Load Control in Highly-Deforming Aeroelastic Systems

Rafael PalaciosDepartment of Aeronautics

http://www.imperial.ac.uk/aeroelastics

Seminar at Vibration UTC, MED30 April 2014

Load Control and Aeroelastics: Research Topics

Computational methods for FSI

Load control in large wind turbines

Dynamics & control of flexible aircraft

Load Control - Overview

Motivation: ever more efficient airframes perpetual flight

Approach: A framework for Simulation of High-Aspect Ratio Planeso Aeroelasticity with large-displacementso Coupling with flight dynamics

Model reduction and control

Examples:o Dynamic stability of very flexible aircrafto Gust alleviation strategies wake encounter

o On-going work

Quick Quiz

Q: What do this companies have in common?A: They all announced a solar-powered aircraft project in April 2014

The challenge of very high efficiency

Extreme efficiency: Solar-powered planes for perpetual flight

QinetiQ Zephyr 7 Span: 22.5 m Weight: 53 kg Flight altitude: 60,000 ft Payload: 2.5 kg Power: Solar panels

Li-S batteries

Solar Impulse 2

see movie

http://www.youtube.com/watch?v=2GbIjALFSP4

B787 (www.aviationweek.com

Large (and flexible) wings on transport aircraft

Who is not interested in higher efficiency?

[source:USPTO]

NASA X-56A

Boeing SUGAR Volt

The Great Flight Diagram*

Wei

gh

t

Wing loading

Conventional aircraft

Solar-powered

Birds

*Noth (2006). Design of Solar Powered Airplanes for Continuous Flight, PhD thesis, ETH

Power management:

The challenge of very high efficiency

Modelling of (very) flexible aircraft dynamics

Some major modelling challenges:

1. Design for jig shape

2. Validity of linear methods even more restricted in flight envelope (e.g., gust loads)

3. Blurred boundaries between aeroelasticity, flight dynamics, and control

Our objective:

Apparent stiffness by means of dynamic load control systems

Modelling of (very) flexible aircraft dynamics

FLUID MECHANICS

STRUCTURAL MECHANICS

RIGID-BODYDYNAMICS

Flight MechanicsAeroelasticity

Flexible Body Dynamics

CONTROL

Flow Control

Vibrationsuppression

Navigation

...and this is geometrically nonlinear

Modelling of (very) flexible aircraft dynamics

Drela (1999): ASWing Nonlinear beams Unsteady lifting line PID control

Patil (1999) & Cesnik (2002) Nonlinear composite beams Unsteady thin aerofoil LQG control

von Flotow (1989): Daedalus Linear beams Unsteady thin aerofoil No controls

(Patil & Hodges, 2006)Wang (2010) Nonlinear beams Unstedy Vortex Lattice No controls

Overview

Motivation: ever more efficient airframes perpetual flight

Approach: A framework for Simulation of High-Aspect Ratio Planeso Aeroelasticity with large-displacementso Coupling with flight dynamics

Model reduction and control

Examples:o Dynamic stability of very flexible aircrafto Gust alleviation strategies wake encounter

o On-going work

Flexible Aircraft Dynamics Simulation (SHARP)

SHARP: Structural Dynamics

SHARP.Cells: Homogenisation of periodic structures*

*Dizyetal. Homogenizationofslenderperiodiccompositestructures,IJSS50(2013)

http://dx.doi.org/10.1016/j.ijsolstr.2013.01.017

Condensation of large FE models*

Stiffness model Lumped mass model

Tree of master nodes (ASET) along wings, fuselage, etc.

