Jean-Charles Antonioli

Armin Taghizad

Thomas Rakotomamonjy

Mustapha Ouladsine

TOWARD THE DEVELOPMENT OF A METHODOLOGY FOR DESIGNING HELICOPTER FLIGHT CONTROL LAWS BY INTEGRATING HANDLING QUALITIES REQUIREMENTS

Piloting a helicopter is a demanding task for human operators: autopilots have been introduced by manufacturers to assist pilots in their piloting task. Designing the gains of the associated control lawstaking into account Handling Qualities requirements from standards such as the ADS-33 -is a difficult industrial problem. NASA has already led many studies on this area. These works have led to the development of CONDUIT© (Control Designer's Unified Interface), a computer aided design tool for rotary and fixed wing aircrafts control laws using interactive optimization techniques. The tool has demonstrated its benefits in terms of time of development reduction. ONERA has been working for several years to the establishment of another process. One of the first ideas was to lead local sensitivity studies, and use the results as design guidance. Then these results have been confronted with some analytical developments led on simplified models. This paper shows how these analytical studies can be used to initialize the gain tuning process efficiently, taking into account the structure of the system and the requirements from handling qualities standards (ADS-33). A tool has been developed: it generates charts of Flying Qualities. Thanks to the charts generated for each case of study, the gains of the control laws can be efficiently initialized for the simplified models, with Flying Qualities objectives. The expected results are compared with those obtained with the full linear model. Sensitivities can then be used to help in designing more precisely the gains. Finally, full nonlinear simulations are led in order to compare the results with the expected Flying Qualities. As a conclusion, all these studies seem to lead to a full and efficient process of gain tuning taking into account the constraints from the control law structures and the requirements from the handling qualities standard. Furthermore, the procedure can be applied from the very first stage of tuning: the initialization of the gains.

1.

INTRODUCTION

Piloting assistances

Helicopters are naturally unstable systems. Pilots must make considerable efforts to stabilize the aircraft. Piloting assistance systems are now available on board (Autopilots (AP), Automatic Flight Control Systems (AFCS), Fly By Wire / Fly By Light control systems (FBW/FBL)). They are designed to improve the system pilotability and safety. In this goal, the development of the associated flight control laws must be addressed carefully. More precisely, tuning the gains of the control laws is crucial and remains expensive in terms of time of development.

Handling Qualities (HQ) and Flying Qualities (FQ)

The pilotability can be evaluated using criteria of Handling Qualities (HQ) [1]: "those qualities or characteristics of an aircraft that govern the ease and precision with which a pilot is able to perform the tasks required in support of an aircraft role". Thanks to years of studies of numerical simulations and analyzes of flight tests around the world, the HQ can now be evaluated using qualitative and associated quantitative criteria. Today, these criteria are defined, explained and plotted in the Aeronautical Design Standard (ADS) [2]. A helicopter showing good results with respect to these criteria is said to have good Flying Qualities (FQ): this means the helicopter shows good performances -not only statically -but dynamically as well.

Designers usually tune the gains of the control laws in order to handle at best the requirements from this standard.

Techniques for tuning the gains of the control laws with FQ objectives

No classical synthesis method (such as LQ, LQG, LQG/LTR, H ∞ , LMI, µ synthesis, etc. [3]) seems to solve this problem. Indeed, these techniques do not manage the specificity of the control laws and the specificity of the requirements. NASA has already led many studies for years to establish methods of tuning taking into account criteria from standards which have led to the development of CONDUIT© [4]: a computer aided design tool for rotary and fixed wing aircrafts control laws using interactive optimization techniques.

It is well known that the usual tuning process used by manufacturers (Fig. 1) can be time consuming. Fig. 2 Direct method of tuning focused by ONERA

MATERIALS AND PROBLEM STATEMENT

Notations

On Fig. 3 the main control inputs used by helicopter pilots are presented. The Fig. 4 shows the main dynamical variables used to represent the flight dynamics of a helicopter. Tab. 1 lists the parameters used for the establishment of the state space representation of the natural system.

Basis of piloting a helicopter

The collective stick is connected to the swash-plate and permits the control of the rotor lift force magnitude by modifying the average component of the blades pitch angle. The cyclic stick allows changing the 1-per-rev harmonics of the blades pitch angle, and thus controlling the roll and pitch moments of the rotor. This results in the orientation of the rotor around its roll axis when acting on the lateral cyclic input, and on the pitch axis when acting on the longitudinal cyclic input. The pedals allow the control of the anti-torque (or tail) rotor, and the motion of the helicopter around its yaw axis. The establishment of this kind of representation is well known [7] [8]. Let U, X, and Y respectively be the input, state and output vectors of the state space representation of a helicopter. Then, the inputs and the states of the helicopter are: (3)

(1) [ ] [ ]      = = t t ped lon lat col r q p w v u X U ψ θ φ δ δ δ δ , , , , , , , , , , , Moreover
   = + = X Y U B X A X . . &
This 9-by-9 linear model has been used for the development of a process aiming to integrate HQ requirements from the early phase of gains design. The control law studied during this work was an Attitude Command Attitude Hold (ACAH) control strategy

Attitude Command Attitude Hold (ACAH) control law

The Attitude Command Attitude Hold (ACAH), as shown on Fig. 5 for the roll axis as an example permits to control the attitudes of the helicopter (ɸ for the roll axis), governed by the pilot cyclic stick.

Fig. 5 ACAH -roll axis only

Then, we can write the feedback equation for this axis (4).

(4)

∫ - + - + = ) ( . ) .( . c i c p lat K K p K φ φ φ φ δ φ φ
The aim of this paper is to set up a method to help designers in tuning the gains of the ACAH control law, taking into account HQ requirements as described in the ADS-33 standards. Only some of these criteria have been selected for this study and are presented in the next subsection.

2.5

Selected criteria from ADS-33 (all others MTE -hover and low speed)

The standard specifies HQ criteria for a wide range of helicopters. All criteria depend on the case study, and they are detailed in a specific classification. For this paper, we will focus on a specific case study, explained hereafter.

The case study

The helicopters are indexed into 4 rotorcraft categories: attack, scout, utility and cargo. This paper will focus on the study of a 10-ton class helicopter: cargo-type. A table in the standard specifies which Mission Task Elements (MTE) the studied helicopter should be capable of, and the required agility needed for each one. For this paper, we will focus on the "all others MTE" requirements only. We will focus on the "hover and low speed" case.

A rating of Usable Cue Environment (UCE: 1, 2 or 3) is provided. We will study the case of UCE 2, which means that the pilot "can make limited corrections with confidence and precision is only fair" [2] on attitude and / or translational piloting. This can be evaluated using a Visual Cue rating scale (provided in the standard as well). Depending on the case study, a table specifies the required response type. Here, the ACAH is needed to be able to achieve Level 1 response type rating. The bloc diagram previously presented corresponds to this response-type requirement.

The next sections will explain the requirements for this case study. The roll axis will be focused. The three selected criteria are eigenvalues placement (Section 2.5.2), attitude quickness placement (Section 2.5.3) and bandwidth / phase delay placement (Section 2.5.4). They respectively evaluate the helicopter's stability, agility and ability to follow high frequency inputs with accuracy. They constitute the basic quantitative criteria to evaluate the expected overall Handling Qualities (HQ) of a helicopter. The standard explains how to calculate and plot the requirements for each criterion. The aim is to place the resulting point(s) calculated for each criterion in the "LEVEL 1" area on its associated plot. "LEVEL 2" area is an indicator of "medium" quality. "LEVEL 3" area should be avoided. "The rotorcraft shall meet the Level 1 standards for all criteria. Violation of any one requirement is expected to degrade Handling Qualities" [2]. The bold black lines on Fig. 6, 8 & 10 represents a limit between two areas. The green points on each of these plots are examples of good tunings, for its associated criterion.

Limits on oscillations: stability criterion

This criterion is evaluated by calculating the eigenvalues of the dynamic matrix of the linearized closed loop system. The requirements for their positioning, as shown on Fig. 6, determine the quality of the helicopter stability. The Level1/Level2 limit can be sufficiently approximated by ζ=0.35 (red dotted line on Fig. 6).

ɸ p K p K ɸ K iɸ ∫ ɸ c
δ lat Helicopter This criterion is evaluated using frequency sweeps capture flight tests. In this paper, Bode diagrams are generated using either equivalent linear models of the closed loop system, if available, or using directly frequency sweep simulations. For the study of the ACAH, this criterion is performed using 3 parameters, as detailed on Fig. 9: the bandwidth ω 180 defined by a cut-off of the phase at -180°, the bandwidth phase ω BWphase using a +45° phase margin from ω 180 cutoff, and the variation of phase ∆ɸ 2ω180 from -180° at the frequency 2*ω 180 . Then, these 3 parameters are used to calculate the phase delay parameter (τ p ), as defined on The Level 1 / Level 2 limit can be approximated by a vertical line at ω BWphase =2rad/sec (red dotted line on Fig. 10). Indeed, the values of phase delay (τ p ) seem to be mainly influenced by the natural system delays. The gains of the control laws seem to have negligible influence on its value [10], for stabilized systems at least.

