IDENTIFICATION OF THE AEROELASTIC MODEL OF A LARGE TRANSPORT CIVIL AIRCRAFT FOR CONTROL LAW DESIGN AND VALIDATION

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1 ICAS 2 CONGRESS IDENTIFICATION OF THE AEROELASTIC MODEL OF A LARGE TRANSPORT CIVIL AIRCRAFT FOR CONTROL LAW DESIGN AND VALIDATION Christophe Le Garrec, Marc Hmbert, Michel Lacabanne Aérospatiale Matra Airbs 316 Rte de Bayonne 316 Tolose Cedex France Abstract Since the introdction of the digital technology into flight control systems the strctral behavior is an important isse of the control law design, firstly to garanty that no instability of a flexible mode is created by the flight control law. However, if a model of the strctral dynamics is in hand, in a form convenient for control design, the flexible mode behavior can be changed from a constraint into a new objective of the control design, offering a wide range of new benefits for the aircraft : ride qality improvement, passenger comfort agmentation, dynamics load redction Sch models can be derived in the state space form from the fltter theoretical models, bt if flight test reslts are available better models are obtained by a direct identification of this model from flight test data. This paper presents an identification procedre of an aeroelastic state space model from flight data, for control law design and validation prposes. The procedre is split into a first estimation of the model by the E.R.A ( Eigensystem Realization Algorithm) followed by a model refinement sing the otpt-error minimization procedre.. Flight tests reslts on a large civil transport aircraft are presented. 1. Context and Objectives Flight mechanics modelizations for control law synthesis have been developed and sed indstrially for a long time. These models are derived from the non linear flight mechanics eqations, and may take into accont many refinements: non linear aerodynamics, introdction of static flexibility effects, adjstment of aerodynamic data from wind tnnel tests In addition to this theoretical modelization process, in-flight identification of the flight mechanics behavior, with dedicated flight tests, is now a common practise. After this identification, a very high accracy is sally obtained, offering the possibility to adjst the control law, or to provide a simlation for the training simlators. With the Airbs A32 and the introdction of the fly-by-wire technology, the strctral dynamics has become an important isse of the design of a flight control system of a civil aircraft. On this aircraft the strctral dynamics was taken as a constraint of the control law design, by setting specific stability margins at the flexible modes freqencies. This constraint was passed throgh with a filtering of the control law, which excldes the flexible modes otside of the bandwidth of the controller. A break in this passive approach was achieved on the Airbs A34, with the first introdction of a flexible mode control throgh the EFCS in a civil aircraft (CIT, Comfort In Trblence). This specific fnction increases the damping of some fselage modes, providing therefore an improvement of passenger comfort. The active approach will be pshed frther on the stretched versions of the A34, with 412.1

2 Christophe Le Garrec, Marc Hmbert, Michel Lacabanne the integration of the strctral dynamics objectives inside the whole control law design process, offering optimal handling qalities together with a flexible mode control in the whole flight domain. This last step is now possible thanks to the development in Aérospatiale-Matra-Airbs of control methodology dedicated to flexible aircraft [1], together with progress in flexible aircraft modelization. When sing the active approach the strctral dynamics modelization is an important stage of the flight control design process. Today s state-of-the-art methodologies sed in aeroservoelasticity (Finite element models, adjstement on grond vibration test, nsteady aerodynamic comptation with doblet lattice or CFD methods, transformation in the state space form of aeroelastic eqations) provide theoretical models accrate enogh for a first design of flexible modes control. However, in a way similar to the flight mechanics procedre, significant improvements of the control performance on the strctral dynamics aspects can be obtained by an adjstment of the controller on flexible aircraft models identified dring flight test. This paper focses on this identification qestion. A methodology for identification of flexible aircraft models for control law design is presented. The link with the sal rigid body identification, and the flight test procedre are addressed. Then some reslts of this methodology on flight test reslts of a large civil test aircraft are shown. Finally, ftre ses of these identified flexible aircraft models, in addition to the original control law design needs are discssed. 2. Aeroelastic Model Identification Procedre 2.1. Model Identification and Model Adjstment The identification of the flight mechanics models can be directly transformed into an identification of aerodynamic coefficient. By this relation, the rigid body identification process can be moreover seen as an adjstement of data of the theoretical model. The flight test identification can be sed to adjst theoretical models at conditions different from the test conditions (eg different cg positions, aircraft mass, dynamic pressres). Sch simple relations between model data (mass, stiffness or aerodynamic data) and model coefficient do not exist on aeroelastic model. Therefore, model identification and model adjstement are two different qestions and ask for different methodologies. This paper concentrates on the identification qestion only : how to extract from flight data only (withot any previos theoretical knowledge) aeroelastic models sitable for control law design? The qestion of aeroelastic model adjstment is addressed in ref [2] General algorithm The algorithm is divided into two main steps: 1/ identification of the implse responses of all the otpts excited throgh all the inpts. 2/Calclation of the aeroelastic state space model from the implse responses sing the ERA (Eigenspace Realization Algorithm) [3] method. A flexible model of the strctre is obtained, which inclded a participation of rigid modes of the aircraft. The next paragraph will show how this interference 412.2

