Loïc Michel
email: loic.michel@ec-nantes.fr.

Ingrid Neunaber

Rishabh Mishra

Franck Plestan ID Caroline Braud

Member, IEEE Jean-Pierre Barbot

F Plestan

J.-P Barbot

P Hamon

J.-P Barbot

A novel lift controller for a wind turbine blade section using an active flow control device including saturations: experimental results

Keywords: Wind energy, Variable structure systems, Actuators, Adaptive control, Aerodynamics

In this paper, a very recent adaptive version of super-twisting is applied to the control of the aerodynamic lift over wind turbine blades, taking into account local disturbances of the air flow. The proposed control law acts as a model-free control strategy that is based on the definition of only two parameters. Using this strategy, the tuning and modeling efforts are reduced: the first parameter is acting on the gain variation speed, whereas the second one is linked to the expected accuracy, thus allowing the control of unknown dynamics. We discuss the capability of the proposed model to track a lift reference of a wind turbine blade under external perturbations and actuator saturation. Experimental results globally illustrate the feasibility of such a control.

I. INTRODUCTION

Wind turbines are subjected to many disturbances (both atmospheric and mechanical) [START_REF] Schepers | IEA Wind TCP Task 29, Phase IV: Detailed Aerodynamics of Wind Turbines[END_REF], which may, at least on average, be compensated by blade pitch control. Even if the blade pitch control [START_REF] Bossanyi | The design of closed loop controllers for wind turbines[END_REF] shows global efficiency, it is possible to improve the performances of the closed-loop system by using control scheme acting on aerodynamic variables. Different types of actuation solutions (for example, flaps [START_REF] Gonzalez | Field test of an active flap system on a full-scale wind turbine[END_REF], microtabs [START_REF] Cooperman | Closed-loop control of a microtab-based load control system[END_REF] or plasma [START_REF] Matsuda | Plasma actuation effect on a mw class wind turbine[END_REF]) developed for control purposes, are associated with sufficiently robust control algorithms that are acting on the blade aerodynamics. A review on the control strategies dedicated to gust alleviation problems using active flow control, is proposed in [START_REF] Williams | Alleviating unsteady aerodynamic loads with closed-loop flow control[END_REF] including modeling techniques [START_REF] Allan | Closed-loop separation control using oscillatory flow excitation[END_REF], [START_REF] Li | Aeroelastic control of wind turbine blade using trailing-edge flap[END_REF]. Feedback and feedforward structures [START_REF] Bartholomay | Pressure-based lift estimation and its application to feedforward load control employing trailing-edge flaps[END_REF] have been studied in the framework of a controlled wind turbine blade for active load reduction based on system identification [START_REF] Barlas | Closedloop control wind tunnel tests on an adaptive wind turbine blade for load reduction[END_REF] [START_REF] Shaqarin | Open and closed-loop experiments to identify the separated flow dynamics of a thick tbl[END_REF] [START_REF] Li | Adaptive flow control of wind turbine blade using microtabs with unsteady aerodynamic loads[END_REF] [13] [START_REF] Becker | Robust control of separated shear flows in simulation and experiment[END_REF]. A proportional controller has been proposed in [START_REF] Jaunet | Experiments on lift dynamics and feedback control of a wind turbine blade section[END_REF] to reduce lift fluctuations in a constant shear inflow simulated by oscillations of a 2D blade section. Micro-jets have been successfully implemented as a fast control technology and are able to significantly dampen the lift oscillations; however, some lift fluctuations remain. The originality of this work is to control the aerodynamic lift at the blade scale considering active flow control devices (see a review of existing strategies in [START_REF] Aubrun | A review of wind turbineoriented active flow control strategies[END_REF]). The work developed in [START_REF] Jaunet | Experiments on lift dynamics and feedback control of a wind turbine blade section[END_REF], involving micro-jets, has been improved by using a model-free control technique [START_REF] Fliess | Model-free control[END_REF]; this controller has been implemented by the authors [START_REF] Michel | Model-free control of the dynamic lift of a wind turbine blade section: experimental results[END_REF] to control micro-jets installed at the trailing edge of a 2D blade section. Indeed, it is well-known that modelling and simulation of aerodynamic dynamics are very complex and take a lot of computation time. Consequently, it is difficult to use model for control design. Afterwards, two ways to design a control of an aerodynamics system are to build an approximated model that is dedicated to control, or to design a control algorithm without needing a model. In [START_REF] Brunton | Closed-loop turbulence control: Progress and challenges[END_REF], several model-free controllers are presented and the advantages of such approach are highlighted. Thus, in [START_REF] Michel | Model-free control of the dynamic lift of a wind turbine blade section: experimental results[END_REF], a model-free control based on the seminal work [START_REF] Fliess | Model-free control[END_REF] is experimented for the blade lift control. The main advantage of this control law is obviously the reduced knowledge with respect to the dynamic of the system; however, it does not offer any guarantee on stability and robustness. It is why, in this work, another class of control, sliding mode control (SMC) [START_REF] Shtessel | Sliding Mode Control and Observation[END_REF] [START_REF] Utkin | Sliding mode control on electro-mechanical systems[END_REF], requesting few information with respect to the dynamic, is proposed. This control law is a robust nonlinear one with respected to matching perturbation [START_REF] Draženović | The invariance conditions in variable structure systems[END_REF] that is particularly well suited to control perturbed uncertain nonlinear systems. Remark that the sliding mode control requests the knowledge of the input-output sign, the relative degree of the system and the boundness of functions describing the dynamic of the system (remark that this latter point is not required in [START_REF] Fliess | Model-free control[END_REF]). Extremum-seeking control (ESC), associated with sliding mode control [START_REF] Shtessel | Sliding Mode Control and Observation[END_REF] [START_REF] Utkin | Sliding mode control on electro-mechanical systems[END_REF], has been implemented in the framework of aerodynamic drag reduction [START_REF] Mariette | Contrôle en boucle fermée pour la réduction active de traînée aérodynamique des véhicules[END_REF]. The ESC method has also been used as a real-time optimization strategy to cope with high-lift problems in the context of flow instability at the blade section scale through active flow control [START_REF] Becker | Adative closed-loop separation control on a high-lift configuration using extremum seeking[END_REF]. However, due to its discontinuous feature, this class of control strategy generates the chattering phenomenon (high frequency oscillations). Several solutions have been proposed to attenuate this drawback; among them, one can firstly cite the concept of high order sliding mode control. This class of controllers allows to reduce the chattering while keeping the robustness and improving the accuracy. One of the most famous high order sliding mode controllers is the super-twisting [START_REF] Levant | Sliding order and sliding accuracy in sliding mode control[END_REF] that is a second order sliding mode algorithm that is a continuous output feedback. Another way to reduce the chattering is the dynamic adaptation of the controller gain: the simple idea is to adapt the controller gain with respect to the accuracy (the gain is increased if the accuracy is not sufficient whereas, when the targeted accuracy is reached, the gain is reduced). Numerous adaptation laws have been proposed for first [START_REF] Plestan | New methodologies for adaptive sliding mode control[END_REF], [START_REF] Bartolini | Adaptation of sliding modes[END_REF], [START_REF] Hsu | Adaptive unit vector control of multivariable systems using monitoring functions[END_REF], [START_REF] Roy | On adaptive sliding mode control without a priori bounded uncertainty[END_REF], [START_REF] Lin | Adaptation of sliding modes[END_REF], [START_REF] Obeid | Barrier function-based adaptive sliding mode control[END_REF] or second order sliding mode controllers such as twisting [START_REF] Shtessel | Twisting sliding mode control with adaptation: Lyapunov design, methodology and application[END_REF], [START_REF] Liu | Twisting sliding mode control with adaptation: Lyapunov design, methodology and application[END_REF], [START_REF] Taleb | Electropneumatic actuator control: solutions based on adaptive twisting algorithm and experimentation[END_REF] or super-twisting [START_REF] Shtessel | A novel adaptive-gain supertwisting sliding mode controller: methodology and application[END_REF], [START_REF] Edwards | A novel adaptive-gain super-twisting sliding mode controller: methodology and application[END_REF], [START_REF] Utkin | Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method[END_REF], [START_REF] Obeid | Barrier function-based adaptive super-twisting controller[END_REF]. In this paper, the choice towards the adaptive super-twisting algorithm has been made for several reasons: this is a continuous controller that does not use the time derivative of the sliding variable while reducing the chattering efficiently and the effort of the actuator. Furthermore, there exist several adaptive versions of super-twisting, from the initial version [START_REF] Shtessel | A novel adaptive-gain supertwisting sliding mode controller: methodology and application[END_REF] to very recent ones [START_REF] Gutierrez | A simplified version of adaptive super-twisting control[END_REF], [START_REF] Plestan | Adaptive supertwisting controller with reduced set of parameters[END_REF], these latter using very few tuning parameters (in [START_REF] Plestan | Adaptive supertwisting controller with reduced set of parameters[END_REF], [START_REF] Gutierrez | A simplified version of adaptive super-twisting control[END_REF], two parameters when six for [START_REF] Shtessel | A novel adaptive-gain supertwisting sliding mode controller: methodology and application[END_REF]). Notice that this class of adaptive controllers requires a very reduced knowledge of the system; only the facts that the uncertainties/perturbations are bounded and that the system can be modelled as a first order model, are required. For the first time in aerodynamics, the adaptive super-twisting algorithm, proposed in [START_REF] Plestan | Adaptive supertwisting controller with reduced set of parameters[END_REF] and based on authors previous work [START_REF] Michel | A novel lift controller for a wind turbine blade section using an active flow control device: experimental results[END_REF], is implemented to control the lift using microjets; only global aerodynamic force measurement is used as a feedback for the control. The physical limitation of the actuator will be also taken into account by means of an associated antiwindup algorithm. Its purpose is to maintain the stability of the adaptation procedure of the proposed algorithm in presence of external perturbations that induce actuator saturation. The paper is structured as follows. Section II describes the experimental setup, whereas Section III presents the adaptive super-twisting algorithm including its main properties and the proposed anti-windup algorithm. Section IV illustrates and analyses some experimental results. Section V gives some concluding remarks and perspectives.

