Sandra Abad

Jozef Nahalka

Margit Winkler

Gabriele Bergler

Robert Speight

Anton Glieder

Bernd Nidetzky
email: bernd.nidetzky@tugraz.at@tel

High-level expression of -amino acid oxidase in

Keywords: D-amino acid oxidase, permeabilization, Pichia pastoris, Rhodotorula gracilis, stability

By combining gene design and heterologous over-expression of Rhodotorula gracilis Damino acid oxidase (RgDAO) in Pichia pastoris, enzyme production was enhanced by one order of magnitude compared to literature benchmarks, giving 350 kUnits/l of fed-batch bioreactor culture with a productivity of 3.1 kUnits/l h. P. pastoris cells permeabilized by freeze-drying and incubation in 2-propanol (10% vv/) produce a highly active (1.6 kUnits/g dry matter) and stable oxidase preparation. Critical bottlenecks in the development of an RgDAO catalyst for industrial applications have been eliminated.

Introduction

 [START_REF] Pollegioni | Properties and applications of microbial D-amino acid oxidases: current state and perspectives[END_REF][START_REF] Tishkov | D-Amino acid oxidase: Structure, catalytic mechanism, and practical application[END_REF]. The most widely quoted use of DAO is in the industrial manufacture of 7-amino-cephalosporanic acid, an important intermediate in the production of semisynthetic antibiotics [START_REF] Riethorst | An industrial view on enzymes for the cleavage of cephalosporin C[END_REF]. For this process, DAO from the yeast Trigonopsis variabilis (TvDAO) is regarded as the most suitable enzyme, essentially because it displays superior specific activity towards the bulky cephalosporin C substrate [START_REF] Pollegioni | Catalytic properties of D-amino acid oxidase in cephalosporin C bioconversion: a comparison between proteins from different sources[END_REF]). More recently, TvDAO has also been considered as catalyst for dynamic kinetic resolution of amino acid racemates [START_REF] Beard | Deracemisation and stereoinversion of α-amino acids using D-amino acid oxidase and hydride reducing agents[END_REF].

However, for this application to become economically viable, there is a clear demand for enhancement of total turnover number (TTN) of the TvDAO preparation used under the industrial process conditions (Fig. 1; [START_REF] Fotheringham | Preparative deracemization of unnatural amino acids[END_REF]. We have developed a Pichia pastoris whole-cell catalyst of TvDAO in which significant improvement of TTN results from two main effects of strain engineering (Abad et al. 2010b).

Firstly, P. pastoris, containing recombinant TvDAO localized in their peroxisomes, displayed oxidase activity in markedly stabilized form, as compared to the free enzyme. Secondly, combining TvDAO overexpression with suitable permeabilization of the Pichia cells provided a catalyst having useful specific activity (per unit mass of preparation; 600 Units/g). Further enhancement of TTN would be achievable through molecular stabilization of the enzyme. With TvDAO, however, this goal remains elusive [START_REF] Nidetzky | Stability and stabilization of D-amino acid oxidase from the yeast Trigonopsis variabilis[END_REF].

(Figure 1)

We therefore considere DAO from the yeast Rhodotorula gracilis (RgDAO) is the most thoroughly characterized microbial member of the DAO group of enzymes [START_REF] Fitzpatrick | Oxidation of amines by flavoproteins[END_REF][START_REF] Pollegioni | Yeast D-amino acid oxidase: structural basis of its catalytic properties[END_REF][START_REF] Umhau | The x-ray structure of D-amino acid oxidase at very high resolution identifies the chemical mechanism of flavin-dependent substrate dehydrogenation[END_REF]. Taking into account that loss of FAD appears to be the preponderant path of inactivation of TvDAO under a wide range of conditions [START_REF] Betancor | Use of physicochemical tools to determine the choice of optimal enzyme: stabilization of D-amino acid oxidase[END_REF][START_REF] Dib | The stabilizing effects of immobilization in D-amino acid oxidase from Trigonopsis variabilis[END_REF][START_REF] Dib | Thermal inactivation of D-amino acid oxidase from Trigonopsis variabilis occurs via three parallel paths of irreversible denaturation[END_REF][START_REF] Pollegioni | Catalytic properties of D-amino acid oxidase in cephalosporin C bioconversion: a comparison between proteins from different sources[END_REF], the ability of RgDAO to bind its cofactor by one order of magnitude more tightly than TvDAO made the enzyme from R. gracilis a promising candidate for development of DAO catalysts showing further enhanced robustness. However, exploitation of the extra stability of RgDAO as compared to TvDAO is hampered by relatively inefficient production of the R. gracilis enzyme in both native [START_REF] Molla | Regulation of D-amino acid oxidase expression in the yeast Rhodotorula gracilis[END_REF] and E. coli [START_REF] Wang | Stabilization of native and double D-amino acid oxidases from Rhodosporidium toruloides and Trigonopsis variabilis by immobilization on streptavidin-coated magnetic beads[END_REF] host strains. We show here that optimized expression of RgDAO in P. pastoris eliminates this bottleneck. By applying cell permeabilization with 2-propanol (Abad et al. 2010b), a potentially useful oxidase preparation was obtained that is superior to reported whole-cell DAO catalysts with respect to specific activity and stability.

Materials and methods

Chemicals and media

Oligonucleotides were from IDT Integrated DNA Technologies BVBA (Leuven, Belgium). DNA-modifying enzymes were from Fermentas (Burlington, Ontario, Canada). Unless otherwise stated, chemicals were from Carl Roth GmbH (Karlsruhe, Germany), Becton, Dickinson and Company (Franklin Lakes, NJ, USA) or Sigma-Aldrich (St Louis, MO, USA).

