained for n Q = n D -1, see [START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF].

q Q 0 + q Q 1 q -1 + • • • + q Q nQ q -n Q , and D d (q -1 ) = 1 + d 1 q -1 + • • • + d n D q -n D , Eq. (
Q D (q -1
) is the dual Youla-Kucera filter where

Q D (q -1 ) = ∆(q -1 ) Γ(q -1 ) (15)
The polynomial Γ(q -1 ) is monic with all its roots strictly inside the unit circle, and the polynomial ∆(q -1 ) has no direct transmission. Under these assumptions, the uncertain plant G(q -1 ) can be written

G(q -1 ) = Γ(q -1 )q -do B o (q -1 ) + ∆(q -1 )S o (q -1 ) Γ(q -1 )A o (q -1 ) -∆(q -1 )R o (q -1 ) (16)
From ( 16), the dual-Youla filter can be expressed from the polynomials of the nominal and uncertain plant as follows

∆(q -1 ) = q -d BA o -q -do B o A (17a) Γ(q -1 ) = AS o + q -d BR o (17b)
and

y(t) = G(q -1 )u(t) + d(t) (18)
If one considers the closed-loop including the system G(q -1 ), ( 17) and the controller C(q -1 ) (12), the output sensitivity function from d(t) to y(t) is obtained directly by combining ( 16), [START_REF] Melendez | Data driven design of tonal noise feedback cancellers[END_REF], and [START_REF] Heuberger | Modelling and identification with rational Orthogonal Basis Functions[END_REF]. The following relation holds:

y(t) = ΓA o -∆R o P o S o -QH R H S q -do B o Γ + QH R H S ∆ d(t) (19)
One can notice that for G(q -1 ) = G o (q -1 ), a stability condition appears (in addition to (5)):

Γ(q -1 ) + Q(q -1 )H R (q -1 )H S (q -1 )∆(q -1 ) (20)
must have all its roots strictly inside the unit circle 10 .

In this context, one has the following result for w(t):

Lemma 2 In case of model uncertainty expressed by the Dual-Youla parameterization as in [START_REF] Ljung | On Positive Real Transfer Functions and the Convergence of Some Recursive Schemes[END_REF], one has

w(t) = Γ(q -1 )Ao(q -1 ) -∆(q -1 )R o (q -1 ) Γ(q -1 ) + Q(q -1 )H R (q -1 H S (q -1 )∆(q -1 ) d(t) (21)
Proof: Taking into account equation ( 10)

w(t) = -q -do B o u(t) + A o y(t) and multiplying both sides by (S o -QH R H S q -do B o ) leads to (S o -QH R H S q -do B o )w(t) = (S o -QH R H S q -do B o )(-B o u(t) + A o y(t)). But ac- cording to (13) one has u(t) = -Ro+QH R H S qAo So-QH R H S q -do Bo y(t). Introducing this expression in the previous ones, yields (S o -QH R H S q -do B o )w(t) = q -do B o (R o + QH R H S A o )y(t) + A o (S o -QH R H S q -do B o )y(t) = P o y(t). But taking into account (19) one has P o y(t) = (ΓA o -∆R o ) So-QH R H S q -do Bo Γ+QH R H S ∆ d(t). Therefore one obtains (S o -QH R H S q -do B o )w(t) = (ΓA o -∆R o ) So-QH R H S q -do Bo ΓAo-∆Ro d(t), hence the result w(t) = ΓAo-∆Ro Γ+QH R H S ∆ d(t).
2 As a consequence, in order that w(t) be an observation of d(t) (which is bounded) the polynomial [START_REF] Tay | High Performance Control, Birkauser[END_REF] must have all its roots strictly inside the unit circle. These observations can be summarized as follows:

Lemma 3 For the case of plant uncertainty represented by the dual Youla Kucera parametrization and in the presence of bounded disturbances d(t), y(t), u(t) and w(t) will be bounded provided that the polynomial (20) will have all its roots strictly inside the unit circle.

Disturbance rejection -known disturbance case

Since G(q -1 ) differs from G o (q -1 ), the minimal solution of (14) denoted Q(q -1 ) does not necessarily leads to the stability of the closed-loop. In such a situation 10 This condition disappears when returning to the hypotheses of a nominal system with a minimal dimension of the Q-filter. Previous works assuming perfect knowledge of the plant model appear as particular case of the results of the present paper.

one can augment the order of Q(q -1 ). Non-minimal solution to ( 14) can be parametrized as Q(q -1 ) = Q(q -1 ) + V (q -1 )D D (q -1 ), and ( 14) becomes [START_REF] Valentinotti | Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite[END_REF] where V (q -1 ) is any polynomial (there is no need for it to be monic). One has the following result about the existence of a polynomial Q(q -1 ) with a degree n Q < ∞ guaranteeing the closed-loop stability:

S -V q -do B o H R H S D d + H R H S q -do B o ( Q + V D d ) = S o
Lemma 4 The existence of a finite dimensional Q which stabilizes the closed-loop and asymptotically reject the disturbance d(t) is assured (sufficient condition) if:

• For the frequencies ω j of the disturbance corresponding to D d (e -iωj ) = 0, the following inequality is satisfied:

So(e -iω j ) e -iω j Bo(e -iω j ) <

A(e -iω j )So(e -iω j ) + e -iω j d B(e -iω j )Ro(e -iω j ) e -iω j d B(e -iω j )Ao(e -iω j ) -e -iω j do A(e -iω j )q -do Bo(e -iω j ) (

• For all other frequencies, the following inequality is satisfied

Q(e -iω ) < A(e -iω )S o (e -iω ) + e -iωd B(e -iω )R o (e -iω ) e -iωd B(e -iω )A o (e -iω ) -e -iωdo A(e -iω )q -do B o (e -iω ) • • • • • • × 1 H R (e -iω )H S (e -iω ) (24)
The proof of this result is given in Appendix.

Adaptive disturbance rejection

In the presence of unknown narrow band disturbances and plant model uncertainties, the polynomials D d , Γ and ∆ are unknown. In this situation one can consider a Q-filter with adjustable parameters:

Q(q -1 , t) = qQ 0 (t) + • • • qQ nQ (t)q -nQ (25)
and the objective is to find a parameter adaptation algorithms driving this parameters towards the values assuring asymptotic rejection of the disturbance. We will follow up to certain extent the development procedure described in [START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF] however including from the beginning the presence of model uncertainties described by the dual Youla Kucera representation and the use of a Q filter of higher order that the minimal one used for the nominal case (when G = G 0 ). When using a Q-filter with constant coefficients, the output of the system y(t) in the presence of a disturbance d(t) can be expressed as:

y(t) = ΓA 0 -∆R 0 P 0 (S 0 -q -do B 0 QH R H S ) Γ + QH R H S ∆ d(t) (26)
By combining ( 26) and ( 21), one obtains

y(t) = S o P o - Q H R H S q -do B o P o w(t) (27)
Since the objective is to drive y(t) asymptotically to zero, it is logically to consider this variable as an adaptation error which will be denoted ε(t). Now replacing in (27) the fixed value of Q by an estimation of Q one gets an expression for the a-priori adaptation error ε o (t + 1):

ε o (t + 1) = S o P o -Q(q -1 , t) H R H S q -do B o P o w(t + 1)
(28) One can define the a-posteriori adaptation as:

ε(t + 1) = S o P o -Q(q -1 , t + 1) H R H S q -do B o P o w(t + 1)
(29) Taking into account Eq.( 14) (resulting from the application of the IMP principle for the case of known disturbances), Eq.(29) can rewritten as:

ε(t + 1) = Q(q -1 ) -Q(q -1 , t + 1) q -do B * o H R H S P o w(t) +v(t + 1) (30)
where v(t + 1) = Dp(q -1 )S (q -1 ) Po(q -1 ) w(t + 1) is a signal which tends towards 0. Set

w 2 (t) = q -do B * o H R H S P 0 w(t) (31)
The a-posteriori adaptation error can be expressed under the form [START_REF] Landau | Adaptive control[END_REF]:

ε(t + 1) = H(q -1 ) θ -θ(t + 1) T φ(t) (32)
where

φ T (t) = [ w 2 (t) • • • w 2 (t -n Q )] θ T = [q Q 0 • • • q Q n Q ] θT (t) = [q Q 0 (t) • • • qQ n Q (t)] and H(q -1 ) = 1
Taking into account the fact that the order of the polynomial Q is higher than the minimal order required by the IMP, the parameter adaptation algorithm proposed in [START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF] has to be completed with a projection of the estimated parameter vector on a bounded domain in order to prove the stability of the adaptive control scheme (see [START_REF] Landau | Adaptive control[END_REF] p.340). The adaptation algorithm to be used is θ(t + 1) = θp (t) + F (t)φ(t)ε(t + 1) (33)

ε(t + 1) = ε o (t + 1) 1 + φ T F (t)φ(t) (34)
F (t + 1) -1 = λ 1 F (t) -1 + λ 2 φ(t)φ T (t) (35) 0 < λ 1 < 1 0 ≤ λ 2 < 2, F 0 > 0 ( 36
)
where θp (t) is the projection of θ(t) which is computed as follows:

θ (t) = F (t) -1/2 θ(t) θ p (t) = θ (t) if θ (t + 1) ∈ D θ p (t) = ⊥ proj of θ (t) on D if θ (t) / ∈ D θp (t) = F (t) 1/2 θ p (t) (37)
The projection domain D is defined as follows:

θ ∈ D, θ (t) = F (t) -1/2 θ(t) ∈ D (38)
where the projection domain D is such that:

D : || θ(t)|| 2 2 < R < ∞ (39)
Two particular choices for the adaptation gain F (t) are mainly used in practice in order to assure the alertness of the adaptation with respect to possible variations of the disturbance characteristics [START_REF] Landau | Adaptive control[END_REF][START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF] 11 :

• Constant trace: for a constant ratio λ 1 (t)/λ 2 (t), λ 1 (t) is chosen such that the trace of the adaptation gain matrix F (t) remain constant (traceF (t)=traceF 0 ) • Constant gain: λ 1 (t) = 1, λ 2 (t) = 0 and F (t) = F 0 = αI; α > 0.