II. EXPERIMENTAL SETUP

The experimental bench, detailed in this section, is composed of a wind tunnel with its perturbation system, a 2D aerodynamic blade profile equipped by micro-jets (for the lift control), and lift and drag sensors.

A. Wind tunnel facility and gust generator

The LHEEA aerodynamic wind tunnel is a recirculating one. The test section has a cross-section of 500 × 500 mm 2 and a length of 2300 mm (Figure 1). The turbulence intensity of an undisturbed inflow in the wind tunnel is around 0.3%. In the present study, a grid is installed at the inlet of the test section to generate turbulent inflow with a turbulence intensity of 3%. This bypasses the laminar-to-turbulent transition occurring at low Reynolds numbers and low angles of attack (AoA) for this blade geometry (see the linear part of the lift curve in Figure 2). The inlet of the test section is additionally equipped with a system which enables the generation of a sudden variation of the mean flow with turbulence superimposed on it. This system is called "chopper" and consists of a rotating bar that cuts through the inlet of the test section (Figure 1(a)). Figure 1(b) displays the energy spectrum of a gust produced by the chopper. In this work, however, the chopper is used in a static way by fixing its position in the inlet to add disturbances (in [START_REF] Michel | Model-free control of the dynamic lift of a wind turbine blade section: experimental results[END_REF], the rotating chopper was used to produce a periodic reduction of the lift).

B. Aerodynamic profile

A 2D blade section of type NACA 65 4 -421 with a chord length of c = 9.6 cm is installed in the test section of the wind tunnel (Figure 5). 1 It is a thick profile with two changes of the lift curve corresponding to a first boundary layer separation at the trailing edge of the profile and a second flow separation at the leading edge, indicating stall (see [START_REF] Soulier | Low-Reynolds-number investigations on the ability of the strip of tell-tale sensor to detect flow features over wind turbine blades: flow separation/reattachment dynamics[END_REF] for more details on the blade aerodynamics). In the present study, the angle of incidence was set to α = 20 • . Open-loop tests for α = {0 • , 10 • , 20 • } have been performed to chose this value (see Fig. 3). It has been shown that only a low range of the lift variation (or controlability margin of the lift) can be reached for α = 0 • when the flow is still attached (i.e. maximum lift force gain ∆F L = 2.5 N). At α = 10 • , the controlability margin is three times higher (∆F L = 7N), but it is decreasing with the inlet pressure from p = 1 bar. An angle α = 20 • is therefore chosen to operate the control algorithm, as the controlability margin is higher and linearly increasing according to the inlet pressure. More investigations are needed to extend the present work to other angles of incidence.

C. Lift and drag measurements

Two sets of Z6FC3 HBM bending beam load cell sensors are used, and they are mounted on both sides of the 2D blade section support to measure the lift and drag forces. As shown in Figure 1(a), each set consists of two load cells mounted with in a 90 • angle to measure the forces in the X (drag) and Z (lift) directions. They are calibrated in situ using gauge weights from 0 -5 kg in steps of 0.5 kg.

D. Micro-jets

To control the flow around the airfoil, holes of 1 mm diameter with equidistant 8 mm spacing are placed at 1.92 cm from the airfoil's trailing edge, along the entire spanwise direction (Figure 1(c)). They are connected to a plenum chamber, itself fed with pressurized air at 6 bar. The air circuit is connected to solenoid valves that are acting as On/Off switches, so that pulsed micro-jets can be generated with a repetition rate of up to 300 Hz.

The action of the micro-jets is physically limited to the injection of pressurized air of maximum 6 bar, thus defining the range of the lift variations that can be compensated by the micro-jets actuator system. It is identified by a simple succession of valves opening and closing.

E. Control hardware

The control is managed by a STM32 Nucleo board H743ZI2 allowing a 16-bit ADC acquisition as well as the possibility to monitor the signals in real-time on the computer (Figure 4 presents the control hardware where the Nucleo board is mounted on a fully featured PCB): the lift force measured by the force balances is used as input signal. It is acquired with a sampling frequency of 20 kHz using the Nucleo board. The signal is filtered using a fourth order Butterworth filter with a cut-off frequency of 20 Hz. The control updates at 20 kHz and drives the duty-cycle of the activation of the valve at 200 Hz in response to the input from the load cell sensors.

III. ADAPTIVE SUPER-TWISTING BASED CONTROLLER DESIGN

A. Problem statement

The control objective is to ensure that the lift of the blade is tracking a reference despite the wind variations and external perturbations. This is achieved using the action of the microjets. As shown in Fig. 6, the control signal drives the signal sent to the solenoid valves to release or block the pressurized air in front of the micro-jets on the airfoil surface. The measured lift is forced to a reference and the valve is driven using a variable duty-cycle (conversion of the output of the control as a PWM signal with a resolution of 0.025 % of the sampling period) at the constant frequency of 200 Hz, which is a TTL (transistor-transistor logic) signal. This allows to directly drive the valves from the control signal that adjusts the mass flow injected to the system. Recall that the flow injected at the top of the blade can be not at all sufficient to compensate strong lift variations, therefore inducing saturation of the actuators, that are managed by a anti-windup algorithm.

Fig. 6: Closed-loop scheme.

B. A solution with limited knowledge of the system

The blade lift control design is based on the following observation: the modeling of the studied system is a very hard task. Thus, a control approach with a limited modeling process is considered. In such way, the model-free controller [START_REF] Fliess | Model-free control[END_REF] has been proposed in [START_REF] Michel | Model-free control of the dynamic lift of a wind turbine blade section: experimental results[END_REF]: it is assumed that the relation between the force generated by the micro-jets and the lift force (see Figure 6) can be modelled by a first-order system. However, the robustness of such a controller is not ensured. The current paper proposes an adaptive robust controller based on a second order sliding mode strategy [START_REF] Shtessel | Sliding Mode Control and Observation[END_REF] that is based on an adaptive version of the super-twisting algorithm [START_REF] Plestan | Adaptive supertwisting controller with reduced set of parameters[END_REF] given that

• it can be applied to a system with a relative degree equal to 1: that is the case here given that, as shown in [START_REF] Michel | Model-free control of the dynamic lift of a wind turbine blade section: experimental results[END_REF], the system can be viewed as a first-order system; • it does not require any modeling information (except the relative degree), its gain being dynamically adapted;

• it is intrinsically robust with respect to uncertainties and perturbations. Indeed, in such conditions, a real second order sliding mode [START_REF] Shtessel | Sliding Mode Control and Observation[END_REF] is established in finite time. Define the tracking error as σ such that σ = y -y * with y the measured lift and y * the reference. The relation between σ and the control input u that is applied to the PWM system controlling the servo-valves, can be viewed as a perturbed firstorder system with unknown static gain k and constant time τ under a perturbation δ(t) [START_REF] Michel | Model-free control of the dynamic lift of a wind turbine blade section: experimental results[END_REF], that is

σ = - 1 τ σ + k τ u + δ(t). (1)
Supposing that parameters k and τ are constant but unknown, system (1) can be written as

σ = a(σ, t) + b • u (2)
with a(σ, t) = -1 τ σ + δ(t) and b = k τ . One supposes that the function a(σ, t) is bounded in the operating domain. Notice that, in sliding mode context, the variable σ is called "sliding variable". Moreover, -1 τ σ is a dissipative term that contributes to the boundedness of a(σ, t). Given that b is assumed to be constant (but unknown), system (2) has a similar form than the systems considered in [START_REF] Plestan | Adaptive supertwisting controller with reduced set of parameters[END_REF]. From [START_REF] Plestan | Adaptive supertwisting controller with reduced set of parameters[END_REF], the adaptive super-twisting controller is defined as

u = -k 1 |σ| 1 2 sgn(σ) + v, v = -k 2 sgn(σ). ( 3
)
where u is the output of the controller and the adaptive gains k 1 and k 2 obtained by

k1 =      β |ψ| + ϵ if |σ| > ϵ -k 1 if |σ| ≤ ϵ (4) k2 =      β 2|σ| 1 2 if |σ| > ϵ -k 2 if |σ| ≤ ϵ (5)
where ψ = -σ, β > 0 and ϵ > 0 are constant parameters; σ is the numerical estimation of σ. For the sake of implementation simplicity, the numerical estimation of σ is performed using the basic Euler method [START_REF] Hairer | Solving Ordinary Differential Equations I Nonstiff problems[END_REF] 2 .