Construction of P. pastoris expression cassettes

E. coli TOP10F (Carlsbad, CA, USA) was the host for cloning. The RgDAO gene (GenBank: CAA96323) was codon-optimized using methods described in Abad et al. (2010b) for expression in P. pastoris (see Supporting Information) and synthesized by GenScript (Piscataway, NJ, USA). To facilitate isolation of recombinant RgDAO, the gene was further modified to also encode an N-terminal Strep II tag. PCR products were purified with QIAquick PCR Purification Kit (Qiagen, Hilden, Germany), digested with EcoRI and NotI (Fermentas, Burlington, Canada), and ligated via EcoRI/NotI restriction sites into in-house E. coli/P. pastoris shuttle vectors pPpT2 and pPpB1 that provide single and multi-copy chromosomal integration of target genes in P. pastoris, respectively (Abad et al. 2010b). Details of these vectors are available upon request.

Transformation of P. pastoris and copy number determination

A Mut S strain derived from P. pastoris CBS 7435 (TU Graz strain collection number: BT 3132) was used for transformation applying the protocol of [START_REF] Lin-Cereghino | Condensed protocol for competent cell preparation and transformation of the methylotrophic yeast Pichia pastoris[END_REF]. Electro-competent cells were transformed using pPpT2 or pPpB1 previously linearized by BglII and purified by QIAquick PCR Purification Kit. After electroporation and regeneration for 2 h at 30°C using agitation at 60 rpm, aliquots (0.2 ml) were plated on solid selection medium containing 100 mg Zeocin/L. The number of copies of RgDAO expression cassettes integrated into the P. pastoris genome was determined by quantitative real-time PCR as described in Abad et al. (2010a), employing the AOX1 promoter as target and the endogenous ARG4 gene as a reference.

P. pastoris cultivation at different scales, and enzyme purification P. pastoris transformants were cultivated in deep well plates (96-well format) or 2 l shake-flasks using conditions described in [START_REF] Weis | Reliable high-throughput screening with Pichia pastoris by limiting yeast cell death phenomena[END_REF]. Sample preparation for intracellular activity measurement and the assay for DAO activity were as reported by Abad et al. (2010b). Bioreactor cultivations were performed with a 1.5-l fed batch-Pro Bioreactor system (Dasgip AG, Juelich, Germany) applying the protocol of [START_REF] Hellwig | Production of carcinoembryonic antigen (CEA) N-A3 domain in Pichia pastoris by fermentation[END_REF]. A methanol feed of 3 ml/h was used (Abad et al. 2010b). Recombinant RgDAO was purified from cells obtained in shake-flask culture, using the procedure described in [START_REF] Dib | Trigonopsis variabilis D-amino acid oxidase: control of protein quality and opportunities for biocatalysis through production in Escherichia coli[END_REF] expanded by a final purification step on MonoQ HR 5/5 column.

Permeabilization of P. pastoris cells and activity measurement for whole-cell enzyme preparations

Cells from bioreactor cultivations were used. Treatment with 2-propanol (10% v/v) in water for 3 h was employed to achieve permeabilization, applying the conditions described in Abad et al. (2010b). Assays for activity and stability of soluble as well as whole-cell oxidase preparations were based on direct measurement of O 2 consumption during oxidation of D-methionine or (D-alanine (Abad et al. 2010b). A bubble-aerated magnetically stirred glass mini-reactor with a working volume of 30 ml was employed to conduct these assays [START_REF] Nahalka | Encapsulation of Trigonopsis variabilis D-amino acid oxidase and fast comparison of the operational stabilities of free and immobilized preparations of the enzyme[END_REF].

For the activity measurements, the reactions were started by adding 20 μL of appropriately diluted P. pastoris cell extract or 4 µg purified protein. Initial rates of O 2 consumption were recorded for activity determination, therefore no aeration was used. For the stability measurements, the reaction mixture contained 20 or 100 mM substrate dissolved in 10 mM or 100 mM Tris/HCl buffer (pH 7.5), respectively, and air was continuously sparged at 30 l/h. Reactions were started by adding 100 µg purified protein.

Results and discussion

Expression design

A previously successful approach of high-level TvDAO expression in P. pastoris combined gene design for optimum codon usage with protein targeting to peroxisomes (Abad et al. 2010b). The codon-optimized sequence of RgDAO is shown in the Supporting Information. RgDAO contains the canonical PTS1 peroxisomal targeting motif (-Ser-Lys-Leu) at its C-terminal end that is known to be well recognized by the corresponding transport machinery in P. pastoris [START_REF] Monosov | Labeling of peroxisomes with green fluorescent protein in living P. pastoris cells[END_REF]. Therefore, unlike TvDAO, in which the absence of a suitable PTS1 motif necessitated enhancement of sub-cellular targeting by protein engineering (Abad et al. 2010b), the native primary structure of RgDAO was expected to support efficient translocalization of recombinant enzyme to host cell peroxisomes. Expression of the RgDAO gene from the methanol inducible alcohol oxidase promoter was chosen. The number of integrated expression cassettes necessary for high-level recombinant protein production cannot be foreseen in P. pastoris. The codonoptimized RgDAO gene was therefore cloned into plasmids enforcing low and multi-copy gene integration into the host cell genome. Screening for transformants displaying high oxidase activity was performed in high through-put format [START_REF] Weis | Reliable high-throughput screening with Pichia pastoris by limiting yeast cell death phenomena[END_REF]. Two strains thought to feature single and multi-copy gene integration events were chosen and are henceforth named RgDAO_sc and RgDAO_mc, respectively.

Quantitative real-time PCR analysis (Abad et al. 2010a) confirmed the presence of 1 (RgDAO_sc) and 12-13 (RgDAO_mc) copies of the expression cassette integrated in the P. pastoris genome.