Stability Analysis

The following theorem summarizes the stability analysis of the adaptive scheme Theorem 1 Under the assumptions:

• Controller C 0 stabilizes unknown plant model G • Disturbance d(t) has the form (8) and is bounded [START_REF] Landau | Benchmark on adaptive regulationrejection of unknown/time-varying multiple narrow band disturbances[END_REF] and assuring that the polynomial (20) has all its roots strictly inside the unit circle.

• It exists Q(q -1 ) ∈ D with n D -1 ≤ n Q < ∞ satisfying (
then one has:

lim t→∞ ε(t + 1) = 0 (40)
and if in addition:

max θ∈D Q -Q 1 ∆ Γ + ∆Q 1 < 1 ( 41
)
where ∆ = ∆H R H S one has: Condition (41) guarantees that w(t) as well as the regressor vector, the output and the input will be bounded. This condition results from the analysis of the equivalent scheme connecting d(t) with w(t) shown in Fig. 3 where Q(t) = Q(t) -Q (see details in the proof below).

w(t), u (
In order that w(t) be bounded the feedback loop should be BIBO. Applying the "small gain theorem" condition (41) results.

Remark : For G = G 0 and ∆ = 0, condition (41) is automatically satisfied. Similar situation occurs for the case 20) is satisfied since the persistence of excitation drives Q(t) = Q(t) -Q to zero. Proof: The equation of the a posteriori adaptation error (32) has the form considered in Theorem 3.2 from [START_REF] Landau | Adaptive control[END_REF] (pp 104-105) and since H(q -1 ) = 1, one immediately concludes that (40) holds. To go further one has to show that φ(t) and respectively w(t) are bounded (φ(t) contains delayed and filtered signals generated by w(t)).

n Q = n D -1 if (
In an adaptive context using ( 21), one can write:

Γ + ∆ Q(t) w(t) = (ΓA o -∆R o ) d(t) (44)
or alternatively:

Γ + ∆ Q(t) ± ∆Q w(t) = (ΓA o -∆R o ) d(t) (45)
Set N = ΓA o -∆R o , and Q(t) = Q(t) -Q, then (45) can be written as:

w(t) = N Γ + ∆Q d(t) -Q(t) ∆ Γ + ∆Q w(t) (46)
which corresponds to a feedback system with an external bounded excitation whose output is w(t), shown in Fig. 3. The input to the equivalent feedback system d = N Γ+ ∆Q d(t) has the property:

d(t) ∞ ≤ N Γ + ∆Q 1 d m (t) ( 47
)
where

d m (t) = sup|d(t)| = d(t) ∞ and
N Γ+ ∆Q 1 is finite. The output of the feedback path x(t) is given by

x(t) = ∆ Q Γ + ∆Q w(t) (48)
and therefore:

w(t) ∞ ≤ d(t) ∞ + Q 1 | ∆ Γ + ∆Q 1 w(t) ∞ (49)
Applying small gain arguments [START_REF] Desoer | Feedback Systems: Input-Output properties[END_REF] and taking into account that the equivalent feedforward path has unitary gain one concludes that condition (41) assures the boundedness of w(t). From the definition of φ(t) given in ( 31) and ( 32) one concludes also that φ(t) is bounded and taking in account (34) one concludes that (43) is true. Since y(t) is bounded in finite time (and goes to zero), w(t) is bounded and Q is bounded one concludes that u(t) is also bounded. 2

An important particular case

When hypothesis H1 is not satisfied but G and G 0 are asymptotically stable one can suppress the central stabilizing controller by taking R o (q -1 ) = 0 and H S = 1 and replace H1 by the stability condition upon G and G 0 . All the previous results remain valid but there are some significant simplifications. In this situation, one obtains Γ(q -1 ) = A(q -1 )S o (q -1 ) • At all other frequencies the inequality (24) is verified.

y(t) = A A o S o -QH R q -do B o AS o + QH R (q -d BA o -q -do B o A) d(t) (50
Proof: Follows directly from Lemma 4 by taking R o = 0 and H S = 1. Lemma 5 shows that, if R o = 0, the feasibility of the disturbance rejection depends on the discrepancy between the nominal and uncertain plant. This result can also be interpreted as the condition that z -(do-d) Bo(z -1 )

Ao(z -1 )

A(z -1 )
B(z -1 ) -1 2 is a strictly positive real transfer function for z = e iωj [START_REF] Ljung | On Positive Real Transfer Functions and the Convergence of Some Recursive Schemes[END_REF], or that the phase of this function is within ] -90 o ; +90 o [ at least at the frequencies of the disturbance.

6 Simulation results

Two examples

Let us consider the nominal plant model with A o (q -1 ) = 1 -1.45q -1 + 0.475q -2 and B o (q -1 ) = 0.5q -1 -0.5q -2 , driven by the central controller R o (q -1 ) = 0.15 -0.14q -1 , and S o (q -1 ) = 1 -0.74q -1 where H R = H S = 1. In a first configuration, the uncertain plant is given by A(q -1 ) = 1 -2.8635q -1 + 2.9811q -2 -1.330q -3 + 0.213q -4 , and B(q -1 ) = 0.59q -1 -1.3566q -2 + 0.9916q -3 -0.2250q -4 , which corresponds to Γ(q -1 ) = 1 -1.4q -1 + 0.45q -2 , and ∆(q -1 ) = 0.09q -1 -0.09q -2 . The sampling frequency is T s = 1s. The frequency characteristics of the nominal and uncertain models are represented in Figure . 4. The uncertain plant is disturbed by an harmonic out- put noise having a frequency of 0.0318Hz (0.2 rad/s), corresponding to D d (q -1 ) = 1 -1.96q -1 + q -2 . Under this assumption, one can show that the minimal order Q-filter is Q(q -1 ) = -8.56 + 11q -1 , (n Q = 1) and one verifies easily that Γ + QH R H S ∆ has not all its zeros within the unit circle. A simulation displayed in Figure .  5 shows that convergence is not obtained. This leads to use an augmented Q-filter: Q = Q + V D, and by choosing V (q -1 ) as a scalar we will have n Q = 2. For V ∈ [0.85; 8.93] the stability and the perfect rejection of the disturbance is guaranteed. Figure . 6 shows that the error signal tends towards zero and stable operation of the adaptive scheme is obtained. Now, in a second configuration, the uncertain system Fig. 6. Evolution of the residual error and parameters for example 1: nQ = 2 differs more significantly from the nominal one, with B(q -1 ) = 0.65q -1 -1.461q -2 + 1.036q -3 -0.225q -4 and A(q -1 ) = 1 -2.8755q -1 + 2.9985q -2 -1.3385q -3 + 0.2138q -4 , corresponding to Γ(q -1 ) = 1 -1.4q -1 + 0.45q -2 and ∆(q -1 ) = 0.15q -1 -0.15q -2 , the corresponding Bode diagram is displayed in Figure 4. It can be verified that no scalar V assuring both perfect disturbance rejection and stability of the closed-loop exists. Indeed the adaptive system shows instability phenomena in this case with n Q = 2 as shown in Fig. 7. If the Qfilter order is augmented to n Q = 3, one can check that for V (q -1 ) = -5 -8q -1 , the polynomial Γ + QH R H S ∆ has all its zeros strictly inside the unit circle. Therefore, for n Q = 3, there exists at least one expression of Q(q -1 ) satisfying the internal model principle condition and providing the closed-loop stability at the same time. Fig. 8 shows that, effectively, for n Q = 3 that stable operation of the adaptive scheme is obtained. The detailed scheme of the control test bench is shown in Fig. 9 and the views of the two implementations which will be considered subsequently are shown in Fig. 10.