3 IDENTIFICATION OF THE AEROELASTIC MODEL OF A LARGE TRANSPORT CIVIL AIRCRAFT FOR CONTROL LAW DESIGN AND VALIDATION from the rigid body movements is managed. Now let s detail the two steps : 1/Calclation of implse responses Each implse response is calclated individally for any inpt/otpt throgh this process: The convoltion prodct of the term of the implse response g l with the inpt gives the otpt y : yj k l gl * j l This eqation in the matrix form is: [ y y1 ym] [ g gk] 1 M M M 1 k this overdetermined system is solved with a Singlar Vale Decomposition (SVD) algorithm. 2/Calclation of state space model With all the implse responses for all the inpt/otpt it is possible to bild a Hankel matrix of the system and then throgh the ERA process calclate the state space model. A chart of this method is presented in fig 2. A description of the Hankel matrix sed is given as well as the expression of A,B,C,D (the matrix of the state space system) from this Hankel matrix is given below: The implse response k of a discrete state space system can be expressed as: D, 1 CB 2 CAB, k CA k-1 B The form of the Hankel matrix is: k k + H ( k 1) k + α 1 1 k + 1 k + 2 k + α k + β 1 k + β k + α + β 1 if k1 we have: 1 2 H () α α β 1 + β α + β 1 Identifying with the implse response of a discrete state space system the Hankel matrix can be expressed as: H(k-1) P α A k-1 Q β (1) Where : P Q α β C CA 2 CA α 1 CA 2 β 1 [ B AB A B A B] P α : Controllability matrix Q β : Observability matrix Applying eq (1) with k1 gives: H() P α Q β H() R n Σ n S n T reslt of the SVD of H() T T where R n R n S n S n I n with I n matrix (n,n)identity A soltion for P α and Q β may be: P α R n Σ n 1/2 from (1): H(1) P α ΑQ β Q β Σ n 1/2 S n T (2) With P α, Q β evalated in (2) ; so H(1) R n Σ n 1/2 A Σ n 1/2 S n T The soltion for the matrix A is then : AΣ n 1/2 R n T H(1) S n Σ n 1/2 B and C are given by : B Σ n 1/2 S n T E r C E T mr n Σ n 1/

4 Christophe Le Garrec, Marc Hmbert, Michel Lacabanne Where : E E T m T r [ Im Om Om] [ I O O ] r m nmber of otpt and r nmber of inpt, with I i identity matrix of order i O i nll matrix of order i H(1) and H() are evalated throgh the implse responses calclated with the method described before Link with the flight mechanics model In the identification process it is spposed that a rigid model response and a strctral model response are smmed together to correctly represent the global response. At this moment the aeroelastic model identified contains both the rigid and the strctral part of the response of the aircraft. To have a pre strctral model, the rigid body movement participation mst be removed. An otpt-error minimization method is carried ot on the aeroelastic model together with a flight mechanics model to remove the bias de to rigid body movements. Either a rigid model identified from flight tests at the same flight point, or a theoretical model may be sed for this process. Dring the otpt error minimization process, the parameters of the aeroelastic model only are adjsted to stick to flight data. The integration of this step is explained in the overall chart of the identification procedre given in fig Flight test process To get the flight data necessary to the method describe above, the aircraft is excited with all the inpts sed by the controller. Rigid body tests are performed at the same flight point to provide an accrate flight mechanics model. Sine sweeps excitations in the freqency range r r of the first strctral modes are sed to identify the strctral dynamics. Different flight conditions and mass cases are flight tested to provide the control law designer with the sfficient nmber of models for control law tning and robstness checks. 3. Example of flight test reslts Reslts of the identification of a large civil aircraft in landing configration are shown in appendix. This flight point can be considered as a very difficlt one, de to a very noisy environment indced by separation on the high lift devices. Time domain flight test reslts with all the inpts are shown in fig 4, whereas an example of comparison between test reslts and time domain simlation with the identified model is given in fig 5. The mode selection is gided by the hankel matrix singlar vales plot and the stabilization diagram, shown in fig 3. One can see in fig 5 that a very good fit between test and simlation reslts is obtained; A frther check is offered by the analysis of the error signal (colmn 4) that is decorrelated from the excitation. The mathematical form, size and accracy of the identified aeroelastic model flfil the reqirements of the design of an active control of the strctral dynamics throgh the flight control system. 4. Conclsions. Additionnal ses of identified aeroelastic models The need for an identification of the strctral dynamics has grown in Aérospatiale Matra Airbs with the development of the flexible aircraft flight control laws, that insre a control of the flexible modes dynamics as well as the flight mechanics mode. It has been shown in this paper that aeroelastic state space models relevant for control law design can be extracted from flight test data, providing 412.4

