MODELING AND IDENTIFICATION OF A UAV WITH A …³es.pdf7 The heart of the data acquisition system architecture, is an on-board computer and control system (NI/MyRio) retrieving information

MODELING ANDIDENTIFICATION OF A UAVWITH A FLEXIBLE WING

Prof. Góes L. C. S., Silva R.A.G, Zuniga, D.F.C., Barbosa, R.C.M.G. and Souza A.G.

[email protected]

Technological Institute of Aeronautics (ITA) - Department ofMechanical Engineering (IEM)

São José dos Campos, São Paulo - Brazil.

1OCTOBER 2019

UAV - EOLO

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INTRODUCTIONINTRODUCTION

THE EOLO UAVTHE EOLO UAV

IDENTIFICATIONIDENTIFICATION

WIND TUNEL CAMPAIGNWIND TUNEL CAMPAIGN

IN-FLIGHT CAMPAIGNIN-FLIGHT CAMPAIGN

CONCLUSIONCONCLUSION

UAV - EOLO

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INTRODUCTION






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INTRODUCTION

This paper resumes preliminary results

of the FINEP/VINNOVA project "Sensing,

Acquisition, and Identification of Flight

Dynamic Systems of Sub-Scale Aircraft

Prototypes.“

This project aims to develop

methodology for flight testing of remotely

piloted aircraft (ARP), as demonstrators of

subscale aeronautical concepts. In

particular to develop inflight aeroelastic

tests of flexible wing aircraft, and subscale

aircraft operating at high angle attack.

ITA – FINEP/VINNOVA PROJECT

Bae hawk

GFF

Éolo

UAV - EOLO

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THE EOLO UAV





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THE EOLO UAV - instrumentation

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The heart of the data acquisition

system architecture, is an on-board

computer and control system (NI/MyRio)

retrieving information of all sensors

onboard the air craft, a microcomputer

(FlightTech SNC-200), an anemometric

system (SpaceAge Subminiature Air

Data Boom 101100), an inertial unit,

accelerometers, strain gauges (CEA-06-

125UW-350), strain rosettes (CEA-06-

250UR-350), electrical actuators and

angular positions sensors.

THE EOLO UAV – general overview

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THE EOLO UAV – mass properties measurements

Accurate values of the inertiamoments and center of gravity (CG)were measured in the Mass Properties Labat the Institute of Aeronautics and Space(IAE), using the Space Electronics device,Model KSR 1320. The principle ofmeasurement of this device is based onthe inverted torsion pendulum concepts.The measurement procedure is shown inthe figure.

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THE EOLO UAV – structural dynamics mathematical model

Starting from the hypothesisthat the airplane is considered acontinuous elastic body it ispossible to obtain its equationsusing the Lagrange Equations andthe principle of the virtual work.

The figure shows the framesdefined with respect to the body.The first hypothesis that allowswriting the structural displacementin a point of the structure of theaircraft like an infinite sum of thecontributions of its normal modes:

� �

�

��

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THE EOLO UAV - mathematical model

The first six equations aredescribed in relation to the bodyreference axis and are formallyequivalent to the classicalequations of the rigid body motion.The last expression is the structuralresponse model in terms of themodal deflectios, �. The model has

� dof, where � is the numberof flexible modes retained in themodel. � represents thegeneralized forces acting in the i-th structural mode and hasaerodynamic origin.

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The aerodynamic forces are assumed to becomposed of a superposition of forces andmoments due to the rigid body motion (labeledR) and due to the flexible response (envelope

). The same strategy is adopted for thegeneralized aerodynamic loads � acting onthe flexible degrees of freedom.

THE EOLO UAV – aerodynamica model

From the strip theory:

The coefficient of lift is:

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THE EOLO UAV - mathematical model

The coefficients for the structuraldynamics are expressed as:

The aeroelastic coefficients �� and

� �̇� are obtained by analyticalexpressions as developed in thereference WASZAK and SCHMIDT, 1988 orestimated by means of parameterestimation from in-flight test data (Pfiferand Danowsky, 2016).

These sums are added linearly tothe equations of rigid body motion ofthe aircraft, so that no majormodifications are required forapplications of the same identificationmethods used for rigid body dynamics.

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The longitudinal dynamics is a special case, where � = � = � = 0. The motion is restricted to theplane os symmetry, oxz, like shown the figure.

The longitudinal motion is normally represented by small displacements from an equilibrium(unaccelerated) flight condition in the longitudinal plane. An approximation of short perioddynamics are presented below according to the work of Pfifer H., and Danowsky B.P. (2016)

THE EOLO UAV - longitudinal dynamics

UAV - EOLO

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IDENTIFICATION




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UAV - EOLO

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IDENTIFICATION

Aerodynamics

Subspace methodSubspace method

Modal - GVT EMAModal - GVT EMA

Modal - GVT OMAModal - GVT OMA

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IDENTIFICATION – aerodynamic (EKF method)

ESDU 88039

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For the measurement of states it was used a simulator of the longitudinal dynamics of the Eolo.This simulator was create in a MatLab software code. For this scenario only the states � and q areconsidered measurable.