The speaker used as the source of disturbances is labeled as 1, the control speaker is 2 and finally, at pipe's open end, the microphone that measures the system's output (residual noise) is denoted as 3. The transfer function between the disturbance's speaker and the microphone (1→3) is named Primary Path, while the transfer function between the control speaker and the microphone (2→3) is named Secondary Path. y(t) is the system's output (residual noise measurement), u(t) is the control signal and p(t) is the disturbance. The Secondary Path is the plant considered throughout the paper. Both primary and secondary paths have a double differentiator behavior, since as input we have the voice coil displacement, and as output the air acoustic pressure. The sampling frequency is 2500Hz. The secondary path models of the two configurations have been identified from experimental data using the methodology described in [START_REF] Melendez | Data driven design of tonal noise feedback cancellers[END_REF]. Fig. 11 shows the frequency characteristics of the identified models. There are important differences between the two models. These characteristics present multiple resonances (low damped complex poles) 12 and anti-resonances (low damped complex zeros). The orders of the two models are summarized in Table 1.

Model nA nB d

Secondary path G0 38 32 8

Secondary path G 27 27 6 Table 1 Orders of the identified models. H R (z -1 ) . M (ω) has local minima at 80, 244, 400, 686, 828, 1110, and 1200 Hz. The inequality [START_REF] Vau | Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties[END_REF] suggests to design So(z -1 ) H R (z -1 ) as series of band-pass filters with a strong amplification at these frequencies. Additionally, H R incorporates zeros at -1 and +1, in order to open the loop at 0 Hz and 0.5/T s Hz. The magnitude of So(z -1 )

H R (z -1 ) is presented in Fig. 12 (bottom). Furthermore, the magnitude e -i(d-do)ωj B(e -iω j )Ao(e -iω j )

Bo(e -iω j )A(e -iω j ) -1 is displayed in Fig. 13, showing that the sufficient condition (51) is satisfied in the ranges [102 Hz; 229 Hz] and [252 Hz; 295 Hz]. This is a sufficient condition for defining the regions where rejection of disturbances can be achieved (in these regions the system has enough gain for achieving rejection of disturbances-see Fig. 11). Bo(e -iω j )A(e -iω j ) -1

Simulation results

The objective is to show that despite the fact that the model of the secondary path used for design is different from the identified model of the current implementation, one can obtains performance similar to the case where the model of the secondary path is known, by augmenting the size of the adjustable Youla Kucera Filter. Two tonal disturbances with variable frequency will be used. Their frequencies are very close, generating a very strong interference phenomenon (hard to attenuate in practice). The first couple of frequencies are 160 Hz and 160.5 Hz. At t=50 s these frequencies will be switched to 150 HZ and 150.2 Hz and then at t=100 s one switches back to 160 Hz and 160.5 Hz. Figure 14a shows the disturbances. Tests have been conducted using plant model G in order to determine what is the dimension of the Q filter assuring the stability of the system. A Q filter with 14 adjustable parameters is necessary (instead of 4 parameters for the nominal case). It was found that 16 parameters assure much better transients. Further increase of the order of the Q filter did not provided significant improvement in performance 13 . For the simulations, the system operates in open loop for the first 5 s. Figure 14b shows the closed-loop behavior on the system G with a Q filter having 16 adjustable parameters. For comparison the same Q filter complexity is used for the nominal plant model and the results are shown in Figure 14c. One can see that the performance of the two systems are very close. Figure 14d shows the results for the nominal plant model when using a Q filter of minimal complexity (4 parameters). 16 . The tonal disturbance is attenuated for about 110 dB. One can see the presence of an harmonic of the disturbance in the residual noise in open loop indicating a small nonlinear behavior of the real system. However, the control algorithm attenuates this harmonic. The Q-filter has 16 parameters. Fig. 17 shows the behavior of the system for the interfer-

Concluding remarks

The paper has demonstrated through the use of the dual Youla Kucera plant parametrization, that in the pres- ence of model uncertainties, adaptive rejection of unknown narrow band disturbances requires to use in most cases an over parametrized Youla Kucera compensator in order to both satisfy the internal model principle and to assure the stability of the whole scheme. Clear conditions for over parametrization have been provided and an appropriate adaptive algorithm have been developed and analyzed. Relevant simulations and experimental results obtained on an active noise control system have illustrated the potentiality of the approach proposed.

9 Appendix A: Proof of Lemma 4

According to [START_REF] Landau | Benchmark on adaptive regulationrejection of unknown/time-varying multiple narrow band disturbances[END_REF], the expression of Γ given in [START_REF] Ljung | On Positive Real Transfer Functions and the Convergence of Some Recursive Schemes[END_REF], and since A o S o + q -do q -do B o R o has all its roots strictly inside the unit circle, a necessary and sufficient stability condition for the closed-loop is that the polynomial AS o + q -d BR o + QH R H S (q -d BA o -q -do q -do B o A) has all its roots inside the unit circle. This condition is equivalent to the stability of a closed-loop including two systems W 1 and W 2 , where W 2 is in negative feedback with W 1 , and where W 1 = QH S H R and W 2 = ∆ Γ = q -d BAo-Aq -do Bo ASo+q -d BRo (Fig. 21). From the small gain theorem, a sufficient stability condition for this closed-loop is that Q(z -1 )H R (z -1 )H S (z -1 ) ∞ < z -d B(z -1 )Ao(z -1 )-A(z -1 )z -do Bo(z -1 )

A(z -1 )So(z -1 )+z -d B(z -1 )Ro(z -1 )

∞ . Consequently a sufficient stability condition for the closed-loop is [START_REF] Vau | Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties[END_REF]. Now at the frequencies ω j , equation ( 14) must be So(e -iω j ) H R (e -iω j )H S (e -iω j )e -iω j do e -do iω j Bo(e -iω j ) , by combining with [START_REF] Vau | Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties[END_REF], one obtains condition [START_REF] Valentinotti | Adaptive rejection of unstable disturbances: Application to a fed-batch fermentation process[END_REF].

Fig. 1 .

 1 Fig. 1. Youla-Kucera direct adaptive feedback regulation scheme.

Fig. 2 .

 2 Fig. 2. Global block diagram of the uncertain system and the controller including the Q-filter 3.2 Adding the Dual Youla-Kucera uncertainty representation

Fig. 3 .

 3 Fig. 3. Generation of w(t).

Lemma 5

 5 In the case where R o = 0 and H S = 1 with G and G 0 asymptotically stable, sufficient conditions for the existence of a finite dimensional Q which stabilizes the closed-loop and ensure the asymptotic rejection of the disturbance are• At the frequencies ω j corresponding to D(e -iωj ) = 0 e -i(d-do)ωj B(e -iωj )A o (e -iωj )B o (e -iωj )A(e -iωj ) -1 < 1 (51)

Fig. 4 .

 4 Fig. 4. Frequency characteristics of the nominal and uncertain plant models

Fig. 5 .

 5 Fig. 5. Evolution of the residual error and parameters for example 1: nQ = 1

Fig. 7 .

 7 Fig. 7. Evolution of the residual error and parameters for example 2: nQ = 2

Fig. 8 . 3 7

 83 Fig. 8. Evolution of the residual error and parameters for example 2: nQ = 3

Fig. 9 .

 9 Fig. 9. Duct active noise control test bench diagram.

Fig. 10 .

 10 Fig. 10. Duct active noise control test bench (Photo): configuration Go (top), configuration G (bottom)

Fig. 11 .

 11 Fig. 11. Bode diagrams of the nominal and uncertain plants 7.2 Control design

Fig. 12 .

 12 Fig. 12. Magnitude of M (e -iω ) (top) and Magnitude of So(e -iω )/HR(e -iω ) (bottom).

Fig. 13 .

 13 Fig. 13. Magnitude of e -i(d-do)ω j B(e -iω j )Ao(e -iω j )

Fig. 14 . 4 7. 4

 1444 Fig. 14. Error Signals from top to bottom a): Open-loop, b): uncertain plant with nQ = 16, c): nominal plant nQ = 16, d): nominal plant nQ = 4

Fig. 15 .

 15 Fig. 15. Evolution of the residual noise for a 180 Hz sinusoidal disturbance (16 parameters).

Fig. 16 .Fig. 17 .

 1617 Fig. 16. Power Spectral density of the residual noise in open loop and in closed loop for a 180 Hz sinusoidal disturbance (16 parameters) . ence phenomenon considered in the simulation subsection. Two tonal disturbances at 160 Hz and 160.5 Hz are applied. At t=50s their frequencies are switched to 150 Hz and 150.2 Hz and at t= 100 their frequencies return

Fig. 18 .

 18 Fig. 18. Evolution of the parameters for step changes in the frequencies of an interference phenomenon (16 parameters) .for a sequence of steps changes on the frequencies of two tonal disturbances. The initial frequencies are 80 Hz and 170 Hz. At t = 25 s one switches to 70 Hz and 160 Hz. At t= 50 s one returns to 80 Hz and 170 Hz and at t = 75, one switches to 90 Hz and 180 Hz. In order to assure simultaneously the asymptotic rejection of the two simultaneous disturbances and the stability of the system over the range 70 Hz to 190 Hz, it was necessary to increase significantly the order of the Q filter (to 60 parameters). One observes that the results are slightly less good when approaching the border of the stability region (however > 60 dB attenuation in steady state). Fig.20shows the evolution of the parameters of the Q filter.