Characterization of the selected RgDAO production strain

Controlled fed-batch bioreactor experiments, following a standard protocol for high-cell density cultivation of P. pastoris (Abad et al. 2010b), were carried out to evaluate strains RgDAO_sc and RgDAO_mc with respect to production of biomass and oxidase activity. Results are summarized in Table 1. The intracellular activity of RgDAO_mc surpassed that of RgDAO_sc by a factor of 6, demonstrating the benefit of multicopy gene integration for strain construction. However, the relationship between enzyme titer and the number of integrated expression cassettes is not completely linear. Interestingly, in P. pastoris expressing TvDAO (Abad et al. 2010b), change from a single-copy strain (767 U/g wcw) to a multi-copy strain harboring 16 -17 copies of the expression cassette resulted in only moderate (1.7-fold) enhancement of specific oxidase activity. The volumetric productivity of RgDAO_mc (3.1 kU/L/h) was about 9-fold that of RgDAO_sc. RgDAO_mc showed about 8.5-fold expression improvement as compared to a previously reported E. coli strain [START_REF] Molla | Overexpression in Escherichia coli of a recombinant chimeric Rhodotorula gracilis D-amino acid oxidase[END_REF]). Its specific oxidase activity was about twice that of the corresponding multi-copy strain of P. pastoris producing TvDAO (Abad et al. 2010b).

(Table 1)

Table 1 shows that enhancement of specific oxidase activity in RgDAO_mc as compared to RgDAO_sc went along with a 1.6-fold decrease in biomass yield. This finding is in agreement with observations from previous studies of DAO expression in P. pastoris (Abad et al. 2010b;[START_REF] Zheng | Expression, purification, and immobilization of His-tagged D-amino acid oxidase of Trigonopsis variabilis in Pichia pastoris[END_REF] and supports the idea that high levels of DAO activity are not readily accommodated by the growing P. pastoris cell. Abad et al. (2010b) showed that the negative effect of DAO over-expression in P. pastoris on biomass formation can be alleviated by using a mixed substrate feed of glycerol and methanol. However, optimization of the yield of RgDAO_mc biomass was beyond the scope of this study. Notwithstanding, a volumetric yield of 350 kU/l for RgDAO activity represents a significant improvement, by one order of magnitude, as compared to literature benchmarks [START_REF] Wang | Stabilization of native and double D-amino acid oxidases from Rhodosporidium toruloides and Trigonopsis variabilis by immobilization on streptavidin-coated magnetic beads[END_REF]. Enzyme production should therefore no longer be a critical bottleneck in the development of RgDAO preparations for applied biocatalysis.

Quality control for DAO production in Pichia pastoris

RgDAO and TvDAO, each harboring N-terminal Strep-tag II and containing the SKL peroxisomal targeting motif at their C-terminus, were produced in P. pastoris and purified to apparent electrophoretic homogeneity, as demonstrated in Fig. 2. The TvDAO derived from P. pastoris mi grated in SDS PAGE with a relative mobility that was identical to that of a reference preparation obtained from E. coli. Specific activities for O 2dependent conversion of D-Ala and D-Met are shown in Table 2. Preference for reaction with D-Met as compared to D-Ala is consistent with reported biochemical data for each enzyme [START_REF] Tishkov | D-Amino acid oxidase: Structure, catalytic mechanism, and practical application[END_REF]. The measured values of specific activity for each oxidase were in good agreement with literature [START_REF] Tishkov | D-Amino acid oxidase: Structure, catalytic mechanism, and practical application[END_REF], indicating that the functionality of enzymes produced in P. pastoris was comparable to preparations obtained through other expression hosts. This is clearly worth noting considering that in vivo assembly of a functional DAO molecule relies on availability of sufficient amounts of FAD cofactor, which can be limiting in a high level expression approach. Furthermore, as shown for TvDAO [START_REF] Nidetzky | Stability and stabilization of D-amino acid oxidase from the yeast Trigonopsis variabilis[END_REF], the target protein may be sensitive to oxidative modification, which appears not to be an issue for the supported peroxisomal localization. We conclude therefore that high-level recombinant production of RgDAO and TvDAO in P. pastoris peroxisomes occurs with excellent retention of quality in enzyme preparations as isolated.

(Figure 2) (Table 2) Data supporting the notion that RgDAO is kinetically more stable than TvDAO were obtained under temperature stress conditions in the absence of the enzyme catalyzed [START_REF] Betancor | Use of physicochemical tools to determine the choice of optimal enzyme: stabilization of D-amino acid oxidase[END_REF][START_REF] Pilone | D-amino acid oxidase as an industrial biocatalyst[END_REF]. However, resistance to high-temperature inactivation may not be an adequate measure of stability under process conditions. Using reported methodology [START_REF] Nahalka | Encapsulation of Trigonopsis variabilis D-amino acid oxidase and fast comparison of the operational stabilities of free and immobilized preparations of the enzyme[END_REF], we therefore determined the loss of activity of purified RgDAO and TvDAO during conversion of D-Met using O 2 supply by bubble aeration (Fig. 3). Because enzyme inactivation occurs at a rate much faster than the rate of depletion of substrate, the observed increase in the concentration of O 2 as a function of the incubation time reflects the activity loss [START_REF] Nahalka | Encapsulation of Trigonopsis variabilis D-amino acid oxidase and fast comparison of the operational stabilities of free and immobilized preparations of the enzyme[END_REF]). Time-course data for the increase in O 2 concentration were fitted exponentially, yielding the inactivation rate constants (k in ) summarized in Table 2. At 100 mM D-Met, RgDAO displayed about five-fold superior stability (lower k in ) as compared to TvDAO. Because at a lower substrate concentration of 20 mM, both enzymes showed similar resistance to inactivation, the difference in enzyme stability at the high substrate level must result from significant destabilization of TvDAO under these conditions.