2.6

Description of the procedure developed at ONERA

The first idea followed in order to establish a "direct method of tuning" was to use the sensitivities of gains to the criteria as design guidance for full linearized systems. A tool (CAST-HEL-AP:

Computer Aided Setting and Tuning tool for Helicopters' Autopilots) was developed at ONERA Salon de Provence for this purpose [10]. The advantage of this procedure is: the designer is not influenced by an optimization tool that could trap his design in a local optimum.

However, due to the non-linearity of the relationship between the gains and the HQ criteria, the sensitivity method can't be efficiently applied if the initial set of gains doesn't already insure the stability of the helicopter with a significant improvement of the overall FQ This means that to be fully efficient with the sensitivity analysis toolbox (CAST-HEL-AP), there is a need to set up a process of gains initialization providing already fair handling qualities. This paper focuses on the establishment of the methodology to initialize the gains of a control law with FQ objectives.

The final full procedure focused by ONERA is summarized on Fig. 11.

The section 3 will focus on the explanation of the new linear initialization process (yellow part on the Fig. 11).

The section 4 will give an example of a complete design and evaluation, using the full procedure.

PROCESS FOR INITIALIZING GAINS OF CONTROL LAWS WITH FQ OBJECTIVES

As shown on Fig. 11, the idea is to create a process that will permit to initialize the gains of the control law, directly from a set of FQ criteria, specified at the beginning of the design studies. If the requirements chosen to be achieved are too restrictive, there is a risk of saturation from actuators. Then, the aim is to achieve sufficient levels of quality for the whole set of requirements, not to improve them more than needed.

The helicopter is complex (hard coupled system), the constraints from the control laws are hard (nonfull state feedback) and the requirements from the standard are very specific (non-common). Therefore, it was decided to establish simplified models of the open loop and the closed loop system. As it is explained thereafter, these models can be used to help in establishing the initialization process.

The methodology is exposed through the example of the tuning of the ACAH control law for the roll axis.

The criteria chosen as design objectives are those exposed in section 2.5 for the study of a 10T class helicopter, cargo-type, with UCE2-type and all other MTE-type requirements. As for an initialization process -with sufficient FQ requirements -the linear models will ignore actuator models and their saturations.

Fig. 11

Full procedure of tuning focused by ONERA

HQ targets

Analyzes and charts

Gains initialized

Implementation of gains on full linear model with CAST-HEL-AP

Expected HQ

Evaluation of the linear initialization process

Adjustments of gains on full linear model with CAST-HEL-AP using linear sensitivities results

Implementation of gains on full nonlinear model

Gains and expected HQ improved

Obtained HQ

Adjustments of gains on full nonlinear model using local linear sensitivities

Evaluation of the linear sensitivities process

Final gains and HQ

Evaluation of the full procedure Evaluation of the initialization of the final system

Analytical studies led to help establishing relationship between gains and FQ criteria

Each axis-control law is created for specific purposes, say for specific control of the axis. The main aim of a control law for one axis is not to control the other axes, which are stabilized thanks to their own axis-control laws (or by the pilot at least). Then, the work made for one axis can be re-used for the other axes. Thanks to these conditions, and due to the complexity of the system, we will consider the establishment of a simplified one-axis open loop (and closed loop) system.

Simplified one-axis open-loop model

The axis chosen to be studied here is the roll axis. The associated states are (p,ɸ). The main input used to pilot this axis is δ lat . Then, from (1), let X 1 , X 2 , U 1 and U 2 be:

(6) [ ] [ ] [ ] [ ] t t t ped lon col t lat r q w v u X p X U U ψ θ φ δ δ δ δ , , , , , , , , , 2 1 2
1 = = = =
Then (3) can be written on another way using permuted matrices of A and B, such that:

                +                 =         2 1 22 21 12 11 2 1 22 21 12 11 2 1 . . U U B B B B X X A A A A X X & & (7) 2 12 1 11 2 12 1 11 1 . . . . U B U B X A X A X + + + = & (8) 2 22 1 21 2 22 1 21 2 . . . . U B U B X A X A X + + + = &
Then, some hypotheses can be used for the establishment of our simplified models.

-Hypothesis 1: X 2 = 0. During a roll change, the pilot or the other control laws take care of the stabilization of the other axes (vertical, pitch, yaw). We consider the associated states will only slightly vary from equilibrium, say zero.

-Hypothesis 2: U 2 = 0.

To pilot the roll axis, the mainly used input is the roll associated input.

For an initialization of gains procedure, even if slight variations of the other inputs are needed to compensate couplings, we consider that the other inputs do not vary from initial equilibrium, say zero.

Applying these two hypotheses on (7) imply:

(9)

1 11 1 11 1 . . U B X A X + = & -Hypothesis 3: φ & = p.
The derivative of the roll angle is approximated to the roll rate (true while in pure lateral flight, and this fits with the conditions of the associated evaluations of ADS33 requirements).

Applying this new hypothesis, using the definitions from (6) and using sensitivities L p =∂(ṗ)/∂(p), L ɸ =∂(ṗ)/∂(ɸ), L δlat =∂(ṗ)/∂(δlat), (9) becomes: Applying this hypothesis on (10) implies:

(11)

lat lat p L p L p δ δ . . + = &

Simplified one-axis closed-loop model

Including the equation of the control law (4) into (11), we obtain:

( )

∫ - + - + + = ) ( ) .( . . c i c p lat p K K p K L p L p φ φ φ φ φ φ δ

&

Using hypothesis 3 again, and applying Laplace transformations (s is the Laplace variable here), this last equation can be written:

(12) ( ) s L L s L s c l c l p φ φ φ φ φ φ δ δ - + - + = . . . . . 2 1 2 (13) with:      = = + = φ δ δ φ δ δ δ i lat l lat l p lat p p K L L K L L K L L L . . . ˆ2 1
Then, the input/output transfer function is:

(14) ( ) 2 1 2 3 2 1 . . ˆ. l l l l c L s L s L s L s L δ δ δ δ φ φ - - - + - =
We obtain an order three model. By analogy to the usual natural modes of the rotorcraft, we choose to impose one real mode and two complex modes to the behaviour of the closed loop model. Then, (14) can be written with an equivalent transfer function:

(15) 2 2 2 1 2 . . . 2 . 1 . 1 n n n c s s s s ω ω ζ ω τ τ φ φ + + ⋅ + + = with: (16) n ω ζ τ τ . 2 1 2 + = and ω n > 0, τ 1 > 0, τ 2 > 0, ζ > 0
A relation between the parameters of the equivalent transfer function and the associated gains of the one-axis piloting assistance can be established (17).

(17)                  + + - = + - = - = lat n lat p p lat n n lat n i L L L K L K L K δ δ δ φ δ φ τ τ ω ζ τ ω τ ω ζ τ ω . . . . 2 1 . . . . 2 . 1 1 1 2 1 1 2
Thanks to these developments, (17) is specifically very interesting. Indeed, if values of ω n , τ 1 and ζ can be chosen, the gains of the simplified model can be directly initialized with (17), using the sensitivity parameters L p and L δlat from the model. Then, the idea is to choose the values of the parameters of the equivalent transfer function in order to satisfy sufficient FQ requirements. A tool can help in that purpose.

Development of a tool generating charts of FQ for simplified models of helicopters

This tool has the aim to help the designer in choosing values of the parameters of the simplified models such that the associated set of expected FQ are sufficiently good.

(18)      < < < < < < 1 1 . 0 3 1 . 0 3 1 . 0 1 ζ τ ω n
Then, all criteria can be calculated for the whole set of models using fast linear simulations.

Here is an example of an algorithm for generating charts of FQ: -Choose a value for ζ and a value for the amplitude of the attitude change ɸ c (necessary for attitude quickness calculations). -For ω n from 0.1 to 3 and for τ 1 from 0.1 to 3 do:

-Create the simplified transfer function (15) (using (16)). -Calculate the attitude quickness parameters using a linear attitude change simulation. -Calculate the bandwidth / phase delay parameters using a phase Bode diagram. -Calculate isopleths of attitude quickness and bandwidth / phase delay parameters. -Calculate isopleth of the approximated Level 1 / Level 2 limit for the attitude quickness criterion (Fig. 8 and equation (5)). -Calculate isopleth of the approximated Level 1 / Level 2 limit for the bandwidth / phase delay parameter (Fig. 10). -Plot the whole set of isopleths in a chart with ω n depending on τ 1 .