Fig. 19 .

 19 Fig. 19. Evolution of the residual noise for step changes in the frequency of two simultaneous sinusoidal disturbances around 80 Hz and 170 Hz.

Fig. 20 .

 20 Fig. 20. Evolution of the parameters for step changes in the frequency of two simultaneous sinusoidal disturbances around 80 Hz and 170 Hz (60 parameters).

Fig. 21 .

 21 Fig. 21. Connection of the Q filter with the dual Youla-Kucera filter satisfied. Since one has D d (e -iωj ) = 0, it results that Q(e -iωj ) =

Preprint submitted to Automatica

In active vibration and noise control the plant is called "secondary path" or "compensation path"

The complex variable z -1 will be used for characterizing the system's behavior in the frequency domain and the delay operator q -1 will be used for describing the system's behavior in the time domain.

Typical examples are: opening the loop at the Nyquist frequency, including the internal model of known disturbance, opening the loop at 0 Hz in active vibration and noise control, see[START_REF] Landau | Digital Control Systems[END_REF]

].[START_REF] Desoer | Feedback Systems: Input-Output properties[END_REF] While this representation is without doubt advantageous for the MIMO systems, it does not seems to offer in our opinion an advantage with respect to the transfer function representation in the SISO case.

If both G and G0 are open loop stable the central controller is not theoretically necessary . See Section 5 for details.

For narrow band disturbances N d has roots on a circle of radius ρ < 1. See[START_REF] Landau | Adaptive and Robust Active Vibration Control[END_REF], pp.261-262 for more details.

This structure preserves the fixed part HR and HR in R and S.

In the adaptive case (see Section 3.3), one does not need to solve this equation in real time.

For other options and connections with recursive least squares and stable gradient algorithm, see[START_REF] Landau | Adaptive control[END_REF][START_REF] Landau | Adaptive narrow band disturbance rejection applied to an active suspension -an internal model principle approach[END_REF].

The lowest damping is around 0.01.

It was observed that augmenting the size of the Q filter leads to a reduction of Q(e -iω ) in the regions concerned by condition[START_REF] Vau | Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties[END_REF]

Gabriel Buche, GIPSA-LAB has collaborated to the experiments.

[START_REF] Landau | Adaptive and Robust Active Vibration Control[END_REF] For all the experiments, a constant trace adaptation gain has been used. The magnitude of the trace was 30 x nb.of

parameters.[START_REF] Landau | Robust and adaptive noise attenuation in ducts[END_REF] PSD evaluated on an horizon of 3s


José Coloma

Yann Guiavarc'h

Peter-Leon Hagedoorn

Ulf Hanefeld
email: u.hanefeld@tudelft.nl

Probing batch and continuous flow reactions in organic solvents: Granulicella tundricula Hydroxynitrile lyase (GtHNL)

Granulicella tundricula hydroxynitrile lyase (GtHNL) is a manganese dependent cupin which catalyses the enantioselective synthesis of (R)-cyanohydrins. The GtHNL triple mutant A40H/V42T/Q110H, previously reported to exhibit a high activity and stability, was immobilised on Celite R-633 by adsorption. The synthesis of (R)-mandelonitrile catalysed by immobilised enzyme in a rotating bed reactor was compared to a continuous flow reactor. A batch reaction was used as reference system and organic solvent (MTBE) was used as reaction medium to suppress the chemical background reaction, ensuring the synthesis of enantiopure cyanohydrin. The rotating bed reactor, designed to boost conversion rates due to enhanced mass transfer, did not greatly enhance the reaction displaying a rate 1.7 times higher than the reference batch model. Moreover, similar conversion (96% after 4 hours) and recyclability were observed as compared to the reference system. The continuous flow reactor displayed rates 2 and 3 times higher than the rotating bed and the reference batch systems, respectively. Good conversions were achieved within minutes (97% conversion in 4 minutes at 0.1 mL/min). The immobilised enzyme displayed excellent enantioselectivity and high operational stability under all evaluated conditions. Overall, GtHNL triple mutant A40H/V42T/Q110H immobilised on Celite R-633 is an excellent catalyst for the synthesis of (R)-mandelonitrile with a great potential for continuous flow production of cyanohydrins.

Introduction

Enzyme catalysed carbon -carbon bond forming reactions are important in organic chemistry to produce chiral compounds. 1,2 In plants, hydroxynitrile lyases (HNLs) catalyse the cleavage of cyanohydrins into aldehydes or ketones releasing toxic hydrogen cyanide (HCN). This mechanism is a defence system against the attack of predators (cyanogenesis) and a source of nitrogen for the biosynthesis of L-asparagine (nitrogen fixation). 3,4 The reverse reaction is of great interest as it enables the synthesis of chiral α-cyanohydrins (Scheme 1). The importance of cyanohydrins as platform molecules lies in their two functional groups, the hydroxyl and nitrile moiety, which can be converted into a variety of valuable chiral products such as α-hydroxy acids, primary and secondary βhydroxy amines, α-hydroxy aldehydes or ketones, etc. All these compounds are known as platform molecules for the production of pharmaceutical and fine chemical products. 1,[5][6][7][8] Recently, a new manganese dependent, bacterial HNL was discovered in the soil bacterium Granulicella tundricula (GtHNL). It was heterologously expressed in Escherichia coli and the crystal structure was solved revealing a cupin fold. 9 The wild type GtHNL (GtHNL-WT) catalysed the synthesis of (R)mandelonitrile with a promising yield and enantioselectivity of 80% and 90% respectively. Site saturation mutagenesis of active site amino acids produced a triple mutant GtHNL-A40H/V42T/Q110H (GtHNL-TM) with a remarkable 490-foldincrease in specific activity in comparison to the wild type enzyme. 10 EPR spectroscopy revealed an unusually high Lewis acidity for the Mn 2+ as essential metal. 11 Moreover Mn +2 was bound more tightly in the triple mutant variant than in the wild type enzyme, which resulted in higher stability and activity.

In this study, we describe the immobilisation of GtHNL-TM on Celite R-633, the silicate skeletons of diatoms, 12 for the synthesis of (R)-mandelonitrile in batch and continuous flow systems. Enzyme immobilisation plays an important role enhancing the enzyme stability toward harsh conditions such as extreme pH values, organic solvents, high ionic strengths, etc. Additionally, it allows a straightforward enzyme separation from the reaction mixture as well as the operation in continuous a. Biokatalyse, Afdeling Biotechnologie, Technische Universiteit Delft, Van Please do not adjust margins Please do not adjust margins flow processes while minimizing the product contamination with enzymes. [12][13][14] Celite was used as carrier for the enzyme immobilisation as it is an environmentally friendly material that has been successfully employed for the immobilisation of several HNLs enabling the production of (R)-and (S)cyanohydrins with good yield, enantioselectivity and recyclability. 5,[15][16][17] Currently the vast majority of enzyme-catalysed conversions are performed in stirred tank reactors. 2 To achieve full conversion extended reaction times are often required (affecting the productivity). Rapid stirring is required to avoid diffusion limitations. Especially at industrial scales, this induces shear forces that affect enzyme stability. 18 To overcome these limitations, synthesis in a rotating bed reactor (RBR) and continuous flow reactor (CFR) are gaining attention. RBR enables efficient stirring and percolation of the substrates through the immobilised enzyme bed resulting in improved mass transfer without mechanical enzyme attrition. 19,20 Biosynthesis in continuous flow is also becoming an attractive way to increase productivity, reduce enzyme inhibition and facilitate downstream processing. [21][22][23][24][25][26] Additionally reaction volumes are reduced, increasing safety; in particular for toxic compounds such as cyanide. 27 Several enzymes have been tested in continuous flow systems such as HNLs, 21,25 transaminases, 26,[28][29][30] oxidoreductases, [31][32][33] and aldolases. 34,35 The aim of this work was to evaluate whether continuous flow reactions facilitate process intensification compared to a rotating bed reactor, reducing shear forces, improving stability and activity of the enzyme. For this purpose, GtHNL-TM was immobilised on Celite R-633 and its catalytic performance and stability were evaluated in RBR and CFR and compared to a batch reaction under the same reaction conditions.

Results and discussion

Celite is an environmentally benign siliceous carrier material, produced by diatoms, a type of microalgae. 38 Several HNLs were immobilised on this environmentally friendly material and performed better than on other carriers. Prunus amygdalus HNL (PaHNL) immobilised on Celite was compared to Avicel, 39 controlled pore glass and Sephadex, 17 in all cases Celite was the best carrier in terms of enzymatic activity. Hevea brasiliensis HNL (HbHNL) immobilised on Celite gave rise to better enantioselectivity compared to Avicel and EP-700 (hydrophobic polyamide), 40 and the very acid sensitive Arabidopsis thaliana HNL (AtHNL) had enhanced stability towards acidic pH values and organic solvents when it was immobilised on Celite R-633. 16 The ability of Celite to bind water enabling a local, water containing environment surrounding the enzyme might explain these results. 38,41 Because of these favourable results and to ensure comparability with previous studies Celite R-633 was utilised as carrier material.