The gains k 1 and k 2 are adjusted based on the proposed adaptation laws (4)-( 5). The adaptation protocol drives the evolution of the gains k 1 and k 2 according to the value of σ.

The main ideas behind the adaptation rules are the following

• if |σ| > ϵ, it can be due to the fact that the gains are not sufficient with respect to the effects of the perturbations and uncertainties (recall that a and b in (2) are unknown, a being bound and b constant). So, the gains are increased (as displayed by first equations ( 4)-( 5)) as long as the 2 Notice that other estimation techniques could be used, for example based on algebraic technique [START_REF] Fliess | Non-linear estimation is easy[END_REF] or homogeneous one [START_REF] Michel | An experimental investigation of discretized homogeneous differentiators: Pneumatic actuator case[END_REF]. A comparison between different differentiators can be found in [START_REF] Othmane | Systematic comparison of numerical differentiators and an application to model-free control[END_REF] as well as discrete time differentiator based sliding modes with polynomial corrector terms with respect to the sampling period [START_REF] Barbot | Discrete differentiators based on sliding modes[END_REF] and differentiators with variable exponent to improve the rejection of the noise [START_REF] Ghanes | A new varying gain exponent based differentiator/observer: an efficient balance between linear and sliding-mode algorithms[END_REF]. desired accuracy is achieved, the parameter ϵ adjusting this accuracy target; • if |σ| < ϵ, the accuracy target is reached. The gains can be assumed to be sufficient with respect to the perturbations and uncertainties. In that manner, the gains can be reduced as displayed by the gain dynamics (second equations of ( 4)-( 5)). When the gains become too small or if a larger perturbation/uncertainty appears, the accuracy can be lost; the previous item is then considered, and so on. Since the convergence zone depends on the parameter ϵ, it is necessary to chose it sufficiently small to ensure the accuracy of the closed-loop system; however, it is necessary to tune it at a sufficient value in order to take into account the sampling period effect (see Section 4 of [START_REF] Plestan | New methodologies for adaptive sliding mode control[END_REF] for the relation between the accuracy target ϵ and the sampling period). The parameter β is acting on the dynamics of adaptive gains and should be chosen according to an initial estimation of the "magnitude" of the open-loop dynamic response of the system including an estimation of the perturbation 3 .

C. Saturated actuator

To deal with the physical limits of the micro-jet actuator, that may create uncontrollable situations and unexpected behavior of the control algorithm, in presence of strong perturbations of the lift, an anti-windup procedure [START_REF] Tarbouriech | Stability and Stabilization of Linear Systems with Saturating Actuators[END_REF] is proposed to manage the integration part of the adaptive supertwisting algorithm when physical saturation occurs. Here, only upper saturation is considered due to physical limitations of the experimental test-bench.

1) Definition of the saturation: The control is affected by a saturation including an hysteresis and an anti-windup algorithm that interacts with the numerical integration schemes of the controller. Denoting u the output of the control law, u out the output of the saturation and u max the upper bound of the saturation, the saturation including an hysteresis is defined as follows

• when u increases and u ≥ u max , then u out = u max ;

• when u decreases and u < 0.9 u max then u out = u;

• when u remains below u max , then u out = u.

2) Anti-windup algorithm: Consider the three numerical integrators, v n , k 1,n , k 2,n and their respective derivatives vn , k1,n , k2,n , associated with an anti-windup based integration scheme

v n = v n-1 + (1 -AW ) h 2 ( vn + vn-1 ) k 1 , n = k 1 , n-1 + (1 -AW ) h 2 ( k1,n + k1,n-1 ) k 2 , n = k 2 , n-1 + (1 -AW ) h 2 ( k2,n + k2,n-1 ) (6)
where n is the discrete time iteration and AW is the variable associated to the anti-windup scheme, that is enabled when 3 Notice that current works are made in order to remove the tuning process of ϵ and β, by using an online tuning process of both these parameters.

entering into the saturation mode. Using Euler numerical differentiation, equation ( 6) becomes

v n = v n-1 + 1 2 (1 -AW )(v n + v n-2 ) k 1 , n = k 1 , n-1 + 1 2 (1 -AW )(k 1,n + k 1,n-2 ) k 2 , n = k 2 , n-1 + 1 2 (1 -AW )(k 2,n + k 2,n-2 ) (7)
which is now independent from the time derivative variables ( vn , k1,n , k2,n ). Before entering into the saturation mode, the anti-windup scheme is disabled (AW = 0) and the integration operates normally.

Entering into saturation mode and assuming that u enters into saturation at the instant n sat in , the anti-windup scheme is enable (AW = 1) thus blocking all integrators to their previous values at the instant n sat in . The integrators read

v n = v n sat in k 1 , n = k 1 , n sat in k 2 , n = k 2 , n sat in (8)
Note that the control (3) is still updated during the saturation mode, holding k 1 , k 2 and v constant.

Exiting the saturation mode and assuming that u exits out of the saturation at the instant n sat out , the integrators are re-enabled from their prior values [START_REF] Li | Aeroelastic control of wind turbine blade using trailing-edge flap[END_REF].

We would like to remark that it is possible to add a scaling coefficient γ on v in order to accelerate the transient response of v at the end of the saturation so that

v n sat out = γ v n sat in , (9)
From a practical point of view, setting γ < 1 allows to accelerate the saturation output, and thus to minimize the associated delay but to the detriment of a less efficient tracking.

IV. EXPERIMENTAL RESULTS

A. Scenarios of operation

The experiments are conducted considering a constant inflow velocity of 20.3 ms -1 (except for scenario 7 which is using an inflow velocity of 19.3 ms -1 ), measured with a Pitot tube in front of the airfoil in the undisturbed flow, and an angle of incidence of the 2D blade section of 20 • . The chopper can create a reduction of the air flow and is used to evaluate the robustness of the proposed adaptive super-twisting control under perturbations of the lift.

The efficiency of the lift tracking is evaluated for several scenarios that illustrate several operating conditions, including change of the wind speed, introduction of the chopper perturbation, and several types of references, for which the characteristics are summarized in the Table I.

To illustrate the operation of the saturation mode, a higher output reference than the maximum reachable lift is considered in order to saturate the micro-jet actuator in the yellow scenarios of Table I

1 X X 2 X X X 3 X 4 X X 5 X X 6 X X 7 X X
TABLE I: Overview of scenarios of operation.

Concerning the scenario 1 and 2, the parameters of the adaptive super-twisting controller are set to β = 7000, ϵ = 0.1 and the initial values of both gains are k 1 (0) = k 2 (0) = 10 Concerning the scenarios 3-7, the parameters are set to β = 15000, ϵ = 20 and the initial values of both gains are k 1 (0) = 10, k 2 (0) = 300. Note that in the different studied cases, with respect to such kind of active flow control, the range of β (resp. ϵ) is between 5000 and 8000 (resp. 0.05 and 0.5) concerning the scenario 1 and 2 and the range of β (resp. ϵ) is between 13000 and 18000 (resp. 10 and 30) concerning the scenarios 3-7.

B. Results and discussion

In each scenario developed below, the tracking of the instantaneous lift is presented according to the time evolution of the duty-cycle and the time evolution of the gains k 1 and k 2 .

Scenarios without saturation:

• Scenario 1: ) that are increased while the perturbations occur. Another perturbation is introduced by moving the chopper blade into the inlet of the test section at t = 50 s. This perturbation isn't strong enough to induce a control reaction. It is increased further by introducing the chopper blade further into the inlet at t = 60 s. As soon as this perturbation is introduced, the control reacts strongly by increasing gains k 1 and k 2 (see figure 8 (b)). Lastly, a new reference is imposed at a lower lift level which allows a greater controlability margin of the actuator, then the gains k 1 and k 2 can be increased to cope with the chopper perturbation. According to the adaptation rules, the gains are dynamically increased while a perturbation is disturbing the lift (either the wind speed or the static chopper) to compensate the perturbation and to maintain the tracking. When starting the control, a certain transient is needed to start the adaptation of the gain to set the initial tracking of the lift (see Figures

Scenario 3: Figure 9 illustrates the tracking of a sine reference at a constant wind speed of 20.3 ms -1 is considered and without chopper perturbation. The gains update quickly (at 10 s for k 1 and at 20 s for k 2 ) and reach higher values before oscillating according to the reference and the rejection of the aerodynamic fluctuations. In particular, some strong aerodynamic fluctuations occur when the reference becomes higher, thus disturbing the tracking, around the maximum of the lift, that is rapidly compensated by the adjustment of the gains. The high frequency variations of the duty-cycle (Figure 9(c)) are probably due to the effect of the binary valves on the closed-loop control. Moreover, the two bumps which appear on k 1 and k 2 are due to the highest reference variation in absolute value.