(Figure 3) Pichia pastoris whole-cell catalyst expressing RgDAO Abad et al. (2010b) have shown that whole cells of TvDAO_mc are poorly active catalysts for the conversion of D-Met because the high level of intracellular oxidase activity was almost completely masked by mass transfer limitations. Lyophilization of cells followed by incubation of dried biomass in the presence of 10% 2-propanol caused dramatic (125-fold) enhancement of utilization of the enzyme activity present (see Table 1). The catalytic effectiveness factor ( ) for permeabilized TvDAO_mc as compared to total intracellular enzyme activity was 0.49 (= 627/1283). Applying the same sequence of treatment to RgDAO_mc, the data shown in Table 1 were obtained. The steps of lyophilization and treatment with organic solvent each contributed about half of the total (58-fold) enhancement of whole-cell oxidase activity achieved in comparison to untreated P. pastoris biomass. The value of 0.59 (= 1624/2762) for permeabilized RgDAO_mc even surpassed the corresponding effectiveness factor for TvDAO_mc. (Note: Because

RgDAO_mc surpassed RgDAO_sc with respect to production of intracellular oxidase activity (Table 1), permeabilization of the single-copy strain was not further pursued.) Stability tests for permeabilized RgDAO_mc were performed as described above for the purified enzyme, taking care that the steady-state level of dissolved O 2 was always limited by the amount of enzyme activity present. Inactivation rate constants for permeabilized RgDAO_mc were at the lower limit of detection of the used assay (k in ≤ 5 10 -4 min -1 ), indicating a very useful operational stability of this whole-cell catalyst.

Conclusions

Optimized expression in P. pastoris alleviates the likely bottleneck of enzyme production in the development of RgDAO catalysts for application in fine chemical synthesis. The best producing P. pastoris strain obtained in this study had 12 -13 expression cassettes integrated into its genome and delivered an enzyme yield of 350 kU/L of bioreactor culture, exceeding relevant literature values by one order of magnitude. After permeabilization, this strain constituted a stable whole-cell catalyst preparation that could make use of 60%

of its total intracellular oxidase activity. Its specific activity surpassed that of comparable whole-cell systems by a factor of 2 or more. RgDAO was obtained from P. pastoris as a high-quality protein preparation. At high D-Met substrate loading, isolated enzyme showed superior operational stability as compared to TvDAO, which is currently used in industry.

Fig. 1 Fig. 2

 12 Fig. 1 DAO-based dynamic kinetic resolution of amino acids[START_REF] Fotheringham | Preparative deracemization of unnatural amino acids[END_REF]). The method relies on the absolute enantioselectivity of the oxidase catalyst. The imino acid produced in the enzymatic reaction is immediately reduced in a non-stereoselective manner. Whole cells of E. coli expressing TvDAO

Fig. 1

 1 Fig. 1

  Fig. 2

Table 1 :

 1 RgDAO expression in P. pastoris. Results are mean values from three independent determinations using D-Met as substrate and have S.D. < 5%.

				Intracellular	Fresh	Lyophilized	Permeabilized
												Biomass
				activity	cells	cells	cells
	Strain	CN	a									Reference
							[U/g wcw]	b				[g wcw/batch]	b
	RgDAO_sc	1		450	n.d.	c	n.d.	c	n.d.	c	210	this study
	RgDAO_mc 12-13	2762	28		769	1624	128	this study
	TvDAO_mc 16-17	1283	5		321	627	117	(Abad et al. 2010b)

a CN: copy number for expression cassette integration b wcw, weight cell weight c n.d., not determined

Table 2 : Characterization of RgDAO and TvDAO, produced in and isolated from P. pastoris.

 2 Resultsare from three independent determinations and have S.D. < 10%.

		Specific activity [U/mg]	Inactivation rate constant [min -1 ]	a
		20 mM D-Met	20 mM D-Ala	20 mM	100 mM
	TvDAO	112	38	0.0195	0.0778
	RgDAO	117	88	0.0155	0.0153

a See text for further details

Acknowledgements

The authors would like to thank Thorsten Bachler and Margaretha Schiller for their excellent technical support. The Österreichische Forschungsförderungsgesellschaft mbH (FFG), the provinces of Vienna, Styria and Tyrol as well as the Steirische Wirtschaftsförderungsgesellschaft mbH (SFG) and Ingenza Ltd. are acknowledged for financial support. BN and JN acknowledge the Slovak-Austrian travel project SK-AT-0024-08.

Supplementary Data

RgDAO sequence (GenBank: CAA96323) re-designed for optimum codon usage in P. pastoris:


B Boussaid

C Aubrun

N Abdelkrim
email: naceur.abdelkrim@enig.rnu.tn

Set-point reconfiguration approach for the FTC of wind turbines

Keywords: FTCS, Reference Governor, Actuator fault, Performance degradation

In this paper, a two-level reconfiguration action is used to design an FTC system. The objective is to adapt the corrective action accordingly to the fault severity. The first level of the procedure is triggered when the impact of the fault on the system performance is limited. At the second level a dynamic reference modification based on reference-offset governor is proposed. The idea consists of updating the controller by the new post-fault system model in first time and; in second time; modifying the set-point or reference according to the system constraints which become more strict after fault occurrence in order to avoid any actuator saturation and ensure system stability. The effectiveness of the proposed solution is illustrated by a wind turbine example subjects to actuator faults and constrained on the actuator dynamic ranges.