Explanation of how to read a chart through an example

The Fig. 12 shows an example of a chart of FQ using the previous algorithm, choosing ζ=0. The coloured lines plotted are isopleths of criteria and parameters of interest for this paper. For example, the red bold line represents all models possible to choose if we want to be sure that their performance in terms of quickness is at the LEVEL 1 / LEVEL 2 limit (as defined by the red dotted line on Fig. 8). This means that if we chose a point on this line, the associated parameters ζ, ω n and τ 1 (and ɸ c ) generate a model (15) which insures to provide a quickness level verifying equation (5), for this case study (ɸ c ).

The example for the red bold line is the same for the blue bold line: if we choose a model on this line, the associated parameters insure that the simplified model presents a sufficient LEVEL 1 quality with respect to the bandwidth criterion (as defined by the red dotted line on Fig. 10). One can choose a point on this kind of chart, depending on its FQ objectives. Then thanks to (17), one can calculate the associated gains that will permit to obtain sufficient FQ levels -for the simplified model at least. These gains can be used as initialization for the complete model.

The differences between the results of the chart and those obtained with full linear models are evaluated in the next sections so that the designer has information on the results he can trust in. The points on Fig. 12 will mainly be used for these evaluations.

Additional criterion for energy evaluation

During an attitude change simulation, an amount of energy is used from the actuators. In order to evaluate this amount of energy spent, a criterion can be used. We will check the energy used until the system will be considered as stabilized, so that the energy usage will be stabilized as well. We decided to consider that a system modelled such as (15) is stabilized once the values of the attitudes do not extend any more over a band of 10% of the final value.

The instant from when the system is stabilized is called settling time to 10%: Ts 10% . To evaluate this settling time, the model (15) can be approximated by (19). The value of δ lat_MAX corresponds to the value of static saturation of actuators. The criterion E can be visualized with the grey area on Fig. 14. Its value will be compared to the maximum of energy the actuator could furnish during the same time. This can be evaluated thanks to the Ue criterion:

(24) ( ) ∫ = % 10 0 2 _ Tr MAX lat dt Ue δ
Finally, the energy criterion chosen to be considered for the tuning will be expressed as a percentage of the maximum amount of energy the actuator could have generated during the attitude change simulation until the settling time to 10%. This criterion will be called Energy Usage Eu (%):

(25) Ue E Eu ⋅ = 100
Isopleths of Eu have been plotted on Fig. 12. If Eu tends to 100%, this means the actuator saturates during the whole attitude change. Then the designer might look for minimizing its value. Later, a (realistic) filter will be used so that the first peak of the actuator usage can be highly reduced, with no significant loss on overall expected FQ. By the way, for more security about saturations due to windups, an antiwindup architecture could be used [11]. -red dots for the expected results with chart.

Evaluation of the chart

Many points of tuning have been chosen on

-blue stars for the obtained results with full linear simulations, using same gains. -black, green and grey squares for full linear and nonlinear design led in section 4.

The points Q1, Q2 and Q3 have been chosen such that the expected bandwidth is at the Level 1 / Level 2 limit. The points W1, W2 and W3 have been chosen such that the expected quickness parameter is at Q=0.5. The points E1, E2, E3 and E4 have been chosen such that all expected criteria are at least at the Level 1 / Level 2 limits. Results are summarized in Tab. 2.

The quickness parameter is expected (simplified model) to be improved by 40% between Q1 and Q2 and by 29% between Q2 and Q3. The obtained results (full linear model) show that they are improved by 23% and 19%. The bandwidth parameter is expected to be improved by 22% between W1 and W2 and by 34% between W2 and W3. The full linear simulations show respectively an improvement of the bandwidth by 33% and 55%. Then, in each case, the sensitivity is verified.

It comes out from Tab. 2 that in each case, the overall FQ obtained with the full linear model are in an area near the expected FQ given by the chart. This result demonstrates that the gains generated by the charts are able to achieve the targeted FQ criteria.

As a consequence, the charts seem to be enough accurate to permit a fast and efficient initialization of the gains with multiple FQ objectives.

Advices for using the chart in order to initialize the gain tuning process with HQ objectives

In order to meet LEVEL 1 HQ, a designer might want to use a chart for his design. The first step is to choose the case study. Depending on this case study, the set point might be fixed, and, in order to meet sufficient LEVEL 1 stability, ζ might be fixed to 0.35. Then, thanks to the algorithm, a chart can be generated. The Fig. 12 has been generated using the recommendations from the standard with ɸ c =20deg and ζ=0.35.

In order to meet sufficient LEVEL 1 quality for bandwidth phase delay criterion, a point might be chosen on the blue bold line. However, if a point is chosen on this line, the associated quality for

Q1 Q2=W2 Q3 W1 W3 E1 E2 E3 E4 Qi W2 W1 W3 Ei E4' E4'' E4''' W2=Q2 Q3 E2 E3 E4 W3 Wi & Q2 Q3 Ei Q1 Q1 E1 W1 E4' E4'' E4''' Q3 W2=Q2 Q1 W1 W3 E1 E2 E3 E4 Q1 Wi & Q2 Q3 E1 E2 E3 E4 E4'=E4'' E4'''
attitude quickness is never at LEVEL 1 for this case study. None of these designs seem interesting to meet good overall FQ.

Then, the designer might choose a point on the red bold line. Indeed, all points on this line generate gains with which the expected quality for attitude quickness is sufficiently at LEVEL 1. Furthermore, the expected quality for bandwidth phase delay is at LEVEL 1 with a large expected margin. Then, if a designer chooses any point on this line, the overall expected FQ might be at LEVEL 1.

A question might appear then: if any point can be chosen on the red bold line (for example E1, E2, E3 and E4), which can be considered as the best? Indeed, the expected FQ objectives seem sufficiently good in all cases. Here, we suggest considering two additional criteria for the initialization procedure: an energy criterion (the energy usage criterion explained before) and a new uncoupling criterion.

The black isopleths on Fig. 12 already give indications on the expected amount of energy used for each design during the attitude change simulation done to generate the attitude quickness, as explained in section 3.4. We suggest minimizing this criterion (in order to minimize the risks associated with potential saturations). Then, in this case study, the left area of this chart might be avoided.

The last objective might be to minimize the coupling of the full system. Eventually, even if the model we established has been simplified for a one-axis study, the coupling of the system can be seen by this model as perturbations.

Indeed, the equations ( 7) and ( 8) can be seen schematically on Fig. 18, using a framework similar to the individual channel design [12]. In section 3.1, U 2 and X 2 have been neglected such as our model has been reduced to the red part of Fig. 18. However, these hypotheses are wrong. Then, we can see these coupling signals as perturbation δ pert from the point of view of the one-axis control law. Then, if we wish to consider these couplings during the tuning process, (9) becomes:

(26) pert U B X A X δ + + = 1 11 1 11 1 . . & with (27)         = φ δ δ δ & & p pert
Then, using hypothesis (3), using Laplace transformations and considering ɸ c =0, (26) and (27) become:

(28) p lat p s K L p L s p & δ φ δ + + =
). ( . . .

K11(s) B11 A11 ∫ K22(s) B22 A22 ∫ B21 B12 A12 A21 2 X 1 X & 1 E         = φ p X 1 2 c X c c X φ = 1 2 E 1 U 2 U 2 X & pert δ
Finally, the new transfer functions between each one of the perturbations and ɸ are:

(31) φ δ δ δ φ i lat l p p K L s L s L s s . . . ˆ1 2 3 - - - = & (32) ( ) φ δ δ φ δ φ i lat l p p K L s L s L s L s s . . . ˆ. 1 2 3 - - - - = &
Then, thanks to the control law, the steady state error to step input like perturbations is zero. Indeed:

(33) 0 ) ( . lim ) ( lim 0 = = = → ∞ → s s t s t s φ ϕ ε
But the steady-state errors to ramp-like perturbations are respectively (using normalized amplitudes):

(34) φ δ φ φ ϕ ε i lat s t p s K L s s t . 1 ) ( . lim ) ( lim 0 _ - = = = → ∞ → & (35) φ δ φ φ φ ϕ ε i lat p s t s K L L s s t . ) ( . lim ) ( lim 0 _ = = = → ∞ → &
The results from (34) and (35) are crucial for decoupling objectives. Indeed, as required by the standard, the tuning must be led by keeping in mind to uncouple the system as much as possible. Here, we can see that we tend to help in that uncoupling by increasing the value of the integral gain. That's why the isopleths of K iɸ have been plotted on Fig. 12 (yellow lines). Here is the full procedure advised for an efficient initialization of the gain tuning process:

-Choose a case study in order to fix the FQ objectives as well as ζ and ɸ c . -Generate the chart for this specific case study of the one axis control law. -Find the area in which the expected attitude quickness and bandwidth phase delay criteria are both at LEVEL 1 (this should be near at least one of the two bold lines, red or blue on Fig. 12). -Choose a point in this area, near at least one of these limits, by making a compromise between maximizing as much as possible the integral gain (for uncoupling) and minimizing as much as possible the energetic criterion during the oneaxis attitude change simulation led.