Scenarios including saturation while starting the control:

• Scenario 4: Figure 10 illustrates the tracking of a constant reference and wind speed of 20.3 ms -1 considering an initial saturation of the control, and the introduction of the chopper at t = 30 s. During the saturation, the gains k 1 and k 2 are maintained constant and the control reacts after the saturation period with a small delay. The oscillations (or chattering) present in the duty-cycle is in relation with the value of the gains. Particularly, the chattering is reduced when the gains are the lowest at around 35 s; this is again certainly related to the binary valves.

Limited circulation. For review only IEEE TCST Submission no.: 22-0932.1

Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

• Scenario 5: Figure 11 illustrates the tracking of the lift considering an initial saturation of the control, piecewisely constant changes of the reference as well as the introduction of the chopper perturbation during the control. The saturation of the control is again reached at the beginning and the chopper is introduced at t = 30 s, similarly as scenario 4, except that changes of the reference are considered. The gains k 1 and k 2 are stabilized until t = 50 s despite the chopper perturbation that is introduced at t = 30 s. The changes of the reference impact the adjustment of the gains k 1 and k 2 for which the gains are strongly reduced when the lift reference is set at the lowest value. Notice that, when the lift reference is set again at its nominal value at t = 90 s, the adaptation of the gains takes more time when re-increasing the lift reference, which induces a slower transient. When the reference is lower, the control is relaxed involving a fast return of the initial state of the flow (separated flow). At the opposite, more energy is needed to force the flow attachment, inducing an increase of the gains k 1 and k 2 . This last operation takes more time by the control (see the time evolution of the gains k 1 and k 2 in Figure 11(c)). This is in good agreement with the study of [START_REF] Shaqarin | Open and closed-loop experiments to identify the separated flow dynamics of a thick tbl[END_REF] who found a faster return to the initial state (flow separation) when the control is removed.

• Scenario 6: Figure 12 illustrates the tracking of the lift considering an initial saturation of the control, piece-wisely constant changes of the reference as well as the introduction of a short-time stronger static chopper perturbation, introduced at t = 30 s and removed at t = 80 s. The wind speed is set at a constant speed of 20.3 ms -1 . This case shows higher aerodynamic perturbations when introducing the chopper, while the control maintains good tracking response. Compared to the previous case, the gains evolves in the same way before the removal of the chopper, but the adaptation of the gains from t = 80 s is faster since the chopper has been removed which tends to indicate that the control efficiency is decreased by the chopper perturbation (more turbulence).

• Scenario 7: Figure 13 illustrates the tracking of the lift considering piece-wisely constant changes of the reference under a lower wind speed of 19.3 ms -1 (lower Reynolds number because the blade section is the same), no external perturbations have been introduced. Globally, due to the low wind speed, less effort is made to maintain the lift despite the changes of the reference. In particular, the gains remain low in average and a reduction of the perturbations is observed at the lowest lift reference that can be correlated with corresponding low gains values and the decrease of the duty-cycle. The chattering effect is then of less importance, in agreement with reduced gains used in this configuration and thus less perturbations from the binary valves.

The rejection of the high frequency perturbations can be managed differently considering another choice of β, ϵ, k 1 and k 2 in equations ( 4) and [START_REF] Matsuda | Plasma actuation effect on a mw class wind turbine[END_REF]. The high frequency perturbations are, to the best of knowledge, also due to the limitations of the dynamic of the micro-jets and measurement noise. An adaptive super-twisting-based control has been used to control the lift force acting on an airfoil by means of micro-jets. Different scenarios of experimental tests have been carried out to illustrate the robustness of the control. Promising results show that satisfying tracking performances have been obtained despite the perturbations made of two types: chopper blade perturbation which is increasing the turbulence intensity level of the inflow, and mean wind inflow variations. Due to the small range of the lift controlability, the microjet action is rather limited. The anti-windup manages the saturation of the control efficiency. To extend the capabilities of the proposed lift control system, the direct control of the angle of attack is envisaged and future investigations will be focused on the lift control design combining the use of blade pitch and the use of micro-jets.

To summarize the results obtained with the test-bed:

• the proposed control is robust to saturation and to external perturbations; • the control needs more energy when the chopper appears (in the considered cases) than when the tracking reference changes; • the adaption of the control takes time with respect to wind perturbation. In order to overcome the chattering due to the binary valves, continuous valves could be tested in the future. Moreover, a spatio-temporal measurement should be used to investigate complex fluidic organisation in closed-loop compared with open-loop behavior.

Fig. 1 :

 1 Fig. 1: (a) LHEEA aerodynamic wind tunnel: a gust generator, named "chopper", can optionally be used. (b) Example of the energy spectrum of the flow generated by the chopper. (c) Setup used for active flow control measurements: a tube with holes is installed at the airfoil's trailing edge and pressurized air is blown out of the holes.

Fig. 2 :

 2 Fig. 2: Experimentally measured lift curves, C L , versus the angle of incidence, α, of the airfoil in dependence of the Reynolds number.

  Limited circulation. For review only IEEE TCST Submission no.: 22-0932.1 Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

Fig. 3 :

 3 Fig. 3: Lift force gain, ∆F L , versus pressure for different AoA.

Fig. 4 :

 4 Fig. 4: Experimental setup: the board control.

Figure 5

 5 Figure 5 displays a view of the experimental setup focusing on the wind tunnel, the measurement system and the air injection system.

  Limited circulation. For review only IEEE TCST Submission no.: 22-0932.1 Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

Fig. 5 :

 5 Fig. 5: Experimental setup: the wind tunnel test section with the 2D blade section, load cell sensors, measurement acquisition, and pressurized air injection system.

  Limited circulation. For review only IEEE TCST Submission no.: 22-0932.1 Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

Figure 7 • Scenario 2 :

 72 illustrates the open-loop behavior of the lift force without air injection before introduction of the closed-loop control. The control tracks the reference considering piece-wisely constant changes of the reference. The introduction of the chopper in the test section during the whole scenario is considered. The wind speed is initially set to 20.3 ms -1 . Using a fixed position of the chopper blade, a perturbation is introduced at the beginning of the test to set the 'nominal' lift value in the open-loop. Then, the control starts at t = 31 s and a transient due to the adaptation of the gains k 1 and k 2 is observed that allows the lift to reach the targeted reference (see Figure7(a)). The control allows to efficiently track the lift reference despite the perturbation via the averaged duty-cycle (Figure7(c)): the gains k 1 and k 2 (see Figure7(b)) quickly increase to compensate the lower value of the lift due to the perturbation. The effort requested to maintain the tracking efficiency depends on the reference and the perturbation; as a consequence, a lower reference at t = 63 s tends to decrease the gains k 1 and k 2 despite the constant perturbation (see Figures7(a) and 7(b)). Figure8illustrates the tracking of the lift considering piece-wisely constant modifications of the reference under a change of the wind speed (maintained during the rest of the scenario) as well as the introduction of a chopper perturbation while the control is running. The wind speed is initially set to 20.3 ms -1 and no perturbation is introduced at the initial time. The wind speed is set at 21.3 ms -1 at t = 12 s until the end of the scenario. The gains are adapting themselves according to this lift increase, with a relatively long time transient of gains until t = 25 s (Figure8(b)). Accordingly, the reaction of the control can be seen both through the value of the averaged duty-cycle (Figure8(c)) that is adjusted when perturbations occur and through the adaptation of k 1 and k 2(Figure 8(b)

  Measured lift and reference lift versus time (sec). (b) Gains k 1 and k 2 versus time (sec). (c) Duty-cycle versus time (sec).

Fig. 7 :

 7 Fig. 7: Scenario 1: open-loop, chopper perturbation while starting the control.

Fig. 8 :

 8 Fig. 8: Scenario 2: wind speed change (+ 1ms -1 ) and chopper perturbations during the control.

Fig. 9 :

 9 Fig. 9: Scenario 3: oscillating reference without any perturbation.

Fig. 10 :

 10 Fig. 10: Scenario 4: constant reference and chopper perturbation during the control.

chopper at 7 %

 7 (a) Measured lift and reference lift versus time (sec). (b) Gains k 1 and k 2 versus time (sec).(c) Duty-cycle versus time (sec).