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Applying the Kalman filter to estimates the states:

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Applying the Kalman filter to estimates the aerodynamics parameters:

UAV - EOLO

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IDENTIFICATION

Aerodynamics

Subspace method

Modal - GVT EMAModal - GVT EMA


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MODELING – A preliminary UAS modelIt was implemented in MATLAB/SIMULINK asimulation environment from previous estimates ofthe UAS model parameter just to providesynthetic data to perform a closed-loop systemidentification since that real experimental datanot available yet.

Trimmed values in equilibrium (“trim”) condition of thestraight and level cruise at velocity V=25m/s and altitudeH=1100m.

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A velocity root-locus for UASThe eigenvalues of the vehicle dynamics corresponding to a true velocity from 13m/s to 61m/s. In thiscase, the flutter phenomenon can not be observed yet because only one flexible mode wasinserted in the simulation environment.

As shown, if the aircraft is flexible the rigid modes are influenced providingmore damping to short-period mode. Initially, the phugoid mode is unstablein both open-loop cases, in the same way, the damping increase with truevelocity variations.

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Trust-to-state-variables frequency response

Note that the flexible mode affectmost significantly the pitch-rateand the pitch-attitude responses.

Both the magnitude and phase plotsshow the longitudinal motionapproximation for the flight trimcondition at V=25m/s and H=1100m.

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Elevator-to-state-variables frequency response

In this case, boththe magnitude andphase plots notdiffer significantly bythe presence of theflexible mode.

This means that in this operation point thestructural flexibility does not appear intime responses and should not be sodetrimental to the control system designbased only in rigid dynamic a priori.

At this point, is important toinclude the effect of the otherflexible modes observedpreliminary by GVT tests.

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• Closed-loop system data of anpicth-atitude autopilot.

• “trim condition: V=13m/s andH=1100m.

Y��=

��

�̇�

An attitude-hold autopilot implemented in MATLAB/SIMULINK.

DATA GATHERING FOR CLOSED-LOOP SYSTEM IDENTIFICATION

U�� = [��]

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IDENTIFICATION – closed loop identification (subspace method)

A subspace method applied bothopen-loop and closed-loop data namedDSR (combined deterministic and stochasticsystem identification and realization)algorithm.

The system is represented by a discrete-time stochastic linear model as given

In formulation of the subspaceidentification problem, it is necessary to denean extended state-space model just togenerate the data space formed by blockHankel matrices of the input and output data.

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The projection equation is given by

Applying a singular valuedecomposition in the projectionmatrix

IDENTIFICATION – closed loop identification (subspace method)

The observability matrix is given by

An estimated state sequence of the sytem is

Thus, from the input-output data and estimatedstate sequence, it is possible to solve the least-squares problem to determine the systemmatrices �∈ ℜ�×�, B ∈ ℜ�×� and the filter Kalmangain �∈ ℜ�×� up to within a similaritytransformation.

� � � = ��/�/��/�

��/�(��)

29Model output prediction using the DSR_e algorithm.

Closed-loop subspace identification

Validation index: the MRSE(mean relative squarederror), in percentual (%).

Time histories of manuever used for identification andthe corresponding energy espectrum.

Reference signal

Control input

Y��=[� V � � �� ̇�]T

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Closed-loop subspace identification

Singular Value Decomposition (SVD)using past horizon J=140 and futurehorizon L=2. The order n=8 wasadopted for the model.

Magnitude and phase plots of the identified model from closed-loop systemdata corrupted by measurements noise. In blue, the identified model. Inblack, the simulated preliminarly UAS model.

UAV - EOLO

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IDENTIFICATION

Aerodynamics

Subspace method

Modal - GVT EMA


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IDENTIFICATION – modal (EMA and GVT setup)

Electromagnetic Shaker and

ICP powertransducer

SCADAS LMS

ICPAccelerome

ters

Free-freesupport

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IDENTIFICATION – modal (EMA - FRF and Coherence)

Excitation Estimator Averages Windowing Bandwidth Spectrallines

Resolution

Burts Random H1 50 Hanning 50 Hz 1024 0.049 Hz

EMA Driving Point FRF

EMA Driving Point Coherence

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IDENTIFICATION – modal properties from EMA analysis

UAV - EOLO

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IDENTIFICATION

Aerodynamics

Subspace method

Modal - GVT EMA

Modal - GVT OMA

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IDENTIFICATION – modal (OMA – GVT)

Left semi-wing acceleration responsesRight semi-wing acceleration responses

Strain responses

The supporting system for GVT-OMA was thesame that for GVT-EMA

Excitation with impulsive inputs Internal instrumentation was used for

response recording.

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IDENTIFICATION – modal properties from OMA Analysis

UAV - EOLO

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WIND TUNEL CAMPAIGN



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WIND TUNEL CAMPAIGN

For this essay, it was programmed to increasethe speed in 5 km/h for every 2 minutes until amaximum speed at 55 km/h (for the wind tunnelair speed).