Lumped masses

3-D FEM

Guyan reduction

Nodal displacements/ rotations

Modal basis Modal velocities and internal forces

Identify coefficients in nonlinear modal EoM

Modal Intrinsic

In modal coordinates

Back to 3-D through Guyan transformation

Solve 1-D nonlinear

*Wangetal. AMethodforNormalModeBasedModelReductioninNonlinearStructuralDynamics, underreview

= q q + L(q)q + Q( ) 0a a aj + =2j M K

SHARP.Beams: Geometrically-nonlinear composite beams

Rigid-body DoF Structural DoF

aR = at FE nodesa

a

v

=

Nonlinear equations of motion

Propagation of body-attached FoR

( ) ( ) ( ) ( ), , , , ,gyr stif extM Q Q Q

+ + =

0 0 0 0

0( ) ( ) ( ) =gyr stiff ext, Q

+ +

M C K

Linearized equations

SHARP.Beams: Geometrically-nonlinear composite beams

*Hesse,Palacios.Consistentstructurallinearizationinflexiblebodydynamicswithlargerigidbodymotion, Comp&Struct 110(2012)

(Simo et al, 1988)

Free-flying flexible beam in vacuum (no gravity)*

http://dx.doi.org/10.1016/j.compstruc.2012.05.011

Flexible Vehicle Structural Dynamics

Adding the unsteady aerodynamics

Structure to Aerodynamics Aerodynamics to structure

Unsteady Vortex Lattice Method (UVLM)

Vortex-ring discretization (Katz & Plotkin, 2001) Potential flow, thin wing Low speed flight, attached flow 3-D, unsteady, free-wake, interference, large (but slow) displacements

Propagation step:

Output step*:

( )

( ),

st

kunst k ct

=

=

F U l

F U l

*Simpsonetal.InducedDragCalculationsintheUnsteadyVortexLatticeMethod, AIAAJournal61 (2013)see movie

http://dx.doi.org/10.2514/1.J052136https://workspace.imperial.ac.uk/aeroelastics/Public/ppt/GolandFlutter.mpg

Monolithic Coupling (linear problem)

Discrete-time state-space formulation* Linearization around given configuration (usually trim) Frozen geometry assumption Prescribed wake

*Muruaetal. Applicationsoftheunsteadyvortexlatticemethodinaircraftaeroelasticityandflightdynamics JPAS55(2012)

http://dx.doi.org/10.1016/j.paerosci.2012.06.001http://dx.doi.org/10.1016/j.paerosci.2012.06.001

Flexible aircraft dynamics (linear/nonlinear)

Flexible aircraft dynamics (linear/nonlinear)

Stability of very light HALE UAV*

Flexible main wing Rigid fuselage and T-tail Total mass: 75.4kg 20km altitude

*Hesseetal.(2014)ConsistentStructuralLinearizationinFlexibleAircraftDynamicswithLargeRigidBodyMotion,AIAAJournal

HALE model characteristics (Patil, 2001)

Aspect ratio 16

Elastic axis (from le) 50 %

Center of gravity (from le) 50 %

Mass per unit length 0.75 kg/m

Torsional rigidity 1104 Nm2

Bending rigidity 2104 Nm2

Trim at V=30m/s

: stiffness parameter

https://spiral.imperial.ac.uk:8443/handle/10044/1/11697

Stability analysis of full aircraft

Phugoid Short period SpiralRigid -0.0110.27i -4.531.67i -0.064

Flexible -0.00440.30i -2.181.57i -0.088

LINEARIZEDISCRETE-TIMESYSTEM MATRIX

TRIM AIRCRAFT(Nonlinear)

EIGENVALUE ANALYSIS

V=30m/s =2

Dynamic stability vs. stiffness

Dynamic stability directly from physical degrees of freedom

Closing the loop

Closing the loop

Linear subsystem

Dynamic aeroelasticity of manoeuvring aircraft

FLEXIBLE-BODYDYNAMICS

AERODYNAMICS

1n n n nS A A

n T nA

A B u B u

y C

+ = + +

= Ay

Au

u

( ) ( ) ( ) ( )0 0 0, , , , ,0T T T T

ext

q q qM C K Q q q

+ + =

Dynamic aeroelasticity of manoeuvring aircraft*

Small number of inputs and outputs (structural modes + rigid body) Model reduction through balanced truncation

o Balance aerodynamic states using controllability/observability Gramianso Truncate least controllable and observable states