Fig. 11 :

 11 Fig. 11: Scenario 5: chopper perturbation during the control.

Fig. 12 :

 12 Fig. 12: Scenario 6: short-time chopper perturbation during the control.

Fig. 13 :

 13 Fig. 13: Scenario 7: lower wind speed (19.3 ms -1 ).

Loïc

  Michel is currently postdoctoral fellow at the Ecole Centrale de Nantes, France, working on advanced homogeneous control and differentiation techniques. He received his Ph.D. in electrical engineering in 2012 from the University of Quebec, Canada. His research interests include advanced techniques for robust and intelligent control with applications in biology, mechatronic systems, aerodynamics and neural networks. Ingrid Neunaber is a postdoctoral fellow at the Norwegian University of Science and Technology, Norway, who previously worked for the CNRS at the LHEEA laboratory at Centrale Nantes, France, as a postdoctoral researcher. She received her Ph.D. in 2019 in experimental wind energy physics from the University of Oldenburg. Her research interests include turbulence, wind energy, wakes, and aerodynamics. Rishabh Mishra is a PhD candidate at the LHEEA laboratory of CNRS and École Centrale de Nantes working on turbulent inflow customisation. He received his MS in Hydrodynamics from Ecole Centrale de Nantes, B.Tech. in Naval Architecture and Ocean Engineering and B.Sc. in Ship Building and Repair from Indian Maritime University. His research interests include theoretical, experimental and numerical analysis of turbulent flow fields. Caroline Braud is a senior CNRS researcher. She received her Ph.D. in Fluid Dynamics in 2003 from Poitiers University, France. She then worked two years as an associate researcher at Syracuse University, USA, NY state. She joined the CNRS in 2005 and was assigned to the LMFL laboratory in Lille, France. She moved to the LHEEA laboratory from Ecole Centrale Nantes in 2015 to work on Wind Energy. Since 2021 she shares her time between the LHEEA laboratory and CSTB-Nantes in France, where she is in charge of the wind energy research development. Her research interests include turbulent shear flows, unsteady aerodynamics, wind tunnel experiments, flow control experiments (AFC: Active Flow Control), wind turbine field tests and wind turbine blade monitoring and control. Franck Plestan received the Ph.D. in Automatic Control from the Ecole Centrale de Nantes, France, in 1995. From September 1996 to August 2000, he was with Louis Pasteur University, Strasbourg, France. In September 2000, he joined the Ecole Centrale de Nantes, Nantes, France where he is currently Professor. His research interests include robust nonlinear control and estimation (higher order sliding mode, time delay), and applications (pneumatic actuator, robotics, wind turbine).

  Limited circulation. For review only IEEE TCST Submission no.: 22-0932.1 Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

  .

				Limited circulation. For review only
				IEEE TCST Submission no.: 22-0932.1
	sc. #	type of reference	type of perturbation
	Cte	sine	piece-wise	wind speed	chopper

Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

Note that "2D blade section" here refers to a two-dimensional shape that is extruded in the third dimension so that the blade section spans the whole length of the wind tunnel.

Preprint submitted to IEEE Transactions on Control Systems Technology. Received: November 30, 2022 11:18:28 Pacific Time

ACKNOWLEDGMENTS

The authors thank Dr. Pierre Molinaro for the design of the electronic control board in the experimental setup. This work is supported by Agence Nationale de la Recherche (ANR) with project CREATIF ANR-20-CE05-0039. and ASAPe Pays-dela-Loire regional project (grant no. 2018 ASAPe).

Jean-Pierre Barbot is Professor at ENSEA Cergy-Pontoise, France and he is actually in secondment at LS2N-CNRS Nantes. He was the former director of the Quartz Laboratory EA 7393 and former member of EPI Non-A at INRIA. After his graduation from the Ecole Normale Supérieure of Cachan (France), he received the Ph. D. degree in automatic control from the University of Paris XI (France) in 1989 and the HDR in 1997. These main research activities deal with sliding mode control and observation, system under sampling, hybrid system, delay system, synchronization of chaotic system, normal form and recently sparsity apply to FDI and Cyber-attack detection. These main application domains are electrical machine, power converter and renewable energy.

Pol Hamon received the M.S. degree in robotics and control from the Institut National des Sciences Appliqu ées, Rennes, France, in 2018. He is curently working toward the Ph.D degree in robotics and control engineering at the Ecole Centrale de Nantes, France. His resarch is focused on robotics hand and model-free control.


Thomas Duigou

Melchior Joan Hérisson

Du Lac

Mahnaz Kenza Bazi-Kabbaj

Sabeti Azad

Gizem Buldum

Olivier Telle

Yorgo El-Moubayed

Pablo Carbonell

Neil Swainston

Galaxy

Galaxy-SynBioCAD: tools and automated pipelines for Synthetic Biology Design and Metabolic Engineering

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Île-de-France -Jouy-en-Josas -Antony Domaine de Vilvert 78 352 Jouy-en-Josas Cedex contact : thomas.duigou@inrae.fr www.inrae.fr

Galaxy-SynBioCAD: tools and automated pipelines for Synthetic Biology Design and Metabolic Engineering


PhD Guillaume Y Millet

MSc Djahid Kennouche

MD Clément Foschia

PhD Callum G Brownstein

PhD Julien Gondin

PhD Thomas Lapole

PhD Diana Rimaud

MSc Nicolas Royer

MD Guillaume Thiery

MD Vincent Gauthier

MD Lydia Oujamaa

MD Marine Sorg

PhD Samuel Vergès

MD-PhD Stéphane Doutreleau

PhD Mathieu Marillier

MD Mélanie Prudent

MD Laurent Bitker

MD-PhD Léonard Féasson

MD Laurent Gergelé

MD Emeric Stauffer

MD Céline Guichon

MD-PhD Jérôme Morel

Cardiorespiratory Fitness and Neuromuscular Function of Mechanically Ventilated ICU COVID-19 Patients*

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Abstract

OBJECTIVES:

The aim of the present study was to investigate the level of cardiorespiratory fitness and neuromuscular function of intensive care unit (ICU) survivors after Covid-19 and to examine whether these outcomes are related to ICU stay/mechanical ventilation duration.

MEASUREMENTS AND MAIN RESULTS:

Patients visited the laboratory on two separate occasions. The first visit was dedicated to quality of life questionnaire, cardiopulmonary exercise testing while measurements of the knee extensors neuromuscular function were performed in the second visit. Maximal oxygen uptake (VȮ2max) was 18.3±4.5 mL•min -1 •kg -1 , representing 49±12% of predicted value, and was significantly correlated with ICU stay/mechanical ventilation (MV) duration (R=-0.337 to -0.446, P<0.01 to 0.001), as were maximal voluntary contraction and electrically evoked peak twitch. VȮ2max (either predicted or in mL•min -1 •kg -1 ) was also significantly correlated with key indices of pulmonary function such as predicted forced vital capacity or predicted forced expiratory volume in 1-s (R=0.430 to 0.465, P  0.001)] and neuromuscular function. Both cardiorespiratory fitness and neuromuscular function were correlated with self-reported physical functioning and general health status. CONCLUSIONS: VȮ2max was on average only slightly above the 18 mL•min -1 •kg -1 , i.e. the cutoff value known to induce difficulty in performing daily tasks. Overall, although low physical capacities at admission in ICU Covid-19 patients cannot be ruled out to explain the association between VȮ2max or neuromuscular function and ICU stay/MV duration, altered cardiorespiratory fitness and neuromuscular function observed in the present study may not be specific to Covid-19 disease but seem applicable to all ICU/MV patients of similar duration. KEYWORDS: Covid-19, cardiorespiratory fitness, muscle, respiration artificial, intensive care unit, quality of life.

Introduction

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2 virus), primarily affects the respiratory system, although other organ systems are also involved (for details about the pathophysiology, see [START_REF] Yuki | COVID-19 pathophysiology: A review[END_REF]). While the majority of people infected with Covid-19 will present no to mild-moderate symptoms, more severe disease is experienced by elderly populations and people with comorbidities. It has been estimated that around 30% of people infected with Covid-19 will require hospitalization and of those hospitalized, 20% will be admitted to an Intensive Care Unit (ICU) [START_REF] Rooney | Systematic Review of Changes and Recovery in Physical Function and Fitness After Severe Acute Respiratory Syndrome-Related Coronavirus Infection: Implications for COVID-19 Rehabilitation[END_REF].

The negative effects of Covid-19 on the respiratory system, combined with the known effects of prolonged immobilization and mechanical ventilation (MV) on cardiorespiratory function, are likely to have severe implications for cardiorespiratory fitness (CRF). Assessment of CRF is most commonly performed through the measurement of maximal oxygen uptake (VȮ2max), which measures the upper limit of O2 transport and utilization during exercise.