Batch reactions

Both, purified GtHNL-WT and GtHNL-TM were immobilised on Celite R-633. All batch reactions were performed at 5°C since it was reported earlier 9 that a significantly higher enantiomeric excess can be obtained under this condition compared to the reaction at 15°C. After immobilisation the GtHNL-TM showed considerably higher activity and selectivity compared to GtHNL-WT (Fig. 1), which is in line with earlier results obtained for the enzyme in solution. 10 The specific activity of GtHNL-TM was 56.5 ± 18 U mg -1 which is 63 times higher compared to the wild type enzyme under the same reaction conditions. This can be ascribed to the additional histidines introduced at positions 40 and 110, improving the deprotonation of the hydrogen cyanide and giving rise to enhanced conversions and enantioselectivities. 10,11 At the same time these mutations greatly improve the binding of the metal to the active site, indeed metal removal was very difficult. 11 Since GtHNL-TM proved to be a better catalyst than the wild type enzyme, only the mutant enzyme henceforth was tested for the synthesis of (R)-mandelonitrile.

Having established Celite R-633 as suitable carrier on which the enzyme displayed similar activity as in solution, a leaching test was performed (Fig. 2). In earlier studies the structurally unrelated PaHNL and AtHNL were found not to leach from Celite R-633 15,16 but the activity of HNLs in organic solvents and at low pH without immobilisation was reported for AtHNL. 16 The GtHNL-TM was also found to be active under the reaction conditions even without immobilisation (Fig. S2). However, it precipitated during the reaction making reuse impossible. In the leaching experiment, the immobilised enzyme was removed from the reaction medium after 30 minutes of enzyme catalysed conversion. A high enzyme-support ratio (4U/mg) was used intentionally to clearly see any enzyme leaching to the reaction medium. The reaction did not proceed anymore for 20 hours, demonstrating that no GtHNL-TM leached from the carrier into the reaction medium. The hydrophilic characteristics of the enzyme -carrier and the insolubility of the enzyme in organic solvents explain this result. 36 Having firmly established that GtHNL-TM was successfully immobilised on Celite R-633, the enzyme loading for the synthesis of (R)-mandelonitrile in batch reactions (BR) was studied. As described earlier for PaHNL the immobilised enzyme was placed tightly packed inside tea bags. 15 Nearly complete conversion and excellent enantioselectivity were achieved after 4 hours of reaction time, regardless of the enzyme loading (Fig. 3). Interestingly, higher enzyme loadings did not show faster conversion, indicating that the reaction is mass transfer limited at high enzyme loading. A recycling study was performed utilising 1U/mg GtHNL-TM immobilised on Celite R-633. With this catalyst loading any loss of activity will be observed directly while higher catalysts loading might mask an initial activity loss. 5,15 The biocatalyst exhibited good recyclability, conversions gradually dropped to >70% over all cycles but remarkably high enantioselectivity (>99%) was observed during all 8 cycles (Table 1). With the BR as reference point, the comparison to the RBR could be performed. The reaction volume was scaled up circa 40 times to evaluate the mass transfer influence on the kinetics of the reaction in a RBR. This device has been designed to improve mass transfer, combining the advantages of fixed bed and stirred tank reactors. 42 At the same time it also displays the typical safety disadvantage of batch reactions; a large scale requires a large amount of a toxic compound in a vessel. 27 A first comparison between BR and RBR showed higher reaction rates for the BR (Fig. 4). Surprisingly, when the same immobilised enzyme was placed tightly packed in the above mentioned tea bags into the RBR the conversions and enantioselectivities were enhanced along the reaction times, displaying a similar feature to the batch reaction (Fig. 5). These results are unexpected since the RBR has been designed to boost the efficiency in biocatalytic reactions by reducing diffusion limitations. However, in an earlier study comparing a RBR and a stirred tank reactor, i.e. a BR; similar conversions were found in both cases. The transaminase and lipase catalysed kinetic resolution of (R,S)-1-phenylethylamine and (R,S)-1-phenylethanol respectively were utilised for that comparison. 20 Tables 2 and3 show a clear effect of the packing on the GtHNL-TM recyclability in the RBR. Tightly packed enzymes were more stable than loosely packed enzymes over 4 cycles. A possible explanation might be higher shear forces exerted on the GtHNL-TM immobilised on Celite freely placed or loosely packed into the RBR, when compared to tightly packed biocatalyst. Shear forces might result in breaking or stretching molecular bonds. Recovery of the enzyme can occur when the shear force is removed. 43 A tightly packed enzyme is better protected against shear forces. The decrease in enantiomeric excess during the first cycle (table 3, cycle 1), can be explained by a more pronounced chemical background reaction when the immobilised enzyme is placed freely inside the RBR. 15 For PaHNL immobilised on Celite this influence of the packing was observed, too. 15 A faster racemic background reaction for loosely packed enzyme was observed in that case as well. Substrate inhibition affecting the RBR reaction by blocking the enzyme active site due to local high concentrations of benzaldehyde or HCN was ruled out by kinetic measurements (Fig. S3). These results (Table 1 andTable 3) show that the recyclability of the enzyme is similar in both batch systems (BR and RBR) when using tightly packed, immobilised enzyme.

Continuous flow reactions

To maximally exploit the potential safety advantage of the flow chemistry, the synthesis of (R)-mandelonitrile was evaluated at different flow rates in a CFR of just 1 mL. As expected a decrease in conversion from 97% to 63% (Fig. 6) was observed by increasing the flow rate from 0.1 mL/min to 1.0 mL/min (residence time: 240 sec to 24 sec). 21,40 More remarkably the enantioselectivity was not influenced although all these experiments were performed at room-temperature, while cooling to 5 °C had been necessary to achieve good enantioselectivity in the BR and RBR. The stability of GtHNL-TM was evaluated at 0.1 and 0.2 mL/min, conditions under which complete conversion was (just) observed. Any weaknesses of the system will immediately be revealed at these flow rates. High stability was observed during 13 and 8 hours respectively (Fig. 7 and Fig. 8). Remarkably the enantioselectivity remained excellent even when the conversion dropped due to enzyme deactivation. In the case of Manihot esculenta HNL (MeHNL) and Hevea brasiliensis HNL (HbHNL), immobilised on siliceous monoliths, this was not the case, as loss of activity was accompanied with loss of enantioselectivity. 21 The biocatalytic synthesis of (R)mandelonitrile in continuous flow using AtHNL immobilised on Celite R-633 has been reported previously. 25 With a packed bed reactor (microbore column 3 mm/50 mm), the best conversion (85%) and enantioselectivity (96%) were achieved with 25 mg of pure AtHNL on 100 mg of Celite at a residence time of 35.3 min. Clearly, the conversions reported here (Fig. 6) are a step forward.

Comparison of the reactors

The different reactors can best be compared via specific rates and productivity, expressed as space-time yield (STY). In batch reactions, the RBR showed a specific rate 1.7 times higher compared to the BR, whereas the CFR proved to be 3 and 2 times faster than BR and RBR respectively (Table 4). Importantly, almost full conversion and excellent enantioselectivities were obtained within minutes instead of 4 hours (batch reactions). In addition to this much higher rate, the substancially lower reaction volume in the CFR constitutes a significant improvement of safety. 27 The increase in productivity of the CFR can also be explained by the apparent turnover number (k app ) observed. BR and RBR displayed k app from 0.77 s -1 and 1.32 s -1 respectively. The CFR exhibited 1.4 s -1 (0.1 mL/min) to 9.2 s -1 (1 mL/min) without reaching the maximum k app , thus the enzyme is capable of converting even more substrate. In spite of the large macropores of Celite R-633 (6.5 µm average diameter), 44 which are favourable to internal mass transfer, differences between the reactor types become apparent. In all reactors with heterogeneous process such as mesoporous materials, some boundary layer limiting substrate and product transfer occurs. This contributes to mass transfer limitations and consequently, turnover rate limitations. Increased flow rates improve the k app due to a reduction and almost depletion of this boundary layer, enabling more substrate to be exposed to the enzyme active site, explaining the advantage of CFR over other reactors. [45][46][47] The STY, a parameter frequently used to evaluate the productivity of different systems normalized to a volume of 1 L, shows that the use of the continuous flow system resulted in a prominent increase in (R)-mandelonitrile synthesized (g product h - 1 L -1 ). In steady state conditions, both batch reactions (BR and RBR) achieved circa 12 g h -1 L -1 whereas CFR at 0.1 mL/min reached 784 g h -1 L -1 . This represents 65 times more product in total. Importantly, increasing the flow rate enables higher specific rates and therefore higher STY without significantly affecting the enzyme stability (Fig. 7 and Fig. 8). However, it is worthy to point that higher flow rates lead to unreacted Please do not adjust margins Please do not adjust margins substrate, which may make downstream processing more difficult. Taking into account the amount of enzyme used for the reaction, the STY was 23 g product h -1 L -1 mg enz -1 at 0.1 mL/min up to 156 g product h -1 L -1 mg enz -1 at 1 mL/min, which shows excellent productivity with a low enzyme loading.