APPLICATION AND EVALUATION OF THE FULL PROCEDURE

The initialization of gains procedure is applied to the full helicopter, for each axis. Then, an analysis is led for the roll axis only (without modifications of the gains on pitch and yaw All FQ objectives are those explained in section 2.5, for the roll axis.

Initialization of the gains of the full linear model using charts

Here, we directly apply the initialization of gains procedure explained in section 3.6. We choose to tune the ACAH for the roll axis with LEVEL 1 FQ objectives. We fix: ζ=035 and ɸ c =20deg. The chart on Fig. 12 has been generated with these conditions. A point on the red bold line generates gains with which all expected FQ are at least sufficiently in the LEVEL 1 area: we will choose a tuning on this line Thanks to this modification, the overall expected FQ with full linear model are at LEVEL 1 for all criteria.

In order to obtain these results, only the derivative gain has been increased by 10% only. Doing this, the quickness parameter has been decreased by 5%, the bandwidth has been increased by 4% and the stability has been increased by 14%.

All of this means that we have initialized the gains efficiently in one step thanks to the chart. The sensitivities results are used only to make slight adjustments at this step. Now, all expected FQ are all in LEVEL 1 area, with a good margin for the bandwidth (as it was already expected by the chart).

Evaluation of the differences of results between full linear models and full nonlinear models

Then these gains are used with full nonlinear models (including actuator model and natural system delay) to evaluate the overall FQ, using exactly same conditions: results are summarized with the fourth row of Tab. 3 and with green square E4'' on Fig. 15, 16 & 17.

As we can see, the quickness falls by 28% and the bandwidth falls by 47% (the stability is evaluated with full linear model, that's why there is no modification on this criterion). The figures show that the bandwidth is still in the LEVEL 1 area. Only the quickness is in the LEVEL 2 area. However, the overall obtained FQ are still in an interesting area, as expected by linear results.

Modifications of the gains on the full nonlinear model using linear sensitivities results

The green square E4'' on Fig. 17 Then, by increasing the proportional gain by 33%, the quickness has been increased by 17%, the bandwidth has been increased by 22% and the stability (obtained with full linear model) by 22%. The overall expected FQ is at LEVEL 1.

Evaluation of the full direct process: comparison of expected results from charts with obtained results from full nonlinear model

The aim was to tune the gains of the control law of the helicopter in order to obtain LEVEL 1 expected HQ for the roll axis. More precisely, there were conditions on quickness, bandwidth and stability parameters. Some gains have been chosen for initialization. Then, in order to meet LEVEL 1 limits, the derivative gain has been increased by 10% and the proportional gain by 33%. During the tuning process, the quickness parameter has been increased by 2%, the bandwidth parameter has been decreased by 5% and the stability parameter has been increased by 22%.

Finally, with this "direct" procedure, the overall expected HQ has been set to LEVEL 1, in few steps, using the FQ requirements from ADS-33. Only slight adjustments have been necessary.

CONCLUSION

ONERA has been working for several years to the establishment of an efficient methodology of gain tuning for helicopter control laws with Handling Qualities objectives, from the early steps of gains design. In this paper, an example of the full procedure has been presented.

Thanks to the methodology developed, the use of Flying Qualities charts generated from an analytical study widely contributes to an efficient initialization of control law gains constrained by Flying Qualities requirements. Moreover, the physical basis of these charts insures not only the initialization of the gains, but also a correct sensitivity of the gains to the Flying Qualities criteria, as well as a good estimation of tuning points near the limits. A tool implementing all this methodology is currently in development at ONERA Salon de Provence. This tool, CAST-HEL-AP -Computer Aided Setting and Tuning tool for Helicopter AutoPilots [10] -might efficiently help a designer in his task of gain tuning of specific control laws with Handling Qualities objectives. Simplified models, full linear models including models of actuators and its natural system delays, and full non linear models can be easily used to generate all necessary Flying Qualities at each step of the tuning process detailed on Fig. 11.

The next steps could be to use PycsHel (Fig. 19), a prototyping and simulation platform for helicopters, currently in development at ONERA Salon de Provence. Indeed, thanks to this platform, technologies such as control laws and associated operational logics can be implemented and tested easily. The gains of these control laws can be tuned using the methodology exposed in this paper. Once this is done, the gains can be implemented in the models (last step of Fig. 11) and they could be tested by pilots to evaluate the overall Handling Qualities of the aircraft with the specific gains designed.

Fig. 19 PycsHel: a prototyping and simulation platform for helicopters currently in development at ONERA Salon de Provence

COPYRIGHT STATEMENT

The author(s) confirm that they, and/or their company or organisation hold copyright on all of the original material included in this paper. The authors also confirm that they have obtained permission, from the copyright holder of any third party material included in this paper, to publish it as part of their paper. The author(s) confirm that they give permission, or have obtained permission from the copyright holder of this paper, for the publication and distribution of this paper as part of the ERF2014 proceedings or as individual offprints from the proceedings and for inclusion in a freely accessible web-based repository.

This work has been done thanks to funds from ONERA and Conseil Régional Provence Alpes Côte d'Azur (Pôle Pégase).

7.

Fig. 1

 1 Fig. 1 Usual method of tuning ONERA has been working for several years to the establishment of processes contributing to the reduction of the control laws development cycles by integrating HQ requirements from the early phase of gains design (Fig. 2) [5] [6] [10].

Fig. 3 Fig

 3 Fig. 3 Main control Inputs used by the pilot

  , A, B, C, D are respectively the state, command, observation and input/output matrices. Using usual linear assumptions around equilibrium, they can be calculated from full representative nonlinear flight dynamic models or identified from dedicated flight tests. In this study, authors have used HOST© (Helicopter Overall Simulation Tool [9]), a modelling and simulation tool developed by Airbus Helicopters, and jointly improved by ONERA. can write the state space representation of the helicopter (3).

Fig. 6

 6 Fig. 6 Stability criterion: pole placement 2.5.3 Requirements for moderate amplitude attitude changes: quickness criterion This criterion is evaluated using attitude capture flight tests. For the gain tuning studies, attitude change simulations are performed. The criterion is computed using 3 parameters (Fig. 7): peak roll rate (p pk ), peak roll change (∆ɸ pk ) and minimum roll change (∆ɸ min ). Then, 2 of these 3 parameters are used to calculate the quickness criterion (Q). The requirement for its positioning depending on the minimum attitude change is shown on Fig. 8. The Level 1 / Level 2 limit can be approximated by (red dotted curve on Fig. 8):(5)

Fig. 9 .Fig. 7 Fig. 8 Fig. 9 QFig. 10

 978910 Fig. 7 Definition of the attitude quickness parameters during an attitude change

-

  Hypothesis 4: L ɸ = 0. The dynamic between the roll angle and the derivative of the roll rate is neglected (negligible value compared with the other sensitivities: usually less than 10 -9 %).

  35 and ɸ c =20deg, for the roll axis. A model of natural delays is included in the calculations. A point on this figure is defined by specific values for ω n and τ 1 . As ɸ c and ζ are fixed, then a point defines a model such as (15). For each point, all criteria and interesting parameters are generated as explained in previous sections. Then, for each point on this figure, we have information on the behaviour of the simplified one-axis model of the helicopter, for the roll axis in this example.

Fig. 12

 12 Fig. 12 Example of a chart generated for the roll axis control law of a cargo-type helicopterAll the coloured lines follow the same rule. Red lines give information on quickness (isopleths of Q parameter). Blue lines give information on bandwidth (isopleths of ω BW parameter). Yellow lines are isopleths of the integral gain K iɸ (used later in the communication). Black lines give information about the need on actuator energy during the attitude change simulation made to calculate the attitude quickness, using an energetic criterion (explained in next subsection). Then, for each point on this chart, a model and its associated FQ are generated and plotted (via isopleths). One can choose a point on this kind of chart, depending on its FQ objectives. Then thanks to (17), one can calculate the associated gains that will permit to obtain sufficient FQ levels -for the simplified model at least. These gains can be used as initialization for the complete model.