5 IDENTIFICATION OF THE AEROELASTIC MODEL OF A LARGE TRANSPORT CIVIL AIRCRAFT FOR CONTROL LAW DESIGN AND VALIDATION the possibility to improve the strctral mode control dring the flight test campaign. In addition to the control law synthesis, sch models allow other applications in the field of aeroservoelasticity. Once the control law is designed, identified models can be sed dring the validation step : aeroservoelastic stability, performance of the flexible mode control, comfort evalation can be carried ot in some cases with identified models, completing the validation performed with theoretical models. Sch applications of identified aeroelastic models do not mean that the theoretical model is forgetten when the identification has been carried ot. It remains the first modelization for stability and performance demonstrations of the flight control system with respect to flexible modes isses. Identified models are limited to the specific flight and mass conditions flight tested. Moreover, the identification procedre provide only black box models, withot any nderstanding of the dynamic behavior, or help in the search for improvement. For these reasons, progress in flexible aircraft modelization is still of first importance in aeroservoelasticity, and is complementary of flight test aeroelastic model identification. References [1] F Kbica. New flight control laws for large capacity aircraft. Experimentation on Airbs. ICAS, [2] S Prdhomme, C Blondea, M Hmbert, A Bcharles: An nsteady aerodynamics identification procedre for fltter prediction. International form on aeroelasticity and strctral dynamics 1999, Williamsbrg [3] Jer-Nan Jang. Applied system identification

6 Christophe Le Garrec, Marc Hmbert, Michel Lacabanne Fig 1 : GENERAL CHART OF THE IDENTIFICATION PROCEDURE Flight data (Us,s) Theorical rigid Model Flight data (Ur, r) Least sqare Otpt-Error minimization method Implse response ERA As,Bs,Cs,Ds Flight Mechanic Model (Ar,Br,Cr,Dr) Redction Otpt-error minimization method Strctral Model (As,Bs,Cs,Ds) Comprehensive Model (Ac,Bc,Dc,Dc) 412.6

7 IDENTIFICATION OF THE AEROELASTIC MODEL OF A LARGE TRANSPORT CIVIL AIRCRAFT FOR CONTROL LAW DESIGN AND VALIDATION Fig 2 : CHART OF THE ERA METHOD Plse-response fnctions (Markov parameters) Hankel matrix H() Left singlar vectors Singlar vales Right singlar vectors Time shifted Hankel matrix H(1) Otpt matrix State matrix Inpt matrix Eigensoltion Mode shape eigenvectors eigenvales Natral freqencies and Modal damping eigenvectors Modal amplitde Redced model Reconstrction and comparison with data Fig 3 : STABILIZATION DIAGRAM 412.7

8 Christophe Le Garrec, Marc Hmbert, Michel Lacabanne fig 4 : FLIGHT TEST DATA 412.8

9 IDENTIFICATION OF THE AEROELASTIC MODEL OF A LARGE TRANSPORT CIVIL AIRCRAFT FOR CONTROL LAW DESIGN AND VALIDATION Fig 5 : COMPARAISON BETWEEN FLIGHT TEST RESULTS AND IDENTIFIED AEROELASTIC MODEL (inner aileron excitation) 412.9