Recently, the performance of MeHNL and HbHNL immobilised on porous, monolithic silica supports has been reported in a continuous flow microreactor. Full conversion and high enantioselectivity were achieved within minutes, but the enzyme stability diminished after 7 and 3 hours operation, respectively. Furthermore, a drastic improvement of the catalytic performance was observed as compared with the batch system, with a 8-fold increase of the specific reaction rate. 21

Conclusion

GtHNL-TM showed a better catalytic performance for the production of (R)-mandelonitrile compared to the wild type enzyme.

Nearly complete conversion and high enantioselectivity were achieved in both BR and RBR systems with tightly packed enzyme on a readily available and environmentally benign carrier, Celite R-633. Unexpectedly, the RBR did not greatly enhance the reaction rate and showed only a 1.7-fold increase in specific rate at 54% conversion but similar STY (g product h -1 L -1 ). By switching to a CFR, full conversions and excellent enantioselectivity were obtained within minutes. Furthermore, continuous flow enabled to operate at higher k app which resulted in a tremendous increase in STY compared to both batch systems evaluated in this study. Additionally the much smaller reaction volume improves safety at the same time. The high activity and enantioselectivity of immobilised GtHNL-TM together with the enhanced stability in batch and continuous flow systems outperform what has been reported for other HNLs and makes this enzyme a new competitor for the production of chiral cyanohydrins.

Experimental section

Chemicals

All chemicals were bought from Sigma Aldrich (Schnelldorf, Germany) unless reported otherwise. Isopropanol and heptane were of HPLC grade (≥99%) and used as HPLC solvents. 1,3,5triisopropylbenzene (97%) was from Fluka Chemie (Buchs, Switzerland). Potassium cyanide (KCN, 97%) from J.T. Baker (Deventer, The Netherlands) was used as cyanide source in the HCN solution. (±)-Mandelonitrile from Across Organics (New Jersey, USA) was purified by flash chromatography (PE/MTBE 9:1/3:7).

Heterologous expression of wild type GtHNL (GtHNL-WT)

The pET-28a-GtHNL expression plasmid containing the GtHNL gene codon optimized for E. coli (Supporting information A) was obtained from Bio Basic INC (Canada). The expression plasmid was transformed into E. coli BL21(DE3). The expression of GtHNL-WT was performed according to literature. 10 A preculture was prepared by inoculating one single colony of E. coli BL21(DE3)-pET28aGtHNL in 10 mL of LB medium with kanamycin (40 µg/mL) and incubated overnight (New Brunswick Scientific Incubator Shaker Excella E24 Series) at 37 °C, 180 rpm. Then, this preculture was used for the inoculation of 1 L of LB medium containing kanamycin (40 µg/mL) and incubated at 37°C, 120 rpm. When the OD 600 reached 0.7 -0.9 the enzyme expression was induced by adding 1 mL of 0.1 M isopropyl β-Dthiogalactoside (IPTG) per liter of culture (0.1 mM IPTG final concentration) and cultivation was continued at 25°C, 120 rpm for 22 hours. Moreover, 100 µL of 1 M MnCl 2 was added per liter of culture at the induction time (0.1 mM Mn 2+ final concentration). Cells were harvested at 4 °C, 3600 rpm during 20 minutes (Sorvall RC6, Thermo Scientific). The supernatant was discarded and the pellet was washed with 20 mL of 10 mM sodium phosphate buffer pH 7 and stored at -80 °C.

Cloning and expression of triple mutant GtHNL-A40H/V42T/Q110H (GtHNL-TM)

The pUC57 shuttle vector containing the GtHNL-A40H/V42T/Q110H gene codon optimized for E. coli (Supporting information A) was obtained from Bio Basic INC (Canada) and transformed into E. coli Top 10. GtHNL-A40H/V42T/Q110H was cloned into pET28a expression vector using NcoI and HindIII restriction enzymes. The resulting pET28a-GtHNL-A40H/V42T/Q110H expression vector was cloned into E. coli TOP 10 to obtain a stable host for plasmid DNA.

Finally, pET28a-GtHNLA-40H/V42T/Q110H was transformed into the expression host E. coli BL21(DE3). The cultivation of the expression strain was performed in TB (terrific broth) medium following the same procedure described before for the GtHNL wild type.

Purification of GtHNL-WT and GtHNL-TM

GtHNL-WT was purified according to the literature 10 with slight modifications. The pellets were resuspended in lysis buffer A (50 mM Bis-Tris buffer + 30 mM NaCl + DNAse) pH 6.8 respectively and lysed in a cell disruptor (Constant Systems Ltd., United Kingdom) at 1.5 kBar and 4 °C to avoid protein denaturation. The cell free extract (CFE) was collected as the supernatant after centrifugation at 48000 g, 1 h, 4 °C. GtHNL-WT was purified from the CFE by anion exchange chromatography with Q Sepharose Fast Flow columns (HiTrap Q FF, 70 mL; GE Healthcare, Uppsala, Sweden) applying an isocratic step of 10% buffer B and then a gradient from 10% to 100% buffer B (50 mM Bis-Tris buffer + 1M NaCl). GtHNL-WT eluted at 10% buffer B. All the fractions were tested with an activity assay, see below.

GtHNL-WT was further purified using ultrafiltration with 100 kDa MWCO Amicon filter (Millipore) in order to remove any large proteins (>100 kDa).

GtHNL-TM was purified following the same method with slight modifications. Loading and elution buffers were at pH 7.4 and the ultrafiltration step was omitted because it had a negative effect on the enzyme stability. GtHNL-TM eluted at 10% buffer B.

GtHNL activity assay

GtHNL activity (wild type and mutant) was measured spectrophotometrically (Agilent Technologies Cary 60 UV-VIS)

Catalysis Science & Technology

Paper

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 7

Please do not adjust margins Please do not adjust margins using a method previously reported. 10,36 The cleavage of racmandelonitrile into benzaldehyde and hydrogen cyanide was followed at 280 nm and 25 °C in quartz glass cuvettes. To 1300 µL of reaction buffer (100 mM sodium oxalate buffer pH 5), 200 µL of enzyme solution (diluted in reaction buffer) and 500 µL of 60 mM rac-mandelonitrile solution (dissolved in 3 mM oxalic acid pH 3) were added. The background reaction was evaluated without enzyme and its slope was subtracted in the final calculation. The activity was calculated based on the following equation: 36 Activity = 2.0/(ε 280 x 1 x 0.2) [U/ml diluted sample] Where ΔA/min = ΔA/min sample -ΔA/min blank ε 280 = 1.376 [mM -1 x cm -1 ] One unit of HNL activity is defined as one micromole of racmandelonitrile converted per minute in sodium oxalate buffer pH 5 at 25 ͦ C.

Preparation of the hydrogen cyanide (HCN) solution in MTBE

An HCN solution in MTBE was prepared as described previously 5,15 with slight modifications. 25 mL MTBE and 10 mL MilliQ water were mixed in a 100 mL Erlenmeyer and kept at 0°C. 0.1 mol potassium cyanide (6.51 g) was dissolved in the mixture and magnetically stirred for 15 minutes. 10 mL of 30% (v/v) HCl solution was added slowly and stirring was continued for 2 minutes. The HCN solution was allowed to reach room temperature (circa 20 °C). The organic and aqueous phases were separated using a separation funnel and the organic layer containing HCN was collected. The separation was performed twice more after adding 7 mL of MTBE each time. Finally, 5 mL of 100 mM sodium acetate buffer pH 4 was added to the organic fraction collected and it was stored in a dark bottle at 4 °C. The HCN concentration in solution in MTBE was determined by titration. 1 mL of the HCN solution was added to 5 mL of 2 M NaOH and magnetically stirred for 2 minutes. A small amount of potassium chromate was added as indicator, then the solution was titrated using 0.1 M silver nitrate. The cyanide reacts 1:1 with the silver and precipitates. If there are no cyanide ions left in the mixture it will change colour from light yellow to brown. 5,37 To determine a concentration between 1.5-2 M is necessary to add 15-20 mL of silver nitrate. The HCN solution was found to be between 1.5 and 2 M. Caution: Potassium cyanide (KCN) and hydrogen cyanide (HCN) are highly poisonous chemicals. All experiments involving KCN and HCN were performed in a ventilated fume hood with 2 calibrated HCN detectors (inside and outside the fume hood). HCN wastes were neutralized over a large excess of commercial bleach (15% sodium hypochlorite solution) for disposal.