Fig. 13 Fig. 14

 1314 Fig. 13 Evaluation of the approximated settling time to 10%.Finally, we can calculate the settling time to 10% of the final value:

  Fig. 12 in order to check the reliabilities of the expected FQ. Full linear simulations (including natural system delays and actuator models) have been led in that purpose (using CAST-HEL-AP [10]). The results are summarized on Fig. 15, 16 & 17:

Fig. 15

 15 Fig. 15 Attitude quickness results (i = {1:4})

Fig. 18

 18 Fig. 18Helicopter architecture with the usual ACAH control law

  might change radically (risk of creation of a pure unstable integrator for example). Furthermore, the impact on the values of the gains (17) can be unacceptable (value of K iɸ can tend to infinity for example). On the other hand, because we are studying a physical and pilotable system, the maximum values of ω n , τ 1 and ζ can be empirically limited. Finally, one can choose to generate a set of models such as (15) with:

The idea for this tool is to generate the criteria for a sweep of models such that the parameters used in (15) (ω n , τ 1 and ζ) are physically suitable. Then, the data can be used to generate charts of FQ. The designer can then use these charts to find associated values of ω n , τ 1 and ζ such that the expected FQ are those recommended by the standard. Then the equations from (17) permit the initialization of the gains. The first step is to establish a range of values of ω n , τ 1 and ζ physically suitable to the system. A quick overview on (15) can help in this. On the one hand, if ω n , τ 1 or ζ are almost equal to zero, the model (15)

  Summary of the results of the full tuning procedure: last three columns show the evolution of gainsThe last column of Tab. 2 gives precisions about the gaps of results between the expected FQ with simplified model and the obtained FQ with full linear model. There is a gap of 6% between the results of quickness, 4% between the results of bandwidth and 14% between the results of stability. This confirms the overall obtained FQ with full linear model are in the area of the overall expected FQ by the chart.

	4.2	Modification of the gains of the full linear
		model using linear sensitivities
	The blue star E4 on Fig. 17 indicates a lack of
	stability for the full linear model with these gains.
	Using local linear sensitivity results [10], the
	derivative gain is increased in order to obtain LEVEL
	1 stability for the associated slow mode. The results
	are summarized with the third row of Tab. 3 and with
	the black square E4' on Fig. 15, 16 & 17.
							. A good
		compromise between reducing energy consumption
		(black isopleths of Eu criterion) and increasing
		uncoupling (yellow isopleths of K iɸ criterion) can lead
		to choose the point E4: red dot Ei for i=4 on Fig. 15,
		16 & 17. The expected FQ and the associated gains
		are summarized on the first row of Tab. 3. The Fig.
		15, 16 & 17 show that the overall expected FQ with
		the simplified model are quite well verified with the
		full linear model (blue star E4). Indeed, the gains
		obtained with the chart have been implemented in
		CAST-HEL-AP [10] to evaluate the FQ (using
		exactly same conditions) with the full linear model:
		this includes model of actuators and natural system
		delay. The results are summarized in the second
		row of Tab. 3.
	Tab. 3 Full tuning procedure	Q (/s)	ω BW (rad/s)	ζ	K p	Kɸ	K iɸ
		Expected FQ from chart and associated gains	1.18	2.84	0.35	-0.27	-0.8	-1.2
		Obtained FQ with full linear model (same gains)	1.35	2.95	0.3	-0.27	-0.8	-1.2
	Modifications of the gains using sensitivities (full linear model)	1.28	3.08	0.35	-0.3	-0.8	-1.2
		Modified gains Implemented on the full non-linear model	1	2.1	0.35	-0.3	-0.8	-1.2
		Modifications of the gains on the full non-linear model	1.2	2.7	0.45	-0.3	-1.2	-1.2


Alexander V Ruban
email: a.ruban@sheffield.ac.uk

Johann Lavaud^

Bernard Rousseau^

Gerard Guglielmi^

Peter Horton

Anne-Lise Etienne^

Photoprotection in Diatom Algae

Keywords: Chlorophyll fluorescence, nonphotochemical fluorescence quenching, absorption spectra, diatoms, Phaeodactylum tricornutum, xanthophyll cycle, diatoxanthin Nonphotochemical chlorophyll fluorescence quenching, PSII -Photosystem

When grown at intermittent light regime, diatom alga Phaeodactylum tricornutum is able to form photoprotective non-photochemical fluorescence quenching (NPQ) 3 -5 times larger than that observed in the higher plants. This quenching is sustained in the dark for 5-10 min, reverses completely within approx. 1 hr and seems to be very tightly related to the presence of the zeaxanthin analogue, diatoxanthin. Addition of the uncoupler NH 4 Cl before illumination can completely abolish formation of NPQ, revealing the pH-dependency of the xanthophyll cycle activity. Once established, NPQ can also be almost completely reversed by the uncoupler. However the higher NPQ is formed the more time is required for its reversal. At the point when the fluorescence was approx. 90% recovered the level of illumination-induced diatoxanthin was found to be only partially reduced. This indicates that the proton gradient is a key triggering factor of NPQ. It was also noticed that NPQ in Phaeodactylum cells was absent even when majority of reaction centers were closed and the plastoquinone pool was significantly reduced. The absence of NPQ at these conditions could be due to very low levels of pH. It is likely that in diatoms alternative sources of protons such as the PSI cyclic electron transfer and/or chlororespiration are important in generating the proton gradient sufficient to trigger NPQ. Absorption changes associated with the xanthophyll cycle activity were found to be larger than those for higher plants. The position of the positive maximum in the difference spectrum illuminated-minus-dark was 512-514 nm in comparison to the 505-508 nm for leaves. The 535 nm band associated with NPQ in plants is absent in

Phaeodactylum. An uncoupler-sensitive absorption change at 522 nm was discovered. Kinetics of NPQ showed linear correlation with the 522 nm absorption change.

Introduction

Diatom algae are dominant phytoplankton component in the vast areas of cold waters of the North Atlantic and Arctic Oceans. They contribute to almost 25% of the primary photosynthetic production on Earth and therefore play an important role in the energy balance of our biosphere (Treguer at al. 1995[START_REF] Field | Primary production of the biosphere: integrating terrestrial and oceaniccomponents[END_REF], Smetacek 1999). It is widely known that the photosynthetic efficiency is dependent upon the light environmenttoo much light can be dangerous for photosynthesis, in particular to the photosystem II (PSII). At conditions of excess light the most powerful oxidant in nature, PSII reaction center, can cause a fatal damage to this photosystem and subsequent decrease in the photosynthetic efficiency [START_REF] Osmond | Photorespiration and photoinhibition. Some implications for the energetics of photosynthesis[END_REF], Horton and Ruban, 1992[START_REF] Barber | Molecular basis of the vulnerability of photosystem-II to damage by light[END_REF]. However, a mechanism does exist to minimise this effect by safely dissipating excess of harmful energy into heat. This process can be monitored by measuring nonphotochemical chlorophyll fluorescence quenching (NPQ)an indicator of the nonradiative excitation energy dissipation in the photosynthetic antenna [START_REF] Krause | Chlorophyll fluorescence and photosynthesis: the basics[END_REF]. The mechanism of NPQ was a subject of intense research in higher plants [START_REF] Demmig-Adams | Photoprotection and other responses of plant to high light stress[END_REF][START_REF] Horton | Regulation of light harvesting in green plants[END_REF][START_REF] Niyogi | Photoprotection revisited: genetic and molecular approaches[END_REF]. So far it is established that it occurs in light harvesting system of PSII, triggered by pH and modulated by xanthophylls [START_REF] Horton | Regulation of light harvesting in green plants[END_REF][START_REF] Gilmore | Mechanistic aspects of xanthophyll cycle-dependent phtoprotection in higher plant chloroplasts and leaves[END_REF]. Recently a PSII protein PsbS was discovered to be a key factor sensing pH [START_REF] Li | A pigment-binding protein essential for regulation of photosynthetic light havesting[END_REF](Li et al., , 2002(Li et al., , 2002b(Li et al., , 2002c)), binding zeaxanthin [START_REF] Aspinall-O'dea | The PsbS subunit of photosystem II binds zeaxanthin and activates it for nonphotochemical fluorescence quenching[END_REF] and probably triggering the conformational changes within PSII antenna [START_REF] Horton | Allosteric regulation of the lightharvesting system of photosystem II[END_REF], which leads to its transition into the dissipative mode. The physical nature of this quenching is still under debate. There exist two major theories. One implies that zeaxanthin is a direct quencher of the chlorophyll excited state [START_REF] Demmig-Adams | Carotenoids and photoprotection in plantsa role for the xanthophyll zeaxanthin[END_REF][START_REF] Owens | Dynamics and mechanism of singlet energy transfer between carotenoids and chlorophylls: light harvesting and nonphotochemical fluorescence quenching[END_REF][START_REF] Frank | Photophysics of the carotenoids associated with the xanthophyll cycle in photosynthesis[END_REF][START_REF] Gilmore | Mechanistic aspects of xanthophyll cycle-dependent phtoprotection in higher plant chloroplasts and leaves[END_REF]. The other theory suggests that the quencher is a chlorophyll dimer or excimer formed during the antenna conformational transition assisted by zeaxanthin as an allosteric activator [START_REF] Horton | Allosteric regulation of the lightharvesting system of photosystem II[END_REF]. Diatom algae possess the capacity for energy dissipation, which in some cases exceeds that of the higher plants. (Ting and Owens, 1993[START_REF] Arsalane | Influence of the pool size of the xanthophyll cycle on the effects of light stress in a diatom -competition between photoprotection and photoinhibition[END_REF][START_REF] Olaizola | Non-photochemical fluorescence quenching and the diadinoxanthin cycle in a marine diatom[END_REF][START_REF] Casper-Lindley | Fluorescence quenching in four unicellular algae with different light-harvesting and xanthophyll cycle pigments[END_REF]. Recently an unusually high NPQ (almost twice the level of control) was found in Phaeodactylum tricornutum cells grown under intermittent light regime (Lavaud et al., 2002a, b). This model alga possesses more than 5 times capacity to dissipate excess energy as compared to higher plants. NPQ is dependent on the build-up of a transthylakoid proton gradient and on xanthophyll cycle activity. This cycle is different from violaxanthin cycle because different xanthophylls, diadinoxanthin (DD) and diathoxanthin (DT), represent it. Also it is a one-step process: deepoxidation of only one oxygen takes place changing the number of conjugated double bonds from 10 to 11, which equals to antheraxanthin-zeaxanthin conversion [START_REF] Hager | Das carotinoidmuster und die verbreitung des lichtinduzieren xanthophyllcyclus in verschiedenen algenklassen. V. Einzelne vertreter der Cryptophyceae, Euglenophyceae, Bacillariophyceae, Chrysophyceae und Phaeophyceae[END_REF]. It is interesting to note that the intermittent light regime had no large effects on the pigment composition and antenna size of Phaeodactylum apart from the dramatic increase in the xanthophyll pool size (Lavaud et al., 2002a[START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF]. At these conditions exceptionally large levels of NPQ have been recorded. In this study we focus on investigation of the relationship between DT concentration, pH and NPQ in diatom algae using uncouplers and simultaneous kinetic measurements of NPQ and DT formation. We show in the present report that the free DT is unlikely to be the fluorescence quencher. It has to undergo pHdependent incorporation/activation into the quenching locus. Since the concentration of DT is often larger than that of zeaxanthin in plants and the maximum deepoxidation capacities are similar it is possible that more DT is involved in the fluorescence quenching than zeaxanthin. All data indicate that the differences between composition and organisation of light-harvesting complex (LHC) of plants and diatoms may be central in determining the NPQ capacity. We have found a new absorption change at 522 nm, which linearly correlates with NPQ and is possibly associated with DT activation in the quenching locus. For understanding of the excess energy dissipation mechanism, comparison with higher plants is essential since diatoms having different xanthophylls and different antenna system, containing specific polypeptides and pigment populations, possess an effective NPQ with mechanistic features similar to that of plants.