Lower levels of aerobic capacity are associated with reduced independence during activities of daily living [START_REF] Arnett | Aerobic reserve and physical functional performance in older adults[END_REF]. For instance, it has been observed that individuals with a VȮ2max lower than 18 ml•min -1 •kg -1 report significant difficulty in performing daily tasks [START_REF] Morey | Is there a threshold between peak oxygen uptake and self-reported physical functioning in older adults?[END_REF]. Clinical cardiopulmonary exercise testing is the established clinical tool for assessing CRF in response to incremental exercise [START_REF] Faghy | Cardiopulmonary exercise testing in the COVID-19 endemic phase[END_REF].

Physical function and fitness have been reported to be impaired following SARS-CoV infection [START_REF] Manocha | Severe acute respiratory distress syndrome (SARS): a critical care perspective[END_REF]. These functional limitations are important because people with SARS-CoV may experience residual impairments in physical function up to 1-2 years after the infection (2).

Similarly, when considering patients with acute respiratory distress syndrome, 69% experienced declines in physical status (Medical Research Council score and/or 6-min walk test) from their post-discharge state over a 5-year follow-up period [START_REF] Pfoh | Physical declines occurring after hospital discharge in ARDS survivors: a 5-year longitudinal study[END_REF]. In Covid-19 hospitalized patients tested 6 months post-infection, those who were more severely ill during their hospital stay had more severely impaired pulmonary diffusion capacities [START_REF] Huang | 6-month consequences of COVID-19 in patients discharged from hospital: a cohort study[END_REF]. However, in this study, only 4% of patients were admitted to ICU, and any potential effects of impaired pulmonary function on CRF was not assessed. Thus, objective physical function measures in Covid-19 patients admitted to ICU have yet to be thoroughly investigated.

In addition to CRF, lower muscle strength during early adulthood was associated with a higher risk of hospitalization, admission in ICU and mortality [START_REF] Geijerstam | Fitness, strength and severity of COVID-19: a prospective register study of 1 559 187 Swedish conscripts[END_REF]. These data, combined with the fact that ICU stay induces muscle deconditioning, particularly in ventilated patients [START_REF] Puthucheary | Acute skeletal muscle wasting in critical illness[END_REF] make the investigation of neuromuscular function in Covid-19 ICU survivors extremely relevant. Neuromuscular function encompasses both the central and the peripheral components. The central component (neural command) assesses the existence of a potential neural deficit, i.e. whether motor units are fully recruited. The peripheral component focuses on the muscle, independently of the neural drive. Maximal strength is the combination of the two components. To the best of our knowledge, such data do not exist in Covid-19 patients.

The aim of this study was thus to thoroughly evaluate the level of CRF and lower limbs neuromuscular function in ICU survivors after Covid-19 and to better understand the etiology of both CRF (e.g. pulmonary/muscle causes) and neuromuscular function limitations.

Methods

Patients and eligibility

The study cohort comprised 60 patients ( 1.

Patients, for whom sequential organ failure assessment (SOFA) and simplified acute physiology score (SAPS 2) were assessed, visited the laboratory on two separate occasions to complete the protocol. Pre-ICU status was determined using Clinical Frailty Score, Charlson Comorbidity Index, and BMI at admission. The first visit was dedicated to questionnaires, cardiopulmonary exercise testing and familiarization to electrical stimulation and force measurements used in visit #2. The second visit, performed 6.7±2.5 days after visit #1, was dedicated to the neuromuscular function measurements. Out of the 60 patients, 10 were not allowed to participate to visit #2 or had adverse effects during the cardiopulmonary exercise testing performed in visit #1. The reasons are detailed in Supplemental Material. To avoid attrition bias, all subjects participating in the study were included in the statistical analysis. To minimize assessment bias, the same experimenter administered all the neuromuscular tests.

The assessments were made blinded to the knowledge of ICU stay duration. To avoid selection bias, the study was proposed to all consecutive volunteers who met the inclusion criteria.

Health-related quality of life (visit #1)

Health-related quality of life was assessed using the French version of the SF-36 questionnaire [START_REF] Mchorney | The MOS 36-item Short-Form Health Survey (SF-36): III. Tests of data quality, scaling assumptions, and reliability across diverse patient groups[END_REF]. A score between 0 and 100 is assigned to various domains, and aggregate into physical and mental components. The questionnaire includes assessments of bodily pain, general health, vitality, limitations in physical function, limitations in usual role activities due to physical problems, limitations in usual role activities due to emotional problems, limitations in social activities, and mental health.

Cardiopulmonary exercise testing (visit #1)

Spirometric tests were completed in all patients to determine forced vital capacity, forced expiratory volume in one second, and maximum voluntary ventilation.

A maximal incremental cardiopulmonary exercise test using a cycle ergometer was conducted using a standard ramp-incremental protocol. Patients were seated on a standard bicycle ergometer with 12-lead electrocardiogram and gas exchange monitoring. Details of protocol and equipment are presented in Supplementary Material. Peripheral oxygen saturations (SpO2) and non-invasive blood pressure were monitored throughout the test. Desaturation during exercise was considered as significant when the difference in SpO2 from baseline was ≥ 4% [START_REF] Benington | Exercise testing in survivors of intensive care-is there a role for cardiopulmonary exercise testing[END_REF].

The highest rolling 30-s average for VȮ2, minute ventilation (VĖ) and respiratory exchange ratio were calculated. VȮ2max was expressed as absolute values (L•min -1 ), and relative to body mass (mL•min -1 •kg -1 ). To describe the cardiorespiratory fitness of our sample, we also compared each participant's VȮ2max with reference values based on age and sex (i.e.

VȮ2max percent predicted values) [START_REF] Kaminsky | Reference Standards for Cardiorespiratory Fitness Measured With Cardiopulmonary Exercise Testing: Data From the Fitness Registry and the Importance of Exercise National Database[END_REF]. Ventilatory limitation to exercise was defined as previously suggested [START_REF] Benington | Exercise testing in survivors of intensive care-is there a role for cardiopulmonary exercise testing[END_REF].

Quadriceps neuromuscular function (visit #2)

Patients sat on an isometric dynamometer (ARS dynamometry; SP2, Ltd., Ljubljana, Slovenia).

Details about the position and the equipment can be found elsewhere [START_REF] Brownstein | Reductions in motoneuron excitability during sustained isometric contractions are dependent on stimulus and contraction intensity[END_REF]. After a standardized warm-up, patients performed the neuromuscular assessment. They first performed one maximal voluntary contraction with no stimulation. Subsequently, patients performed two maximal voluntary contractions (separated by 60 s) with single peripheral nerve stimulation delivered during the maximal voluntary contraction plateau followed by a single stimulation within 2 s of relaxation, for the calculation of maximal voluntary activation as an index of maximal central drive, as follows:

Voluntary Activation = [ 1-superimposed Twitch Peak Twitch ] × 100
where peak twitch, also used as an index of muscle function, is the amplitude of the potentiated twitch. Maximal voluntary contraction torque was defined as the highest value.

Peak twitch is expressed absolute values (in Nm) or relative to body mass (Nm•kg -1 ).

Comparison with other cohorts

To compare maximal voluntary contraction of our patients with healthy subjects, we used data from previous studies performed in our laboratory (n=77; age 51.8±12.1 yr; body mass 77.1±16.2 kg) and collected on the same isometric dynamometer. We also compared our patients with a small cohort (n=33, age 50.3±12.8 yr; body mass 75.6±7.6 kg) of non-ICU Covid-19 patients.

Statistical analysis

To assess the effects of ICU stay, MV duration and disease severity on CRF and neuromuscular function, Pearson's product moment correlations were performed against the objective variables of the study. Pearson's correlations were also used to test the relationships between indices of health-related quality of life and the objective variables and between VȮ2max and pulmonary and NM functions. An unpaired t-test was used to test the characteristics of patients with and without adverse events during the cardiopulmonary exercise testing. No imputation of missing values was performed. The alpha level was set at 0.05. To compare our cohort with both healthy subjects (for maximal voluntary contraction) and Covid-19 patients who have not stayed in ICU (for CRF), a multiple linear regression to understand the effect of ICU stay, sex, age and body mass on different outcomes was used.

All the possible interactions up to the 4 th order were tested, using likelihood ratio test and a backward heuristic approach.

Results

Before admission, 42% of our patients were considered as obese (BMI>30 kg/m 2 ). On average, patients had a Clinical Frailty Score of 2±1 and a Charlson Comorbidity Index of 2.9±1.5. There was no correlation between the pre-comorbid status (i.e. Charlson Comorbidity Index, Clinical Frailty Score or Pre-BMI) and the ICU stay duration, MV duration, SOFA or SAPS2 scores.

Median and range of ICU stay duration was 29 days and [6-80 days], respectively.