INTRODUCTION

In industrial processes, systems to be controlled are becoming more and more complex. One of these complexities relies in the necessity of satisfying input/state constraints which are dictated by physical limitations of the actuators and by the necessity to keep some plant variables within safe limits. In general, these constraints are integrated in the selection of the process equipment and the design of the nominal controllers. Another complexity is the occurrence of faults in plants which make the design of a controller tolerant to faults a very important issue.

Nowadays, wind turbines which generate electrical energy from the wind energy are considered one of these complex systems. The installed turbines are often in megawatt size and are very expensive which need more availability (See [START_REF] Odgaard | Fault Tolerant Control of Wind Turbines -a benchmark model[END_REF]). Besides, physical and functional limitations should be kept in safe limits which need to handle with care any abnormal operating especially after fault occurrence. So that, degraded mode is needed to ensure safe functioning.

From Fault-Tolerant Control (FTC) design point of view, the post-fault system should recover the original performance which is usually a quiet ambitious objective. In refs. [START_REF] Jiang | Accepting Performance Degradation in Fault-Tolerant Control System Design[END_REF] and [START_REF] Zhang | Fault Tolerant Control System Design with Explicit Consideration of Performance Degradation[END_REF], it is considered that the system can always operate under degraded performance. In practice, once a fault occurs, the degree of the system redundancy and the available actuator capabilities can be significantly reduced. Further, the FTC may lead to actuator saturation, or worse still, to cause damage to the system, and even result in lose of the system stability (See [START_REF] Jiang | Graceful performance degradation in active fault tolerant control systems[END_REF]).

A significant amount of work has been done to deal with actuator saturation. Model predictive control is an effective control algorithm for dealing with actuator saturation (See [START_REF] Mayne | Constrained model predictive control: stability and optimality[END_REF]). Anti-windup research was largely discussed and many constructive design algorithms were formally proved to induce suitable stability properties (See [START_REF] Kothare | Multiplier theory for stability analysis of anti-windup control systems[END_REF], [START_REF] Wu | Anti-windup control design for exponentially unstable LTI systems with actuator saturation[END_REF]). Other class of framework consists of modifying the reference input so that the constraints are not violated (See [START_REF] Angeli | On feasible setmembership state estimators in constrained command governor control[END_REF], [START_REF] Bemporad | Nonlinear Control of Constrained Linear Systems via Predictive Reference Management[END_REF], [START_REF] Casavola | Robust Command Governors for Constrained Linear System[END_REF], [START_REF] Gilbert | Discrete-time reference governors and the nonlinear control of systems with state and control constraints[END_REF], [START_REF] Gilbert | Linear Systems with State and Control Constraints: The theory and Application of Maximal Output Admissible Sets[END_REF]). These approaches are able to handle input and/or state-related constraints, using methods based on model predictive control ideas, to synthesize Command or Reference Governor (RG). In ref.

citekol06, Parameter Governor (PG) unit is proposed which enforces pointwise-in-time constraints on the evolutions of relevant system variables. Later, both Reference Governor (RG) and Parameter Governor (PG) actions are integrated in a single unit as Reference-Offset Governor (ROG) (See [START_REF] Casavola | Reference-Offset Governor approach for the supervision of constrained networked dynamical systems[END_REF]), which adds many advantages especially in enlarging the set of feasible evolutions of the system. The function of ROG device is to modify, whenever necessary, the reference and add an offset to the nominal control action in order to enforce pointwise-in-time constraints and to improve the overall system transient performance (See [START_REF] Casavola | Supervision of Networked Dynamical Systems Under Coordination constraints[END_REF], [START_REF] Casavola | Reference-Offset Governor approach for the supervision of constrained networked dynamical systems[END_REF]).

In this paper, a new reconfiguration system approach based on Reference-Offset Governor and separate LQ controller is proposed. The reconfiguration capability of ROG unit is basically the respect of system constraint obligations and the dynamic modification of the reference according to an acceptable performance degradation. Furthermore, the stability of the closedloop system is ensured.

The main contribution of this paper is to deal with performance degradation in the case of wind turbines subject to actuator faults. A nonlinear reference management is used to ensure actuators saturation avoidance and system stability with accept-able performance degradation via dynamic reference modification.

The paper is organized as follows. The formulation of the problem statement is presented in section 2. Section 3 is reserved to deal with the design of the FTC system. Section 4 is dedicated to illustrate the idea with an example of a wind turbine benchmark followed by simulation results interpretations. Finally, the paper is ended by a conclusion.

PROBLEM FORMULATION

Standard LQ Control

Let us consider the following Linear Time-Invariant (LTI) system in discrete time

x(t + 1) = Ax(t) + Bu(t) + G d d(t) y(t) = Cx(t) (1)
Where [START_REF] Staroswiecki | Actuator faults and the linear quadratic control problem[END_REF], [START_REF] Harkegard | Resolving actuator redundancy optimal control vs. control allocation[END_REF]), the optimal control law is given by :

x(k) ∈ R n is the state vector, u(k) ∈ R m is the input vector, y(k) ∈ R p is the output vector, d(t) ∈ R n d is
u(t) = -Kx(t) + K r r(t) (2)
with

K = R -1 B T P (3) K r = R -1 2 (C(BK -A) -1 BR -1 2 ) + (4)
where Q is a positive semi-definite matrix and R is a positive definite matrix. Q and R are preselected by the designer to achieve the nominal performance. P is a unique positive semidefinite and symmetric solution of the Algebraic Riccati Equation (ARE)

A T P + PA + Q -PBR -1 B T P = 0 (5)

Limitation of the LQ solution in constrained control

Assume that one has constraints on control signal, so one should use a block to limit input signal to the upper and lower saturation values (see Fig. 1). The new control signal with the consideration of a piecewiselinear saturation is described as

u s = σ (u) =    u j,max if u j ≥ u j,max u j if u j,min ≤ u j ≤ u j,max u j,min if u j ≤ u j,min (6)
for j = 1, 2, . . . , m and m is the number of actuators.