Materials and Methods

Material

Phaeodactylum tricornutum cells were grown photoautotrophically in sterile natural seawater as described in (Lavaud et al., 2002a). Briefly, cultures were incubated at 18 C in airlifts continuously flushed with air. They were grown under a white light intensity of 40 µmol photons . m -2. s -1 provided by fluorescent tubes (Claude, Blanc Industry, France) with a 5 min light/55 min dark cycle. Cells were collected after 30-40 days still in their exponential growth phase, since the growth rate under the intermittent light regime is extremely low. Part of the culture was then diluted in fresh medium to maintain cells in exponential growth phase. Arabidopsis taliana cv Columbia plants were grown in growth chambers at 8 hrs photoperiod and 200 μM quanta . m -2. s -1 for 8 weeks.

Thylakoid preparations and treatments

Thylakoids were prepared either from dark-adapted (1 hr after the end of 5 min illumination period) or illuminated (5000 µmol photons . m -2. s -1 for 25 min) algae. Cells were broken in a standard buffer used for spinach thylakoid preparation (Ruban et al., 1999) by 3 cycles of French press treatment and centrifugation. In this procedure thylakoids were released from approx. 90 % of all cells. Final step included peletting of thylakoids and resuspending in the medium, which contained 0.35 M sorbitol, 1mM EDTA, 5 mM MgCl 2 and 50 mM HEPES. All handling of material was carried out in a dark room. The diadinoxanthin de-epoxidation was carried out at pH5.5 for 1 hr at chlorophyll concentration of 50 µM in 200 ml of medium with the constant stirring at room temperature. Intact spinach chloroplasts were prepared as described earlier (Ruban and Horton, 1999). LHC from algae was prepared using solubilisation of dark-adapted and low-pH-treated thylakoid membranes with digitonin for 1 hr on ice and subsequent sucrose gradient centrifugation at 200000 g for 18 hrs (for more details see [START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF].

Pigment analysis

Pigment analyses were performed using HPLC as described previously (Arsalene et al., 1994[START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF]. Pigments were extracted by a phase separation procedure: samples were first mixed with a methanol:acetone (50:50, 1 volume) solution completed with ether (1 volume) and water-NaCl 10 % (2 volumes). Deepoxidation state index was calculated as: DES = (DT)/((DD)+(DT)), where (DT) and (DD) are concentrations of diatoxanthin and diadinoxanthin, respectively.

Chlorophyll fluorescence measurements

Chlorophyll fluorescence traces were measured using PAM-101 Walz fluorometer (Walz, Effeltrich, Germany) and a standard thermostatic cell for liquid samples as described by Lavaud et al. (Lavaud et al., 2002a). NPQ was calculated as (F m -F m ')/F m '. qP was calculated as (F m '-Fs)/(F m '-F o '). F m and F m ' are the maximum levels of fluorescence before and during actinic illumination, respectively. F s is the steady-state fluorescence level. F o ' is the dark level of fluorescence measured immediately after switching off the actinic light. The saturating white light pulse intensity was 6000 µmol photons . m -2. s -1 .

Absorption measurements

Absorption spectra and simultaneous chlorophyll fluorescence and absorption kinetics in the 505-522 nm region were measured using DW2000 Aminco Spectrophotometer (American Instrument Co., USA) in a single or double beam mode. Spectral resolution was 0.5 nm and 2 nm for stationary and kinetic measurements, respectively. To induce absorption changes, sample was illuminated at 90 o with respect to the measuring beam. For illumination a 150 W tungsten halogen bulb light filtered by RG610 Schott filter, transmitting efficiently above 610 nm, (Optical Glass Inc., USA) was used. To protect the photomultiplier from actinic light a combination of Corning 4-96 and OCL1 Cyan T400-570 filters, transmitting in the region of 400-570 nm was used (Corning Co, USA). The actinic light intensity was 700 µmol photons . m -2. s -1 for Arabidopsis leaves (500-700 and 2000-2500 µmol photons . m -2. s -1 respectively). In Phaeodactylum fluorescence was quenched quickly and almost monophasically. The fluorescence level went far below the F o and the total NPQ reached as far as 9 in some cases after only 5 min of illumination. In plants, fluorescence decrease was less intense (NPQ only 1.9 -2.1) and more complex with a visible slow phase. The slow phase was similar to the previously observed fluorescence quenching induction in spinach leaves and attributed to the gradual formation of zeaxanthin (Ruban and Horton, 1999). Removal of actinic illumination caused fast relaxation of the fluorescence level in leaves, whereas in diatoms fluorescence remained completely quenched during 5 -10 minutes of dark-adaptation. It took almost 50 minutes to restore the F m in Phaeodactylum. The second illumination cycle showed much faster fluorescence quenching in leaves, but not in diatoms, where the rate of quenching was almost the same as during the first illumination cycle. It is worth to notice that the fluorescence relaxation in Arabidopsis leaves after the second illumination phase was almost 50 % slower than the recovery after the first illumination phase but still much faster than that in diatoms. NPQ after the second phase was increased to 2.6 -2.8, which is due to additional zeaxanthin formation (Ruban and Horton, 1999, Ruban, unpublished). As was noticed earlier in experiments on isolated chloroplasts the presence of zeaxanthin enhances not only NPQ but also the time required for its relaxation [START_REF] Rees | Enhancement of the pHdependent dissipation of excitation energy in spinach chloroplasts by light-activation: correlation with the synthesis of zeaxanthin[END_REF]. In diatoms grown under intermittent light regime xanthophyll cycle pool size is almost doubled comparing to control cells (Lavaud et al., 2002a[START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF]. There are minimum 2 diadinoxanthin molecules per LHC monomer in cells grown under intermittent light regime [START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF]. That is twice the maximum amount of violaxanthin found in LHCII of plants (Ruban et al., 1999). This could cause an increase in relaxation time in agreement with the observations made on plants. Hence, the tendency for large NPQ to reverse slowly seems to be a common feature for plants and diatoms. To explore further the relationship between the extent of NPQ and the extent of its recovery and rate in diatoms varying periods of actinic light illumination were employed to modulate the amount of quenching. Figure 2 shows the results of this approach. Indeed, fluorescence level was almost restored within 5 min of dark adaptation following the illumination when the NPQ level was small. The proportion of reversible quenching (restored after 5 min) was becoming smaller with the increase of the illumination time and NPQ respectively.