The main parameters for lung function and at peak exercise during incremental cardiopulmonary exercise testing are presented in Tables 2 and3 There were significant correlations between VȮ2max and indices of muscle strength, either expressed both in absolute values (i.e. in L•min -1 and Nm: R=0.696, P<0.001) or in relative values (i.e. mL•min -1 •kg -1 body mass and Nm•kg -1 body mass: R=0.675, P<0.001, Figure 2B). Relative VȮ2max was also correlated to relative peak twitch (R=0.693, P<0.001, Figure 2C). Forced vital capacity, forced expiratory volume in 1-s and maximum voluntary ventilation were 83.7±18.6%, 89.4±19.6% and 96.7±20.2% of predicted values. There were significant correlations between VȮ2max either in percent predicted values or in mL•min -1 •kg - 1 body mass and indices of lung function, i.e. predicted forced vital capacity (R=0.491, P<0.001 and R=0.430, P=0.001), predicted forced expiratory volume in 1-s (R=0.520, P<0.001 and R=0.465, P<0.001) and maximum voluntary ventilation (R=0.440, P<0.001 and R=0.249, P=0.072).

Significant desaturation during exercise from baseline levels was observed in 41.7% of the patients (mean desaturation 5%). Minimum SpO2 during the cardiopulmonary exercise testing was significantly correlated with predicted forced vital capacity, and forced expiratory volume in 1-s (R=0.614, R=0.579, R=0.561, respectively; all P<0.001). Based on the criteria defined by Benington et al. [START_REF] Benington | Exercise testing in survivors of intensive care-is there a role for cardiopulmonary exercise testing[END_REF], 29% of the patients were classified as having pulmonary limitations to exercise. Removing these patients did not change VȮ2max (18.2±4.4 mL•min - 1 •kg -1 ). At VȮ2max, respiratory exchange ratio was 1.14±0.11. Three minutes after task failure, finger blood capillary lactatemia was found to be 7.0±2.0 mmol/L. Finally, indices of health-related quality of life (see Table 3) were correlated with objective CRF and neuromuscular function outcomes. In particular, VȮ2max (relative to body mass) was correlated with PF, RP, and GH (R≤0.385-408 and P<0.004). Similarly, maximal voluntary contraction and peak twitch (relative to body mass) were correlated with RP and GH (R≤0.325-388 and P<0.028).

Discussion

The present study aimed to investigate the cardiorespiratory and neuromuscular characteristics of ICU survivors after Covid-19 and to examine whether these outcomes were related to ICU stay/ventilation duration. The main results are that mean VȮ2max was (i) slightly above the 18 mL•min -1 •kg -1 cut-off value known to induce difficulty in performing daily tasks (e.g. climbing stairs will require an aerobic capacity close to this value, i.e. 5 METS), (ii) negatively correlated to ICU stay/MV duration, (iii) correlated with key indices of pulmonary and neuromuscular functions and (iv) associated with limitations in self-reported physical function. The present results also showed that muscle strength and quality of life was deteriorated when compared to a healthy control population.

VȮ2max: effects of Covid-19 vs ICU stay

In the present study, VȮ2max was directly assessed 4 to 8 weeks post-ICU and was found to be very low, i.e. 18.3 mL•min -1 •kg -1 or 49% of predicted values. Braga et al. ( 2022) assessed CRF a median of 25 days after discharge in hospitalized Covid-19 patients and reported a VȮ2peak of 18.7 mL•min -1 •kg -1 . This is similar to the present study, despite their patients being less severely ill, since not all (58%) were admitted in ICU and only 18% needed invasive MV, probably because their patients were tested following a shorter time lapse after discharge (25 days vs 52 days post-discharge in the present study). Our data are also similar to another study with a smaller cohort showing that Covid-19 ICU patients had 57% of predicted values [START_REF] Blokland | Exercise capacity after mechanical ventilation because of COVID-19: Cardiopulmonary exercise tests in clinical rehabilitation[END_REF] compared to 49% in the present study. In our own comparison with non-ICU Covid-19 patients, we found that, when normalizing to other relevant explanatory variables (i.e. age, sex, body mass), VȮ2max was significantly higher in non-ICU than in ICU Covid-19 patients. It has also been reported that non-Covid-19 ICU survivors tested 24±14 days after hospital discharge had VȮ2max of 13.8 mL•min -1 •kg -1 [START_REF] Benington | Exercise testing in survivors of intensive care-is there a role for cardiopulmonary exercise testing[END_REF]. Since ICU stay or MV duration were comparable in the two cohorts, the higher values in ICU Covid-19 patients of the present study could be due to the fact that our patients were tested following a longer time lapse after discharge. ICU Covid-19 patients may have had low VȮ2max before going to the hospital [START_REF] Brawner | Inverse Relationship of Maximal Exercise Capacity to Hospitalization Secondary to Coronavirus Disease 2019[END_REF]. However (i) the Clinical Frailty Score (2 ± 1) and Charlson Comorbidity Index (2.9 ± 1.5) show that the patients were not fragile and did not have major comorbidities at admission and (ii) the Charlson Comorbidity Index was not correlated to VȮ2max. Overall, this suggests that the deteriorated CRF is not specific to ICU Covid-19 patients (despite their ventilatory limitations, see below) but is applicable to all ICU/MV patients. Three quarter of the patients hospitalized due to Covid-19 (not only ICU patients) have been shown to have persistent pulmonary symptoms, in particular breathlessness [START_REF] Arnold | Patient outcomes after hospitalisation with COVID-19 and implications for follow-up: results from a prospective UK cohort[END_REF].

VȮ2max was significantly correlated with predicted forced vital capacity and forced expiratory volume in 1-s in the present study. Altogether the present results may suggest that the pulmonary limitations are significant during exercise in patients with severe forms of Covid-19. However, we speculate that this correlation was related to the effects of ICU stay/MV duration on both VȮ2max and spirometry parameters rather than to the effects of Covid-19 per se. Only one patient demonstrated significant desaturation during exercise from baseline levels (> 4%) in Benington et al. [START_REF] Benington | Exercise testing in survivors of intensive care-is there a role for cardiopulmonary exercise testing[END_REF] compared to 42% in the present study and 23% in Skjorten et al. [START_REF] Skjorten | Cardiopulmonary exercise capacity and limitations 3 months after COVID-19 hospitalisation[END_REF]. However, removing the patients with pulmonary limitations in the present study did not change VȮ2max so that they cannot fully explain the low CRF of our patients, as previously suggested in SARS patients [START_REF] Ong | Pulmonary function and exercise capacity in survivors of severe acute respiratory syndrome[END_REF].

Importantly, VȮ2max was also associated with self-reported limitations in physical function as well as limitations in usual activities due to physical problems in the present experiment (two items of the SF-36 questionnaire). This is in line with data showing that lower levels of aerobic capacity are associated with deteriorated functional independence during activities of daily living (2). Glimelius Petersson et al. [START_REF] Glimelius Petersson | Factors and health-related quality of life associated with participation in a post-ICU follow-up. A register study[END_REF] reported mental and physical components of the SF-36 collected two months after (non-Covid-19 patients) ICU discharge of 43±29 and 32±24, respectively, that is in line with our findings of 42±17 and 43±16. In contrast, when comparing our data with normative values for a similar age [START_REF] Jenkinson | Short form 36 (SF36) health survey questionnaire: normative data for adults of working age[END_REF], it is clear that our patients are below those of healthy subjects.

Neuromuscular function

Maximal voluntary contraction, i.e. the combination of both central drive (assessed by maximal voluntary activation) and muscle function (assessed by peak twitch), was significantly lower in Covid-19 ICU survivors compared to healthy subject. VȮ2max correlated with muscle (i.e. peripheral component) strength, including when both VȮ2max and peak twitch were normalized to body mass. One possibility is that muscle limitations may have contributed to impaired CRF. Alternatively, it could be argued that the physical function (including both maximal strength and CRF) was negatively impacted by ICU duration or that people with a higher VȮ2max were more active, and as a result had greater muscle strength.

Importantly, ICU acquired weakness has been reported as a major symptom in ICU patients [START_REF] Batt | Mechanism of ICU-acquired weakness: skeletal muscle loss in critical illness[END_REF][START_REF] Vanhorebeek | ICU-acquired weakness[END_REF]. For example, over one quarter of patients develops significant muscle wasting [START_REF] Puthucheary | Acute skeletal muscle wasting in critical illness[END_REF] and weakness [START_REF] De Jonghe | Paresis acquired in the intensive care unit: a prospective multicenter study[END_REF] during ICU stay, particularly in the lower limb muscle groups.