Ideally, the nominal LQ Controller is designed to work inside the allowed control limit. However, a slight saturation is possible during short time without destabilizing the system. In faulty case, these constraints become more strict and the probability to reach the saturation region increases with the fault severity especially in the case of loss of actuator effectiveness which may destabilize the system or induce severe performance degradation through a decrease of feedback gain, [START_REF] Kapasouris | Design of feedback control systems for stable plants with saturating actuators[END_REF].

In general, nonlinear control laws are required to stabilize linear systems subject to input saturation and, for more generality, subject to input/state constraints. Our approach consists in associating a reconfigurable Reference Offset-Governor block to a reconfigurable LQ Regulator in order to solve the problem of actuator saturations and input/state constraints in general. Besides, the performance degradation is taken account by modifying the references by the ROG unit with the consideration of system constraints and nominal objectives.

Reference-Offset Governor solution

Let us consider the global system including the ROG unit and the feedback controller, as depicted in Fig. 2.

ROG Kr Plant K r c x y u g θ r + + -

Fig. 2. Global system diagram including Controller and ROG blocks

According to Fig. 2, the control input can be written as :

u(t) = -Kx(t) + K r g(t) + θ (t) = -Kx(t) + K z z(t) (7)
where

K z = [K r I m ] and z(t) = [g(t) θ (t)] T .
One replaces ( 7) in (1), one gets

x(t + 1) = (A -BK)x(t) + BK z z(t) + G d d(t) = Φx(t) + Gz(t) + G d d(t) (8) Where Φ = (A -BK) and G = BK z .
Besides, if one considers only the control input constraints, and one puts

H c = -K and L = K z c(t) = H c x(t) + Lz(t) + L d d(t) (9) So, the LTI system in (1) becomes    x(t + 1) = Φx(t) + Gz(t) + G d d(t) y(t) = H y x(t) c(t) = H c x(t) + Lz(t) + L d d(t) (10) with x(t) ∈ R n the
-Φ) -1 G g = I p
where z(t) = [g(t) θ (t)] T ∈ R p+m , is the ROG output and the following matrices are defined

G = [G g G θ ], L = [L g L θ ].
The ROG design problem consists of generating, at each time t; the command input z(t) as an algebraic function of the current state x(t) and reference r(t) z(t

) := z(x(t), r(t)) (11)
The ROG output is based on the minimization of a cost function subject to prescribed constraints. The cost function has the following form

J(x(t), z(t), r) = g(t) -r 2 Ψ g + θ (t) 2 Ψ θ (12)
where

Ψ g = Ψ T g > 0 m , Ψ θ = Ψ T θ > 0 m and v 2 Ψ := v T Ψv.
Thus, at each time t ∈ Z + , the ROG output is chosen according to the solution of the following constrained optimization problem, [START_REF] Casavola | Reference-Offset Governor approach for the supervision of constrained networked dynamical systems[END_REF],

z(t) := arg min z∈V (x(t)) J(x(t), z(t), r) (13)

FTC SYSTEM DESIGN

Let us consider the following proposed scheme in FTC solution (See Fig. 3). The bloc FDD is assumed perfect and the matrices A f and B f of the system post-fault are detectable.

Controller reconfiguration design

After the fault occurrence and the FDD action, the updated space state representation of the system is

x(t + 1) = A f x(t) + B f u(t) y(t) = Cx(t) (14)
Assuming that the system post-fault is controllable and (A f ,B f ) is still stabilizable, from the Bellman's optimality principle, the optimal reconfigurable strategy (See [START_REF] Staroswiecki | Actuator faults and the linear quadratic control problem[END_REF]) consists in applying a new optimal control action to the system ( 14)

u f (t) = -K f x(t) + K f r r(t) (15)
with

K f = R -1 B T f P f (16) K f r = R -1 2 (C(B f K f -A f ) -1 B f R -1 2 ) + (17)
where P f is a unique positive semi-definite and symmetric solution of the Algebraic Riccati Equation (ARE)

A T f P f + P f A f + Q -P f B f R -1 B T f P f = 0 (18)

ROG reconfiguration design

Hereafter, an extension of the ROG principle in the faulty case is proposed. It is assumed that the system post-fault dynamic is (A f ,B f ) and the controller feedback and feed-forward gains are denoted K f and K f r .

In closed-loop scheme, the system state space representation is given by

x(t + 1) = A f x(t) + B f u(t) + G d d(t) (19) = (A f -B f K f )x(t) + B f (K f r g(t) + I m θ (t)) + G d d(t)
Thus, the state space description of the plant (19) becomes :

   x(t + 1) = Φ f x(t) + G f z(t) + G d d(t) y(t) = H y x(t) c(t) = H f c x(t) + L f z(t) + L d d(t) (20)
where

Φ f = A f -B f K f (21) G f = B f K f z (22) K f z = [K f r I m ] (23)
with Φ f and G f represented the global system dynamics in closed-loop after fault occurrence.