Results and Discussion

NPQ induction and reversibility in diatoms in comparison to higher plants

Effect of an uncoupler on the NPQ relaxation

To find if the slow relaxation of NPQ is linked to the sustained pH and protonation of the quenching locus, we employed ammonium chloride (NH 4 Cl) as an uncoupler.

When NH 4 Cl is added before the illumination NPQ can be completely inhibited (Figure 3 A, trace 1), indicating efficient permeability of the uncoupler into the algal chloroplast (Lavaud et al, 2002b). Figure 3B shows typical rapid fluorescence level recovery upon addition of uncoupler to isolated intact chloroplasts. The effect of NH 4 Cl on the NPQ in diatoms is very different. When added at different stages of NPQ formation in diatoms, NH 4 Cl reverses promptly the fluorescence level when NPQ is within the range of that observed in plants (Figure 3 A, traces 2-3). But it is clear that the reversal becomes much slower for larger values of NPQ. For NPQ values up to 1.7-2.0 the level of diatoxanthin was decreased during 5 min after addition of uncoupler only by 20%. When the quenching level approached 3 and above, the NPQ relaxation time started to rise dramatically (Figure 4) as well as the extent of DT epoxidation (not shown). For NPQ level around 6 the relaxation time of NPQ became close to 15 minutes. For the same duration of dark recovery more DT was found to be re-epoxidised in the presence of NH 4 Cl than in the control. This observation suggests that NH 4 Cl has accelerated not only the reversibility of NPQ but also the rate of diatoxanthin epoxidation, since the dark adaptation time required to epoxidise completely diatoxanthin at this level of NPQ was found to be more than 30 min (Lavaud at al., 2002b). These results raised a few important mechanistic and physiological issues. DT is certainly not the only factor that controls NPQproton gradient and protonation are essential triggers of it, as was suggested earlier (Lavaud et al., 2002b). It is possible that after illumination a residual level of pH still remains and is sufficient to sustain high level of NPQ in darkness and the presence of DT. The chlororespiration could be an important factor contributing to the proton gradient in diatoms [START_REF] Jakob | Activation of diadinoxanthin de-epoxidase due to a chlororespiratory proton gradient in the dark in the diatom Phaeodactylum tricornutum[END_REF], Lavaud et al., 2002c). This situation was observed in some higher plant species [START_REF] Ruban | An investigation of the sustained component of nonphotochemical quenching of chlorophyll fluorescence in isolated chloroplasts and leaves of spinach[END_REF], particularly under conditions of combined light and cold stress (Verhoeven et al., 1998). Indeed, comparing the data on spontaneous (Figure 1) and uncoupler-dependent recovery of NPQ (Figure 3), it is feasible to conclude that the uncoupler accelerates the slow release of protons out of the quenching locus. Though being not the most lypophilic agent, NH 4 Cl is still effective to prevent NPQ. Trials to employ more lipophilic uncoupler nigericin have failed, since it was not able to diffuse through the cell wall (not shown). However, the addition of NH 4 Cl has reversed NPQ in all cases. Still, the relaxation time remained to be dependent upon the extent of quenching. The effects of NH 4 Cl on the slow reversal of NPQ in diatoms are rather consistent with the NPQ model described by Horton and Ruban for higher plants [START_REF] Horton | Regulation of photosystem-II[END_REF]. The model suggests a gradual conformational transition within the LHCII antenna into the quenching state. The key element of this change is zeaxanthin, which acts as an allosteric controller. Zeaxanthin analogue, DT, has most likely a similar function in diatoms. One would predict that the structure of their antenna is capable of a conformational change favouring transition into a very efficient energy-dissipative state. A recent paper on thermodynamics of the fluorescence quenching in isolated LHCII antenna supports this view and suggests that the oligomerisation state of antenna is one of the factors controlling dynamics of the complex together with zeaxanthin, protonation and domain structure (Wentworth et al., 2003). The general NPQ formation scenario may involve the following sequence of events: formation of DT and protonation of antenna, cooperative conformational transition of the latter into the quenching state involving partitioning of DT into the more hydrophobic regions and more hydrophobic dislocation of proton-binding domains. This should serve as an NPQ 'lock', preventing a quick relaxation in the absence of a bulk proton gradient. The clear evidence of the co-operative manner of NPQ formation is a progressive distinct sigmoidicity of the fluorescence relaxation curve with an increase of the extent of quenching (compare Figure 3A, traces 2 -6).

Relationship between super-NPQ and qP

Diatoms grown under intermittent light regime possess particularly large levels of energy dissipation (Lavaud et al., 2002a). At this light environment diatoms possess very low photosynthetic rate. Indeed, as was mentioned earlier, the PSII saturating light intensity for Phaeodactylum is about 4 times less than that for Arabidopsis leaves. A large percentage of PSII reaction centers have to be closed before the photoprotective NPQ can be activated. Figure 5 illustrates this observation showing relationship between qP and NPQ in plants and diatoms. In higher plants this relationship seems to be almost linearly reciprocal. Photoprotection is closely following the PSII redox-state. In diatoms grown at intermittent light regime relationship between qP and NPQ is rather hyperbolic. It looks like these two processes can be relatively independent. The adaptation of Phaeodactylum to this rather unusual light regime is such that NPQ is standing-by and can be readily triggered only when the PSII redox-state is very close to saturation. It is likely that some additional sources of protons are required here to trigger NPQ. Those could originate, for example, from the cyclic electron transport around PSI, which is activated when the linear electron transport is saturated [START_REF] Caron | Chlorophyll fluorescence transients from the diatom Phaeodactylum tricornutum: relative rates of cyclic phosphorylation and chlororespiration[END_REF]. This is coherent with the recent finding on Arabidopsis mutant lacking the protein controlling the PSI cycle [START_REF] Munekage | PGR5 is involved in cyclic electron flow around photosystem I and is essential for photoprotection in Arabidopsis[END_REF]. NPQ in this mutant is significantly reduced suggesting the important role of protons generated by PSI in controlling the energy dissipation in PSII antenna. Therefore the apparent absence of coordination between NPQ and PSII electron transfer activity is an illustration of the relative independence of the PSII redox-state from the proton-motive electron transfer and subsequently NPQ.

Comparison of the absorption changes associated with NPQ in diatoms and plants

Illumination of diatom cells induces significant absorption changes in the carotenoid region. Figure 6A shows spectra of dark-adapted and illuminated samples. The distinct maximum around 490 nm in the spectrum of dark-adapted cells is strongly decreased and a shoulder above 500 nm emerges after illumination. Calculation of a difference spectrum illuminated-minus-dark revealed a major maximum at 512 nm and a minimum at 490 nm corresponding to DT-minus-DD spectrum (Figure 6B, trace 1). The similar absorption difference spectrum for the violaxanthin cycle, zeaxanthinminus-violaxanthin is shown as a dotted line (Figure 6B). Although, both zeaxanthin and DT have the same number of conjugated double bonds, DT absorption is 4 nm red-shifted comparing to zeaxanthin. Interestingly the similar difference spectrum for the isolated LHC antenna complex from Phaeodactylum thylakoids has 508 nm maximum instead of 512 nm and the positive DT band is much narrower (Figure 6B, trace 2, see also [START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF]). This suggests that the environment of DT in the intact thylakoid membrane is different from that of the isolated complex, likely due to tighter interaction within hydrophobic antenna domains of high polarisability.

The difference spectrum cells-minus-LHC represents the additional absorption change in the xanthophyll region under conditions of NPQ (Figure 6B, trace 3).

Another key difference between spectra 1 and 2 of Figure 6B is the presence of a strong 690 nm band in chlorophyll a region, which is similar to that observed in higher plant thylakoids when NPQ was formed [START_REF] Ruban | Mechanism of pH-dependent dissipation of absorbed excitation energy by photosynthetic membranes. II. The relationship between LHCII aggregation in vitro and qE in isolated thylakoids[END_REF]. This band was found to be present only when the fluorescence quenching in isolated LHCII was induced. Although the work is in progress to understand the nature of this band, it is likely to originate from chlorophyll-chlorophyll or chlorophyll-xanthophyll association in the quenching locus.