Immobilisation on Celite R -633 for batch and continuous flow reactions

Enzyme immobilisation on Celite was performed according to literature. 5 Celite R-633 was washed with 100 mM sodium acetate buffer pH 4 using a Büchner funnel and dried 24 h under vacuum in a desiccator over silica gel. Given volumes of wild type GtHNL or triple mutant GtHNL were concentrated with Amicon ultrafiltration filters with a 10 kDa MW cut-off, and subsequently added dropwise to Celite R-633 and dried 24 h under vacuum in a desiccator over silica gel. The ratio of enzyme solution to carrier (µL:mg) was 2:1. The enzyme concentration in solutions was adjusted to the required amount of enzyme for the immobilisation. By using this ratio of enzyme solution to Celite, the enzyme solution was completely absorbed by the carrier, ensuring that all the enzyme was immobilised into the porous material. The immobilised enzyme was stored in the fridge at 4 °C. Synthesis reactions of (R)-mandelonitrile in batch systems Batch reaction (BR) -Tea bag approach.

Several biocatalytic reactions were performed using GtHNL-TM immobilised on Celite R-633 and tightly packed into tea bags as described in the literature. 15 Tea bags can be made from nylon with pore size 0.4 mm 5 or indeed a regular tea bag. 15 The reaction conditions were: benzaldehyde (100 µL, 1 mmol), 27.5 µL 1,3,5-tri-isopropylbenzene (internal standard), 2 mL HCN in 100 mM acetate buffered MTBE pH 4 (1.5-2 M), tea bag filled with 50 mg immobilised enzyme (0.1, 0.5, 1, 2 and 4 U/mg), 700 rpm and 5°C. The ratio benzaldehyde to HCN solution was 1:4.

Rotating bed reactor (RBR) reaction

The reaction was scaled up to a 42 times larger reaction mixture volume, utilising a rotating bed reactor (Spinchem, Sweden). The reaction conditions were: benzaldehyde (4.25 mL, 42 mmol), 1.16 mL 1,3,5-tri-isopropylbenzene (internal standard), 85 mL HCN in 100 mM acetate buffered MTBE pH 4 (1.5-2 M), immobilised GtHNLA-40H/V42T/Q110H on 773 mg Celite (1 U/mg Celite), 700 rpm and 5°C. The ratio benzaldehyde to HCN solution was 1:4.

Enzyme recyclability in batch systems (BR and RBR)

The enzyme recyclability was determined by several cycles of (R)-mandelonitrile synthesis as described earlier. 15 Between each cycle the immobilised enzyme was washed for 1 minute with 100 mM acetate buffered MTBE pH 4.0 and stored after every second reaction cycle overnight at 4°C in clean acetate buffered MTBE pH 4.

Synthesis reactions of (R)-mandelonitrile on continuous flow

Immobilised GtHNL-TM on Celite R-633 (1 U/mg) was placed into a 1 mL stainless steel flow reactor. It was filled with 150 mg of non-porous glass beads and 150 mg of Celite R-633 containing immobilised enzyme. The packed bed reactor had a reaction volume of 0.394 mL (Supporting Information-C). 20 cm of polytetrafluoroethylene (PTFE) tubing with 1.5 mm inner diameter connect a high-pressure pump (Knauer, Germany) with the starting materials. Initial conditions were as follow: 0.5 M benzaldehyde, 1.5-2 M HCN in 100 mM acetate buffered MTBE pH 4 and 50 mM 1,3,5 tri-isopropylbenzene as internal standard. The synthesis of (R)-mandelonitrile was evaluated at different flow rates (from 0.1 to 1 mL/min) by chiral HPLC. The flow rate was checked at each sampling time by the difference of weight. Reactions were performed at room temperature.

Stability study in continuous flow

Synthesis reactions with immobilised GtHNL-TM on Celite R-633 (1 U/mg) were performed for 13 hours (0.1 mL/min) and 8 hours (0.2 mL/min) continously to test the enzyme stability at room

The Netherlands tel: +31-15-278 9304 fax: +31-15-278 1415 e-mail: u.hanefeld@tudelft.nl

Table of contents

M E I K R V G S Q A S G K G P A D W F T G T V R I D P L F Q A P D P A L V A G A S V T F E P G A R T A W H T H P L G Q T L I V T A G C G W A Q R E G G A V E E I H P G D V V W F S P G E K H W H G A A P T T A M T H L

A I Q E R L D G K A V D W M E H V T D E Q Y R

M E I K R V G S Q A S G K G P A D W F T G T V R I D P L F Q A P D P A L V A G H S T T F E P G A R T A W H T H P L G Q T L I V T A G C G W A Q R E G G A V E E I H P G D V V W F S P G E K H W H G A A P T T A M T H L A I H E R L D G K A V D W M E H V T D E Q Y R R A

Aminoacids in red show the mutations at positions 40, 42 and 110.

C. Calculation of reaction volume in continuous flow

Interbead volume (Non porous glass beads)

A commonly used inter-beads volume for non-porous beads of similar or close diameters even for well packed columns is between 30% and 40% of the total volume. Since 150 mg of glass beads correspond to 0.5 mL bulk volume, the inter-beads volume is about:

Scheme 1 .

 1 Scheme 1. GtHNL catalysed hydrocyanation of benzaldehyde yielding (R)-mandelonitrile.

Figure 1 .

 1 Figure 1. Synthesis of (R)-mandelonitrile using GtHNL-WT and GtHNL-TM. Conditions: Ratio benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, 100 µL benzaldehyde (1 mmol), 2 mL HCN solution in acetate buffered MTBE (1.5-2 M) pH 4, 27.5 µL (0.1 mmol) 1,3,5-tri-isopropylbenzene as internal standard (I.S.), tea bag filled with immobilised enzyme (5 U) on 50 mg (0.1 U/mg) Celite R-633. The reaction was stirred at 1000 rpm at 5 °C. Error bars correspond to duplicate (n=2).

Figure 3 .

 3 Figure 3. Synthesis of (R)-mandelonitrile using different enzyme loadings. Conditions: Ratio benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, benzaldehyde (100 µL, 1 mmol), 2 ml HCN solution in acetate buffered MTBE (1.75 M) pH 4, 27.5 µL (0.1 mmol) 1,3,5-tri-isopropylbenzene as I.S. and a tea bag filled with different amounts of GtHNL-TM immobilised on 50 mg Celite R-633. The reaction was stirred at 700 rpm at 5 °C. Error bars correspond to duplicate (n=2).

4 |

 4 loosely packed), [final ee>99%] RBR (enzyme no packed), [final ee=85%] BR (enzyme tightly packed), [final ee=98%] J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins

Figure 4 .

 4 Figure 4. Synthesis of (R)-mandelonitrile using GtHNL-TM immobilised on Celite R-633 in BR and RBR. Reaction conditions RBR: Ratio benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, 85 mL HCN (1.5 -2 M), 4.25 mL (42 mmol) benzaldehyde, 1.16 mL (4.2 mmol) 1,3,5 tri-isopropylbenzene as I.S., immobilised enzyme on 773 mg Celite (1 U/mg = 773 U) loosely packed or unpacked, 700 rpm, 5°C. Reaction conditions BR: Ratio benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, 2 mL HCN (1.5 -2 M), 100 µL (1 mmol) benzaldehyde, 27.5 µL (0.1 mmol) I.S., immobilised enzyme on 18 mg Celite R-633 ( 1 U/mg = 18 U) tightly packed. Error bars correspond to duplicates (n=2).

Figure 5 .

 5 Figure 5. Comparison between RBR and BR for the synthesis of (R)-mandelonitrile using GtHNL-TM immobilised on Celite R-633 always tightly packed. Reaction conditions RBR: Ratio benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, 85 mL HCN (1.5-2 M), 4.25 mL (42 mmol) Benzaldehyde, 1.16 mL (4.2 mmol) 1,3,5 tri-isopropylbenzene as I.S., immobilised enzyme on 773 mg Celite (1 U/mg = 773 U), 700 rpm, 5°C Reaction conditions BR: Ratio benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, 2 mL HCN (1.5 -2 M), 100 µL (1 mmol) benzaldehyde, 27.5 µL (0.1 mmol) I.S., immobilised enzyme on 18 mg Celite (1 U/mg = 18 U). Error bars correspond to duplicates (n=2)

5

 5 tightly packed), [final ee=98%] RBR (enzyme tighly packed), [final ee=99] is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | Please do not adjust margins Please do not adjust margins

Figure 6 .

 6 Figure 6. Synthesis of (R)-mandelonitrile using GtHNL-TM immobilised on Celite R-633 in CFR. Conditions: Ratio benzaldehyde : HCN in buffered MTBE pH 4 1:4, benzaldehyde (0.5 M), HCN solution in acetate buffered MTBE (1.5-2 M) pH 4, 1,3,5 triisopropylbenzene (50 mM, I.S.) with GtHNL-TM immobilised on 150 mg Celite R-633 (1 U/mg = 150 U). Reactions were performed at room temperature. Error bars correspond to duplicates (n=2).

Figure 7 .

 7 Figure 7. Stability of GtHNL-TM for the synthesis of (R)-mandelonitrile in CFR at 0.1 mL/min. Conditions: Ratio benzaldehyde : HCN in buffered MTBE pH 4 1:4, benzaldehyde (0.5 M), HCN solution in acetate buffered MTBE (1.5-2 M) pH 4, 1,3,5 triisopropylbenzene (50 mM, I.S.), with GtHNL-TM immobilised on 150 mg Celite R-633 (1 U/mg = 150 U). Error bars correspond to duplicates (n=2).