ICU acquired weakness was reported to be 27% at hospital discharge post-ICU due to Covid-19 [START_REF] Van Aerde | Intensive care unit acquired muscle weakness in COVID-19 patients[END_REF]. The present study did not allow to ascertain the existence of ICU acquired weakness since no Medical Research Council scores were performed and it has been shown that muscle strength was associated with the risk of Covid-19 hospitalization (9, 26) so that the patients may have been weak before admission. Yet, it is worth reporting that significant correlations were found in the present study between indices of muscle function and self-reported limitations in physical function as well as limitations in usual role activities due to physical problems. Maximal voluntary activation (87±8%) was found to be in normal range of values for healthy population (e.g. 87±9% in endurance-trained athletes, [START_REF] Besson | Sex Differences in Neuromuscular Fatigue and Changes in Cost of Running after Mountain Trail Races of Various Distances[END_REF]). Still, voluntary activation was correlated with self-reported limitations in usual role activities due to physical problems. Both VȮ2max and indices of neuromuscular function were thus correlated with the general health status and limitations in usual role activities due to physical problems in the present study. Altogether, the neuromuscular function data presented in the present study reinforce the need for tailored rehabilitation in this population, as recently suggested [START_REF] Van Aerde | Intensive care unit acquired muscle weakness in COVID-19 patients[END_REF][START_REF] Belli | Low physical functioning and impaired performance of activities of daily life in COVID-19 patients who survived hospitalisation[END_REF][START_REF] Chikhanie | Effectiveness of pulmonary rehabilitation in COVID-19 respiratory failure patients post-ICU[END_REF].

Effects of ICU stay and MV duration

In the present study, significant correlations were found between the length of the ICU stay and VȮ2max. There are two possible explanations for this finding. Firstly, a negative relationship between VȮ2max and hospitalization following Covid-19 infection has previously been demonstrated [START_REF] Brawner | Inverse Relationship of Maximal Exercise Capacity to Hospitalization Secondary to Coronavirus Disease 2019[END_REF]. Accordingly, it is possible that patients with a lower VȮ2max prior to Covid-19 infection had a greater risk of more severe symptoms, and thus a longer ICU stay.

Conversely, given that inactivity is associated with reductions in VȮ2max in a dose-response manner [START_REF] Huang | Dose-response relationship of cardiorespiratory fitness adaptation to controlled endurance training in sedentary older adults[END_REF], the more prolonged ICU stay would be expected to induce more severe deconditioning and reductions in VȮ2max. This could be partly due to longer usage of sedative medications and neuromuscular blockades. Regardless of the cause, these results highlight the necessity of also providing structured aerobic training interventions in ICU Covid-19 patients. Based on the association between VȮ2max and ICU stay, we suggest that this is particularly important for people who have stayed more than 32 days in ICU. Those data agree with a recent paper arguing that cardiopulmonary exercise testing shows great promise in the guidance of rehabilitation in functionally limited ICU survivors [START_REF] Whittle | Objective assessment of metabolism and guidance of ICU rehabilitation with cardiopulmonary exercise testing[END_REF].

The same reasoning as above applies to neuromuscular function. Indeed, as mentioned above, muscle strength has been found to be associated with the risk of Covid-19 hospitalization [START_REF] Cheval | Muscle strength is associated with COVID-19 hospitalization in adults 50 years of age or older[END_REF] and immobility induces muscle deconditioning [START_REF] Vanhorebeek | ICU-acquired weakness[END_REF]. Significant correlations were found in the present study between maximal strength/peak twitch and ICU stay/MV duration. This is in line with a previous study showing that patients with ICU acquired weakness post-Covid-19 had longer ICU stays than their non-ICU acquired weakness counterparts (30 vs 19 days) [START_REF] Van Aerde | Intensive care unit acquired muscle weakness in COVID-19 patients[END_REF]. It has also been suggested that the rate of limb muscle weakness found in Covid-19 ICU patients was higher than in non-Covid-19 ICU patients, potentially due to the longer MV duration [START_REF] Medrinal | Muscle weakness, functional capacities and recovery for COVID-19 ICU survivors[END_REF]. We also found a strong correlation between VȮ2max and maximal voluntary contraction (both absolute et relative to body mass) and peak twitch (an index of muscle function), both variables being correlated with ICU stay and MV durations as discussed above. This suggests that resistance training may also be beneficial to VȮ2max in these patients.

Limitations

We cannot exclude the possibility that the ICU Covid-19 survivors who made themselves available for testing were not representative of all the survivors [START_REF] Benington | Exercise testing in survivors of intensive care-is there a role for cardiopulmonary exercise testing[END_REF] or, on the contrary, that some fragile patients (e.g. with neuromyopathy) were not able to be recruited for the present study, so some degree of bias could have thus been present. It is also unclear whether the findings from the present study are generalizable to all Covid-19 patients from different demographic and cultural backgrounds, or for all variants. Cardiopulmonary exercise testing was performed with testing filters that have an inherent resistance to flow which in most circumstances are unlikely to limit ventilation and impact exercise performance [START_REF] Faghy | Cardiopulmonary exercise testing in the COVID-19 endemic phase[END_REF]. Despite that these filters are not recommended when performing cardiopulmonary exercise testing, they were used for safety reasons [START_REF] Venturelli | Safety procedures for exercise testing in the scenario of COVID-19: a position statement of the Societa Italiana Scienze Motorie e Sportive[END_REF].

Conclusion

Cardiorespiratory fitness of Covid-19 patients after 32 days in ICU was extremely low as shown by the mean VȮ2max being less than 50% of predicted values and just above the cut-off value known to induce difficulty in performing daily tasks. This low VȮ2max was associated with selfreported limitations in physical function and general health status. Other important findings of the present study are that key indices of pulmonary and neuromuscular functions were associated with VȮ2max and that were both correlated with ICU stay and mechanical ventilation duration. These data emphasize the need for tailored (aerobic or resistance or combined training) rehabilitation programs for severe Covid-19 patients, particularly those who have stays at ICU over a month. However, these findings may not be specific for Covid-19 patients but be applicable to all ICU/mechanically ventilated patients for a similar duration.

Figures Legends

DESIGN:

  Prospective non-randomized study. SETTING: Patients hospitalized in ICU for Covid-19 infection. PATIENTS: 60 patients hospitalized in ICU (mean duration: 31.9±18.2 days) were recruited 4 to 8 weeks post-discharge from ICU. INTERVENTIONS: None.

  , respectively. Most ventilatory and CRF outcomes were below the normative values. Fixing the values of all the other relevant explanatory variables (i.e. age, sex, body mass), forced vital capacity, forced expiratory volume in 1-s, and VȮ2max were significantly lower in ICU than non-ICU Covid-19 patients (P <0.001 to 0.019). No difference was found between the two groups for maximal voluntary ventilation. The Charlson Comorbidity Index was negatively correlated with maximal voluntary contraction relative to body mass (R=-0.322, P=0.024) but there were no correlations between the Charlson Comorbidity Index and relative (R=-0.117, P=0.392) or absolute (R=-0.135, P=0.322) VȮ2max. The percentage of patients put in prone positioning, receiving extracorporeal membrane oxygenation, neuromuscular blocking drugs and corticosteroids were 84%, 7%, 89% and 40%, respectively. There was a significant correlation (R=-0.303; P=0.031) between Wmax and the SOFA score but not with SAPS2. No other correlations were found between SOFA and any of the CRF or neuromuscular function variables measured in the present study. ICU stay duration was significantly correlated with VȮ2max expressed in mL•min -1 •kg -1 body mass (R=-0.446, P<0.001, Figure 2A) as well as with maximal voluntary contraction in both absolute (R=-0.504, P<0.001) and relative to body mass (R=-0.449, P=0.001) values and absolute peak twitch (R=-0.334, P=0.033). Similarly, MV duration was significantly correlated with VȮ2max expressed in percent predicted values (R=-0.320, P=0.016). MV duration was also correlated with several indices of strength such as maximal voluntary contraction in absolute values (R=-0.429, P=0.002). Maximal voluntary contraction was significantly lower in Covid-19 ICU survivors compared to healthy subjects (P<0.001) [fixing the values of all the others relevant explanatory variables (i.e. ICU stay, age, sex and body mass)].

Fig. 1 .

 1 Fig. 1. Flowchart of the study.

Fig. 2 .

 2 Fig. 2. Relationship between ICU stay duration and VȮ2max (panel A, n=56), between VȮ2max

Acknowledgements

The authors would like to than Florianne Rambaud, Kévin Guillemin and Bernard Januel for their help in collecting the data.

This study was funded by a fellowship grant and a Covid funding from IDEX Lyon.

Conflict of interest:

The authors have no conflicts of interest to declare.

Corresponding Author:

Prof. Guillaume Y. Millet, LIBM, Campus Santé Innovations, 10 rue de la Marandière, 42270 Saint-Priest en Jarez, France Email: guillaume.millet@univ-st-etienne.fr VȮ2max: maximal oxygen uptake, Pred: predicted, Wmax: maximal aerobic power, VĖmax: maximal ventilation, SpO2: arterial saturation in oxygen, RER: respiratory exchange ratio, exh: exhaustion, MVC: maximal voluntary contraction, PTw: peak twitch, VA: maximal voluntary activation.

Table 3 R1 Clean

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