Considering the ROG unit in the faulty case as shown in Fig. 3, and we assume that :

B.1) Φ f is a stable matrix; B.2) system (20) is offset-free w.r.t. g(t) i.e. H y (I n -Φ f ) -1 G f g = I p
The solution of the cost function ( 12) is :

z(t) := arg min z∈V f (x(t)) J(x(t), z(t), r) (24) with V f (x(t))
is the set of the disturbance-free virtual evolution of the constraints vector c f (k, x(t), z) after fault occurrence

V f (x(t)) = {z ∈ W f δ : c f (k, x(t), z) ∈ C f k , ∀k ∈ Z + } (25)
where c f (k, x(t), z) is given by :

c f (k, x(t), z) = H f c Φ k f x(t) + k-1 ∑ i=0 Φ k-i-1 f G f z + L f z (26)
and the two sets; W f δ and C δ f ; are given by :

W f δ := {z ∈ R p+m : cz ∈ C δ f } (27) C δ f := C f ∞ ∼ B δ (28) Note that C f ∞ is constructed from recursive sets C f k C f ∞ := k f 0 k=0 C f k (29)
where the sets

C f k are defined from k ∈ {0, 1, . . . , k f 0 } as C f 0 := C f ∼ L d D . . . C f k := C f k-1 ∼ H f c Φ k-1 f G d D (30)
with C f is the prescribed constrained set after fault occurrence.

The following properties hold true for the above described ROG in faulty case.

Theorem 1. Let assumptions (B.1) be fulfilled. Consider system (20) along with the ROG selection rule (24), and let V f (x(0)) be non-empty. Then: 1. The minimizer in ( 24) uniquely exists at each t ∈ Z + and can be obtained by solving a convex constrained optimization problem, viz.

V f (x(0)) = V (x(t f )) non-empty implies V f (x(t))
non-empty along the trajectories generated by the ROG command (20). Such the time of fault occurrence t f is determined by the FDD stage.

2. The set V f (x(t)), ∀x(t) ∈ R n , is finitely determined, viz. there exists an integer

k f 0 such that if c f (k, x(t), z) ∈ C f k , k ∈ {0, 1, . . . , k f 0 }, then c f (k, x(t), z) ∈ C f k ∀k ∈ Z + .
Such a constraint horizon k f 0 can be determined off-line. 3. The constraints are fulfilled for all t ∈ Z + . 4. The overall system is asymptotically stable; in particular, whenever r(t) ≡ r, lim t→∞ θ (t) = 0 m , and g(t) converges either to r or to its best steady-state admissible approximation r, with

ẑ(t) := [r 0 m ] T := arg min z∈V (x(t)) J(x(t), z(t), r) (31)
Consequently, by the offset-free condition (B.2), lim t→∞ ȳ(t) = r, where ȳ is the disturbance-free component of y.

Proof. The proof is similar to that presented in [START_REF] Casavola | Reference-Offset Governor approach for the supervision of constrained networked dynamical systems[END_REF].

WIND TURBINES

Wind turbine description and model

In this paper, a specific variable speed turbine is considered. It is a three blade horizontal axis turbine with a full converter. The energy conversion from wind energy to mechanical energy can be controlled by changing the aerodynamics of the turbine by pitching the blades or by controlling the rotational speed of the turbine relative to the wind speed. The mechanical energy is converted to electrical energy by a generator fully coupled to a converter. Between the rotor and the generator a drive train is used to increase the rotational speed from the rotor to the generator. The objective of the control system is to track the power reference while keeping the mechanical vibrations to minimal value. A more detailed description of the general function of the wind turbine can be seen in [START_REF] Odgaard | Fault Tolerant Control of Wind Turbines -a benchmark model[END_REF].

In principle, wind turbine system can be divided in three sub-systems: blade and pitch system, drive train system and Generator/conversion system. Fig. 4 shows the relation-ships between each sub-system and the controller, see e.g [START_REF] Odgaard | Fault Tolerant Control of Wind Turbines -a benchmark model[END_REF]. The turbine controller operates in four zones. Zone 1 is start up of the turbine, Zone 2 is power optimization, Zone 3 is constant power production and Zone 4 is high wind speed, see e.g. [START_REF] Johnson | Control of variable-speed wind turbines -standard and adaptative techniques for maximizing energy capture[END_REF]. The focus of this work is on the normal operation consequently only Zone 3 is considered. In this zone the control objective is to follow the power reference. The aerodynamics of the wind turbine is modeled as torque acting on the blades. This aerodynamic torque,τ r , can be represented by, see [START_REF] Odgaard | Fault Tolerant Control of Wind Turbines -a benchmark model[END_REF]:

τ r (t) = j=3 ∑ j=1 ρπR 3 C q (λ (t), β j (t))v w (t) 2 6 ( 32
)
where C q is the torque coefficient, λ , is the tip speed ratio, ρ, is the air density, R, is the radius of blades, v w , is the wind speed and β j , is the pitch angle referring to blade j. This formula is valid for small difference between β j values. Notice that β r refers to reference values and β m refers to measured values of pitch angles.

In this benchmark model, the hydraulic pitch is piston servo mechanism witch can be modeled by a second order transfer function:

β (s) β r (s) = ω 2 n s 2 + 2ξ ω n s + ω 2 n ( 33
)
The model of the drive train system is given by the state space representation as ẋdt (t) = A dt (η dt )x dt (t) + B dt u dt (t) (34) where x dt = [ω r ω g θ ∆ ] T , is the state vector and u dt = [τ r τ g ] T , is the input vector of the drive train sub-system. ω r , is the rotor speed, ω g , is the generator speed, θ ∆ , is the torsion angle of the drive train and τ g , is the torque of the converter. A dt is modulated by a parameter of the drive train efficiency, η dt , see [START_REF] Odgaard | Fault Tolerant Control of Wind Turbines -a benchmark model[END_REF].

The converter dynamics can be modeled by a first order transfer function, consult [START_REF] Odgaard | Fault Tolerant Control of Wind Turbines -a benchmark model[END_REF]:

τ g (s) τ g,r (s) = α gc s + α gc (35)
The power produced by the generator is given by P g (t) = η g ω g (t)τ g (t) (36)

Simulation Results

The model of the real wind turbine is linearized for a power setpoint, P r , of 4.8MW and a wind speed, v w , of 13m/s. A white noise is added to wind speed sequence in ordre to simulate a real wind variations. The parameters of the wind turbine used are: R = 57.5; ρ = 1.225; ξ = 0.6; ω n = 11.11, α gc = 50, η g = 0.98. The considered turbine is subject to physical constraints on pitch angles, β j .