Figure 8 .

 8 Figure 8. Stability of GtHNL-TM for the synthesis of (R)-mandelonitrile in CFR at 0.2 mL/min. Conditions: Ratio benzaldehyde : HCN in buffered MTBE pH 4 1:4, benzaldehyde (0.5 M), HCN solution in acetate buffered MTBE (1.5-2 M) pH 4, 1,3,5 triisopropylbenzene (50 mM, I.S.), with GtHNL-TM immobilised on 150 mg Celite R-633 (1 U/mg = 150 U). Error bars correspond to duplicates (n=2).

6 |

 6 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

A 6 F 9 A

 69 . Gene and amino-acid sequences ..................................................................................................... 3 B. SDS-PAGE purified GtHNL-A40H/V42T/Q110H ......................................................................... 4 C. Calculation of reaction volume in continuous flow ......................................................................... 5 D. Progress of the synthesis of (R)-mandelonitrile with non-immobilized GtHNL-TM ..................... . Substrate incubation for evaluation of background reaction during 8 hours ................................... 8 G. Identification of substrates and products during the synthesis of (R)-mandelonitrile .....................

0. 5

 5 mL x 35% = 0.175 mL Pore volume (Celite R-633) According to El-Sayed 1 , Celite R-633 has a total pore volume of 1.46 mL g -1 . 0.150 g Celite R-633 x 1.46 mL g -1 = 0.219 mL Reaction volume = 0.219 mL + 0.175 mL = 0.394 mL PAPER Please do not adjust margins Please do not adjust margins Received 00th March 2020, Accepted 00th January 20xx DOI: 10.1039/x0xx00000x Probing batch and continuous flow reactions in organic solvents: Granulicella tundricula Hydroxynitrile lyase (GtHNL) José Coloma, a,b Yann Guiavarc'h, a,c Peter-Leon Hagedoorn, a and Ulf Hanefeld a *a. Biokatalyse, Afdeling Biotechnologie, Technische Universiteit Delft, Van der Maasweg 9, 2629 HZ Delft, The Netherlands. b. Universidad Laica Eloy Alfaro de Manabí, Avenida Circunvalación s/n, P.O. Box 13-05-2732, Manta, Ecuador. c. Laboratory Reactions and Process Engineering, University of Lorraine, CNRS, LRGP, F-54000 Nancy, France. *Corresponding author: u.hanefeld@tudelft.nl Electronic Supplementary Information (ESI) available: See DOI: 10.1039/x0xx00000x

Time (h) Conversion (%) ee (%) Catalysis Science & Technology Paper

	Please do not adjust margins
	Figure 2. Leaching assay for GtHNL-TM immobilised on Celite R-633. Conditions: Ratio
	benzaldehyde : HCN in acetate buffered MTBE pH 4 1:4, benzaldehyde (100 µL, 1 mmol),
	2 ml HCN solution in acetate buffered MTBE (1.75 M) pH 4, 27.5 µL (0.1 mmol) 1,3,5-tri-
	isopropylbenzene as I.S. and a tea bag filled with GtHNL-TM immobilised on 50 mg Celite
	R-633. The reaction was stirred at 700 rpm at 5 °C. Diamonds and the dashed line is the
	enzyme catalysed reaction (50 U), dots and the solid line is the reaction where the
	immobilised enzyme (200 U) was removed after 30 min. Error bars correspond to
	duplicate (n=2).	(%)	Conversion mutant (%)
	ee mutant (%)		ee WT (%)
	This journal is © The Royal Society of Chemistry 20xx		J. Name., 2013, 00, 1-3 | 3
	Please do not adjust margins

Table 1 .

 1 Recycling of the GtHNL-TM immobilised on Celite R-633 (1 U/mg) in eight successive BR cycles

	Cycle	Conversion (%)	ee R-mandelonitrile (%)
	1	98.0 ± 0.2	>99
	2	90.0 ± 0.3	>99
	3	88.0 ± 0.9	98.7
	4	88.0 ± 0.1	>99
	5	87.0 ± 0.1	>99
	6	77.0 ± 0.7	>99
	7	74.0 ± 1.0	>99
	8	73.0 ± 0.4	>99

Conditions: Ratio benzaldehyde : HCN in buffered MTBE pH 4 1:4, 100 µL benzaldehyde (1 mmol), 2 ml HCN solution in acetate buffered MTBE (1.5-2 M) pH 4, 27.5 µL 1,3,5-tri-isopropylbenzene (0.1 mmol, internal standard), a tea bag filled with GtHNL-TM immobilised on 50 mg Celite R-633 (1U/mg = 50 U). The reaction was stirred at 700 rpm at 5°C; reaction time: 4h. The enzyme was washed for 1 minute with 100 mM acetate buffer saturated MTBE pH 4 after each cycle.

Table 2 .

 2 Recycling of GtHNL-TM immobilised on Celite R-633 (1 U/mg) in four successive RBR cycles. Loosely packed enzyme in tea bags.

	Cycle	Conversion (%)	ee R-mandelonitrile (%)
	1	88.9 ± 0.2	>99
	2	79.0 ± 0.6	>99
	3	82.9 ± 0.3	>99
	4	60.7 ± 0.2	>99
	Conditions: 85 mL HCN (1.5 -2 M) in 100 mM acetate buffered MTBE pH 4, 4.25
	mL (42 mmol) benzaldehyde, 1.16 mL (4.2 mmol) 1,3,5 tri-isopropylbenzene as
	internal standard (I.S.), immobilised enzyme on 773 mg Celite (1 U/mg = 773 U) ,
	700 rpm, 5°C. The enzyme was washed for 1 minute with acetate buffer saturated
	MTBE pH 4 after each cycle.

Table 3 .

 3 Recycling of GtHNL-TM Immobilised on Celite R-633 (1 U/mg) in four successive RBR Cycles. Tightly packed enzyme in tea bags.

	Cycle	Conversion (%)	ee R-mandelonitrile (%)
	1 a	90.3 ± 0.3	85.4
	2 b	96.0 ± 0.2	99.3
	3 b	93.5 ± 0.3	96.3
	4 b	84.8 ± 0.2	99.4
	Conditions: 85 mL HCN (1.5 -2 M) in acetate buffered MTBE, 4.25 mL (42 mmol)
	benzaldehyde, 1.16 mL (4.2 mmol) 1,3,5 tri-isopropylbenzene as I.S., immobilised
	enzyme on 773 mg Celite (1 U/mg = 773 U) , 700 rpm, 5°C. The enzyme was washed
	for 1 minute with acetate buffer saturated MTBE pH 4 after each cycle.

a Immobilised GtHNL-TM was placed without tea bags. b Immobilised GtHNL-TM was placed in tightly packed in tea bags.

Table 4 .

 4 Specific rates for the different reactor types

		Batch reactions	CFR
		BR	RBR	0.7 mL/min	0.8 mL/min
	Specific rates (mmol min -1 g enz -1 )	3.51 a	6.30 a	7.93 b	8.37 c
		2.51 b	3.93 c
	a calculated at ̴ 54% conversion

b calculated at ̴ 76% conversion c calculated at ̴ 70% conversion

Acknowledgements

This project is financed by the Secretary of Higher Education, Science, Technology and Innovation of Ecuador and Universidad Laica Eloy Alfaro de Manabí (ULEAM).

Paper

Catalysis Science & Technology 8 | J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins temperature. Samples were withdrawn at regular intervals (Fig. 7 &8) and analysed by chiral HPLC. Analysis Samples (10 µL) were taken at different times during the reaction run and added to 990 µL of heptane:2-propanol 95:5 in 1.5 mL Eppendorf tubes. A small amount of anhydrous magnesium sulphate (MgSO 4 ) was used to remove the water from the solution. The Eppendorf tubes were centrifuged at 13000 rpm for 1 min. 850 µL of the supernatant was transferred to a 4 mL HPLC vial and 10 µL was injected into the HPLC (Chiralpak AD-H column, column size: 0.46 cm I.D x 25 cm). Heptane and 2-propanol were used as mobile phase with a flow rate of 1 mL/min and the UV detector was set at 216 nm. The column temperature was set at 40 °C. The samples in the autosampler were maintained at 4 °C.

Conflicts of interest

There are no conflicts to declare. Continuous processes are the standard approach for the catalytic production of bulk chemicals. Yet at the same time enzymes are not often utilized in continuous processes. In this paper we describe the successful and straightforward immobilization of the new Hydroxynitrile lyases from Granulicella tundricula and its application in the continuous flow for enantioselective synthesis.

Comparing the common batch reaction, the spin chem reactor and the flow reactor the credentials of the flow process are demonstrated. Additionally the Space Time Yields of all systems were compared and our Hydroxynitrile lyase performed best under flow conditions. Remarkably all this was achieved utilizing a very straightforward and cheap immobilisation protocol. This opens up a new approach for the industrial application of enzymes in flow.

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