To separate the xanthophyll cycle-associated from NPQ-dependent absorption changes an uncoupler NH4Cl was employed. Figure 6C, traces 1 and 2, represent the absorption changes in the blue and red regions due to addition of NH4Cl and rapid removal of NPQ. In the red region the 690 nm positive band was similar to that in the spectrum 1, Figure 6B. The main maximum in the xanthophyll region is even more red-shifted towards 514 nm and the band is 4 nm broader than that in the difference spectrum 1 of the Figure 6B. As was stated above, during the uncoupler treatment a partial DT epoxidation process took place. This could cause the presence of the DTminus-DD component at 508 nm in the uncoupler-induced spectral change. Therefore, the subtraction of this component using the deepoxidation difference spectrum for LHC from the uncoupler-induced difference spectrum reveals purely protonationdependent change (Figure 6C, trace 3). The latter has the same maximum as the spectrum 3 from the Figure 6B but it is dominating in the uncoupler-dependent spectrum. The NPQ-associated absorption band at 522 nm in diatoms is analogous to that in higher plants at 535 nm (Figure 6C, dotted trace). This band was found to be zeaxanthin-dependent and recently has been assigned to the special, activated state of zeaxanthin into NPQ locus, probably associated with PsbS proteina key trigger of NPQ in plants (Ruban et al., 2002a, Aspinal-O'Dea et al., 2002). The strong absorption shift of almost 25 nm was attributed to a zeaxanthin dimer. It was postulated to be a head-to-tail type of dimer. In analogous spectrum of diatoms 522 nm band could represent the activated DT. However the red shift (around 10 nm) is much smaller than in the higher plant spectrum. This is possibly because DT is very asymmetric compared to zeaxanthin and conjugation of optical -electrons extends only into one end-group (Figure 7) it is less probable that it can form dimers with similar optical properties to zeaxanthin. It is also possible that because of likely differences of plant and diatom antenna structures, DT environment in the NPQ locus is very different from that of zeaxanthin. These implications will be tested in a near future for the LHC of diatoms by biochemical work and spectroscopic approaches developed for higher plants (Ruban et al., 1999[START_REF] Ruban | Configuration and dynamics of carotenoids in light-harvesting antennae of the thylakoid membrane[END_REF](Ruban et al., , 2002a(Ruban et al., , 2002b)).

Direct measurement of the NPQ and diatoxanthin formation kinetics

Using HPLC determination of DT, a point-by-point correlation close to linear was observed between DT and NPQ (Lavaud et al., 2002a, Lavaud et al., 2002b). A more precise determination of the relationship between NPQ and the different absorption peaks attributed to the xanthophyll cycle was done in simultaneous kinetic measurements as was performed on higher plant leaves [START_REF] Ruban | Induction of nonphotochemical energydissipation and absorbency changes in leavesevidence for changes in the state of light harvesting system of photosystem II in vivo[END_REF]. Figure 8A shows kinetics of chlorophyll fluorescence at F m level and absorption at 514 nm induced by saturating light. The kinetic of fluorescence quenching was found to follow hyperbolic function similarly to that of spinach chloroplasts and leaves (Ruban and Horton, 1999). This observation is yet another evidence of the fundamental resemblance between the energy dissipation mechanism in diatoms and plants. NPQ was in linear correlation with the appearance of the 522 nm band, which, as hypothesised above, may reflect an activated, partitioned into the hydrophobic quenching locus DT (Figure 8,B). Clear deviation from linearity can be observed in correlation of NPQ with absorption change in more short-wavelength region at 514 nm. This observation could provide another support to the idea that a sub-population of DT molecules in diatoms, as zeaxanthin in plants, undergoes incorporation into the NPQ locus. The red shifted peak is indicative of either a direct fluorescence quencher or/and a state of allosteric activator of the quenching, promoting conformational change within the antenna.

Factors controlling the extent of NPQ

The results mentioned above indicate tight but not direct relationship between DT and NPQ. After 1 hr of light treatment we have found that only 65 % of DD was converted into DT. This is about the same as was obtained during illumination of spinach leaves (Ruban and Horton, 1999). However in spite of a similar extent of deepoxidation the differences in NPQ are large. Moreover the low-pH induced deepoxidation of isolated thylakoids from Phaeodactylum cells is reaching 80%, which is similar to that reported for spinach (Ruban et al., 1999). Therefore these diatoms have very much the same maximum de-epoxidation capacity as higher plants.

The super-NPQ (8 -15 for diatoms against 2 -3 for Arabidopsis and spinach) can be due to the larger xanthophyll pool size in diatoms grown under intermittent light while the antenna size remains the same than for algae grown under a classical light/dark regime. For a smaller pool size associated with the same antenna size, smaller values of NPQ are obtained closer to the values found in higher plants (Lavaud et al., 2002a[START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF]. In P. tricornutum Lavaud et al. [START_REF] Lavaud | Enrichment of the light-harvesting complex in diadinoxanthin and implications for the nonphotochemical fluorescence quenching in diatoms[END_REF] have shown that the additional DD molecules of intermittent light grown cells are mainly associated with LHC fraction. Recent experiments on Arabidopsis indicate that doubling of amount of xanthophyll cycle carotenoids in PSII antenna had no visible effect on the maximum NPQ [START_REF] Davison | Overexpression of beta-carotene hydroxylase enhances stress tolerance in Arabidopsis[END_REF]. Therefore these contradicting observations could probably be explained by differences in the concentration of quenching centers in the two antenna systems. The proportion of activated DT in the NPQ locus can be larger than that of the activated zeaxanthin. Indeed, judging from the absorption difference spectra shown on the Figure 6B andC, the amplitude of NPQ-associated change at 522 nm in diatoms is reaching 25-30% of the total DT absorption, whereas the absorption at 535 nm is about only 10% of the total zeaxanthin absorption.

The role of PsbS protein -a likely antenna associate -has been in a center of recent mechanistic research on NPQ in plants (Li et al., 2002a, 2002b, 2002c, Aspinal-O'Dea et al., 2002). The amount of this protein was shown to correlate closely with the extent of the fluorescence quenching in vivo (Li et al., 2002c). However so far the presence of PsbS in diatoms has not been shown but a complex with a similar role could be present and its concentration could be increased by intermittent light regime together with the increase of the DD pool size while the antenna size remained constant. It is clear that the next step in the investigation of the NPQ mechanism in diatom algae should be concentrated on the biochemical, biophysical and molecular biological studies of the PSII complexes involved.

Conclusions

Figure 1

 1 Figure 1 shows typical traces of chlorophyll a fluorescence quenching induced by

  Super-NPQ in diatom alga Phaeodactylum tricornutum is closely related to DT concentration. Parallel measurements of NPQ and DT absorption kinetics suggest indirect involvement of this xanthophyll in the fluorescence quenching process. The fast reversible phase of NPQ as well as the 535 nm absorption band are absent in this alga. Fluorescence quenching was found to correlate closely with the absorption change at 522 nm. This band is hypothesised to belong to an activated DT interacting with the NPQ locus in antenna. The hyperbolic type of the fluorescence quenching and gradual co-operative character of NPQ formation are the most fundamental common features of the mechanisms of the excess energy dissipation in diatoms and plants. Due to the low photosynthetic rates and danger of a sudden exposure to excess light NPQ in diatoms can be significantly higher than that in plants and shows more sustained character. The causes of a large NPQ in diatoms could originate from the unique organisation and dynamic properties of light-harvesting antenna components, affinity of a DT binding into the quenching locus and structural properties of this xanthophyll. obligatory event in the regulation of photosynthetic light harvesting. J Biol Chem: 277, 7785-7789 Ruban AV, Pascal AA, Lee PJ, Robert B, Horton P (2002b) Molecular Configuration of Xanthophyll Cycle Carotenoids in Photosystem II Antenna Complexes. J Biol Chem: 277, 42937-42942 Smetacek VA (1999) Diatoms and the ocean carbon cycle. Protist 150: 25-32 Ting CS, Owens TG (1993) Photochemical and non-photochemical fluorescence quenching processes in the diatom Phaeodactylum tricornutum. Plant Physiol 101: 1323-1330 Tréguer P, Nelson DM, vanBennekom AJ, DeMaster DJ, Leynaert A, Quéginer B (1995) The silica balance in the world ocean: a reestimate. Science 269: 375-379 Verhoeven AS, Adams WW, Demmig-Adams B (1998) Two forms of sustained xanthophyll cycle-dependent energy dissipation in overwintering Euonymus kiautschovicus. Plant Cell and Environment 21: 893-903 Wentworth M, Ruban AV, Horton P (2003) Thermodynamic investigation into the mechanism of the chlorophyll fluorescence quenching in isolated photosystem II light-harvesting complexes. J Biol Chem, in press.

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Reversibility of the NPQ level in Phaeodactylum tricornutum cells after

Figure 3 .

 3 Figure 3. Fluorescence traces showing the uncoupler-dependent reversibility of NPQ

Figure 4 .

 4 Figure 4. Relationship between the amplitude of NPQ and time required to recover

Figure 5 .

 5 Figure 5. Relationship between photochemical (qP) and nonphotochemical (NPQ)

Figure 6 .

 6 Figure 6. A. Room temperature absorption spectra of dark-adapted (Dark) and light-

Figure 7 .

 7 Figure 7. Structural formulae of zeaxanthin and diatoxanthin.

Figure 8 .

 8 Figure 8. A. Simultaneous kinetics of chlorophyll fluorescence quenching (open

  Figure 1

Acknowledgements

AVR thanks administration of the Ecole Normale Superieure for invited Professorship and CNRS for a visiting Fellowship during the summer-autumn 2002. JL was supported by the University of Paris VI. This work is supported by UK BBSRC.