C = {β j ∈ [0 • ; 90 • ], j = 1, . . . , 3} (37)
The sub-system to be studied in this work is the drive train system where the parameter of the efficiency decreases in function of the severity of the fault. Two cases are given below, the fault-free and post-fault model of the drive train and the controller are given also.

Fault-free case: In this case, the efficiency parameter, η dt , for nominal functioning of the drive train system is fixed to 0.98. So that, the state space model is The simulation results of the wind turbine output are shown in Fig. 5. Before the fault occurrence, the plant can track the nominal set-point of power, 4.8 10 6 W . After the fault occurrence at 30s, the efficiency parameter of the drive train system decreases enormously and the plant performance is degraded respectively which requires to reconfigure the setpoint. The set-point reconfiguration is parameterized by the fault severity and by the plant constraints which become more probable to be violated (see Fig. 6). In Fig. 6, and before the fault occurrence, the control inputs are inside the control limits required by the constraints set C in (37). However, and after the fault occurrence, the pitch angles decreases in order to compensate the fault effect to their minimal value without compensating the fault. The second action of reconfiguration is needed now in order keep the plant operating with degraded performance: the set-point reconfiguration. This action is ensured by the ROG unit like as mentioned in Fig. 3.

K f = [K f 1 K f 2 ] and K f r , where K f 1 =    0.

Performance evaluation

To evaluate the performance of the closed-loop system, one could use the following performance index

π(t) = 1 - y(t) -r(t) 2 r(t) 2 ( 38
)
where r is the reference or the nominal set-point and y is the regulated output. x 2 is the norm 2 of x.

Fig. 7 shows the evolution of the performance index, π, of the plant before and after the fault occurrence. This index can help the supervisor to monitor the plant by fixing a threshold for admissible performance degradation. The selection of the admissible threshold for acceptable performance degradations depends on safety and quality requirements. In this case of study, the maximal reference tracking error is 0.0782 (about 8%) which is acceptable if the selected threshold of π is 90%.

CONCLUSION

This paper presents a new approach to fault accommodation with performance degradation based on Reference-Offset Governor. The degraded ROG based FTC modify the set-points and add an offset to the control inputs after fault occurrence in order to accommodate the fault with acceptable degraded performance. The degradation of performance is supervised by the operator through a performance index. The simulation results proof that this approach improves the system performance degradation and ensure a safe and stable plant operation.

Fig. 1 .

 1 Fig. 1. LQ Regulator with input signal limitation block

  Fig. 3. Proposed scheme of FTC system design

Fig. 4 .

 4 Fig. 4. Simplified wind turbine diagram.

  after setting Q and R of the LQ controller to,Q = 100 * diag([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]), R = 4 * diag([21, 21, 21, 1]), the feedback and feed-forward gains are K = [K 1 K 2 ] and K r , where -45.0414 -0.2418 319.8854 0.0004 3.2685 -45.0414 -0.2418 319.8854 0.0004 3.2733 -45.0414 -0.2418 319.8854 0.0004 -0.1553 15.7775 -0.1725 -258.3093 0case: In this case, an actuator fault on the drive train system is considered at time 30s. This fault is reflected by the decrease of the efficiency parameter, η dt , to 0.0828 value. The FDD stage in Fig.3is supposed perfect, so the faulty model of the drive train system is A dt (0.0828) =   -1.4229 * 10 -5 1.4842 * 10 -7 -49.0909 0.0017 -0.1169 6.0340 * 10 3 1 -0.0105 0   After the first reconfiguration action, the new controller gains are

Fig. 5 .Fig. 6 .

 56 Fig. 5. The generated electrical power by the wind turbine.

Fig. 7 .

 7 Fig. 7. The performance index in-time evolution.

  ∈ R n d an exogenous bounded disturbance satisfying d(t) ∈ D; ∀t ∈ Z + with D a specified convex and compact set such that 0 n d ∈ D; y(t) ∈ R p the output, viz. a performance related signal; c(t) ∈ R n c the constraints vector, c(t) ∈ C ; ∀t ∈ Z + ; with C ⊂ R n c a prescribed constrained set.

	It is assumed that:
	A.1) Φ is a stable matrix;
	A.2) System (10) is offset-free w.r.t. g(t) i.e.
	H y (I n

state vector which includes the controller states; g(t) ∈ R p the manipulable reference which would essentially coincide with the reference r(t) ∈ R p ; θ (t) ∈ R m an adjustable offset on the nominal control law which is assumed to be selected from a given convex and compact set Θ, with 0 m ∈ intΘ; d

(t)

  Notice that, for reason of paper width, K and K f are divided into two matrices K 1 , K 2 and K f 1 , K f 2 respectively.

			2606 2.9599 0.2157 2.9551 0.2157	
			0.2157 2.9551 0.2606 2.9599 0.2157	
			0.2157 2.9551 0.2157 2.9551 0.2606	
			0.0089 -0.0449 0.0089 -0.0449 0.0089
			3.2685 -45.0414 -0.2418 319.8854 0.0004 
	K f 2 =	 	3.2685 -45.0414 -0.2418 319.8854 0.0004  3.2733 -45.0414 -0.2418 319.8854 0.0004 
		-0.1553 15.7775 -0.1725 -258.3093 0.2498
					-0.2169	
			K f r = 1.0 * 10 -4	 	-0.2169 -0.2169	 
					0.0205

Preprints of the 18th IFAC World Congress Milano (Italy) August 28 -September 2, 2011