The UAV was beingpiloted outside the

tunnel

Due to the large wingspan, thetest was realized outside the

typical section test.

Pitot - airspeed inthe windtunnel.

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WIND TUNEL CAMPAIGN - On board collected data accelerometers

The left side of the wingThe right side of the wing

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WIND TUNEL CAMPAIGN - OMA Analysis

Fdd of theaccelerometers data

Wind tunnel air speedy25 km/h (6.94 m/s)

Mode Frequency [Hz]

1st wing S bending 4.150

Tail-boom torsion

1st wing A bending 11.328

1st Fus bending+ 2nd SWB+ SWT 14.966

1st S Torsion 19.605

1st A Torsion + 2nd SWB 21.045

2nd AWB 30.518

3rd SWB 34.888

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Fdd of theaccelerometers data.

Wind tunnel air speedy40 km/h (11,11 m/s)

Mode Frequency [Hz]


Tail-boom torsion



1st S Torsion


2nd AWB 30.542

3rd SWB 34.790

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Wind tunnel air speedy50 km/h (13.89 m/s)

Mode Frequency [Hz]


Tail-boom torsion



1st S Torsion


2nd AWB 30.933

3rd SWB 35.425

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Wind tunnel air speedy55 km/h (15,28 m/s)

Mode Frequency [Hz]

1st wing S bending

Tail-boom torsion

1st wing A bending


1st S Torsion


2nd AWB 31.397

3rd SWB 35.840

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0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60

Fre

qu

en

cy

[H

z]

Velocity [ km/h ]

1st wing S bending

1st wing A bending

1st Fus bending+ 2nd SWB+ SWT

1st S Torsion

1st A Torsion + 2nd SWB

2nd AWB

3rd SWB

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IN-FLIGHT CAMPAIGN


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IN - FLIGHT CAMPAIGN

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IN - FLIGHT CAMPAIGN - OMA Analysis


Air speedy 25 knots(12.86 m/s)



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IN - FLIGHT CAMPAIGN - OMA Analysis





UAV - EOLO

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CONCLUSION

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CONCLUSION AND ONGOING WORKS

This article is ongoing research that will consist ofvalidating the simulator dynamic using experimental data.

From the synthetics data, it was possible to apply the EKFmethod to identification of the aerodynamics derivativesand compare them with well known the results such as AVLand Waszack formulation.

The model identification with the subspace model swasapplied to synthetic data obtained wit a simulation modelusing the aerodynamic derivatives calculated by theWaszack formulation and also with AVL simulation. Bothmodels considered just one flexible mode. With the GVT andthe wind tunnel campaign it was possible to identify sevenflexibles modes. The in-flight test has just started, and a firstanalysis shows approximately the same modal behavior,

The next step of this research will be the completeidentification of aerodynamics and control derivatives usingin-flight data and a theorical considering more flexiblemodes.

UAV - EOLO

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53

Souza, A. G.; D. C. Zuniga ; GOES, L. C. S. ; SOUSA, M. S. (2019)Parameter Identification for a Flexible Unmanned Aerial Vehicle UsingExtended Kalman Filtering DINAME 2019

D. C. Zuniga. ; Souza, A. G; GOES, L. C. S. (2019)Development of an Aeroelastic In-Flight Testing System for a Flexible WingUnmanned Aerial Vehicle using Acceleration and Strain Sensors AIAA 2019

D. C. Zuniga. ; Souza, A. G; GOES, L. C. S. (2019)Operational Modal Analysis using Impulsive Input of a Flexible WingUnmanned Aerial Vehicle DINAME 2019

Souza, A. G.; D. C. Zuniga ; GOES, L. C. S. ; SOUSA, M. S. (2018)Identificação de parâmetro da dinâmica longitudinal de uma aeronaveflexível usando o método de erro na saída CONEM 2018

D. C. Zuniga. ; Souza, A. G; GOES, L. C. S. (2019)Flight dynamics modeling of a flexible wing unmanned aerial vehicle ICEDYN2019

D. C. Zuniga. ; Souza, A. G; GOES, L. C. S. (2019)Planning of an in-flight aeroelastic testing of a flexible unmanned aerialvehicle using a combined accelerometers-strain sensors operational modalanalysis ICEDYN 2019

BARBOSA, R. C. M. G.; GOES, L. C. S. ; SOUSA, M. S. (2019)Closed-loop System Identification of an Unmanned Aerial System (UAS) with Flexible Wings using Subspace Methods. DINAME 2019

BARBOSA, R. C. M. G.; GOES, L. C. S. (2018)Closed-loop system identification of a large flexible aircraft using subspacemethods. ICAS 2018

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Thank you for your attention…

Questions?

Prof. Luiz Carlos Sandoval Gó[email protected]

Aeronautics Institute of Technology – ITADepartment of Mechanical Engineering (IEM)

Documents

MODELING AND IDENTIFICATION OF A UAV WITH A …³es.pdf7 The heart of the data acquisition system architecture, is an on-board computer and control system (NI/MyRio) retrieving information