AERODYNAMICS

Ay

Au

u

1n n n nS A A

n T nA

A B u B u

y C

+ = + +

=

1 1 1 1n n n nB B S A An T nA B

T AT T B u T B u

y CT

+ = + +

=

BT =

B

AERO-DYNAMICS

*Hesseetal.ReducedOrderAeroelasticModelsfortheDynamicsofManeuveringFlexibleAircraft,AIAAJournal(2014)

http://dx.doi.org/10.2514/1.J052684

Load Alleviation for a HALE UAV

Composite beam

Nonlinear Trim

Dynamic Stability

Linear Plant

Loads Plant

Linear ROM

Loads ROM

Load Simulation

HinfSynthesis

Load Alleviation

Wake Vortex Encounters (WVE)

Kier, T, 2011. An integrated loads analysis model including unsteady aerodynamic effects for position and attitude dependent gust fields. IFASD 2011.

Generating wake modelled following Kier (2011)

Wake vortices modelled as vortex filaments from

bG= 50 m, WG=2800 kg, VG= 8 m/s

Biot-Savart Law and exponential decay around

viscous core radius

Are wake encounters important?

Open-Loop results*

*HesseandPalacios.DynamicLoadAlleviationinWakeVortexEncounters,underreview

Hybrid control for load alleviation

aileron Sflap S

elevator P elevator S

flap Paileron P

bending strains S

Linear ROM for control synthesis (50 states)

H controller

Robustness vs. performance (actuator constraints

not in the model)

Control surface inputs to root bending strain

Hybrid control for load alleviation

Load envelopes for open and close loop responses

Effective approach for load alleviation less structure less weight

Right wingLeft wing

Towards Predictive Control

1-cos gust on cantilever wing Control via trailing edge flap MPC vs. LQR with same weights

Roo

t to

rsio

nR

oot

ben

din

g

timetime

Flap

def

lect

ion

*Simpson et al. (2014). Predictive Control for Alleviation of Gust Loads on Very Flexible Aircraft. AIAA SciTech, Washington, DC

see movie

http://hdl.handle.net/10044/1/12917https://workspace.imperial.ac.uk/aeroelastics/Public/ppt/GolandMPC.avi

Applications to wind energy*

*Ngetal.(2014)EfficientAeroservoelasticModelingfortheControlofTrailingEdgeFlapsonWindTurbines,UKACC

NREL 5-MW test case in storm (gusty wind and waves) Flaps actuated to reduce blade loads

see moviesee movie

https://workspace.imperial.ac.uk/aeroelastics/Public/ppt/WT_float1b.gifhttps://workspace.imperial.ac.uk/aeroelastics/Public/ppt/WT_float3b.gif

Conclusions

Physics-based state-space realizations of 3-D aeroelasticity with potential-flow unsteady aerodynamics

Coupling of rigid-body, structural, unsteady aerodynamics, and control system. Monolithic approach.

integration of load alleviation strategies in Flight Control System

Demonstration on Wake Encounter Loads

On-going work:o Coupling with RANS (no longer monolithic!)o MPC implementation for simultaneous flight & load control

Load Control in Highly-Deforming Aeroelastic SystemsLoad Control and Aeroelastics: Research TopicsLoad Control - OverviewQuick QuizThe challenge of very high efficiencyLarge (and flexible) wings on transport aircraftThe challenge of very high efficiencyModelling of (very) flexible aircraft dynamicsModelling of (very) flexible aircraft dynamicsModelling of (very) flexible aircraft dynamicsOverviewFlexible Aircraft Dynamics Simulation (SHARP)SHARP: Structural DynamicsSHARP.Cells: Homogenisation of periodic structures*Condensation of large FE models*SHARP.Beams: Geometrically-nonlinear composite beamsSHARP.Beams: Geometrically-nonlinear composite beamsFlexible Vehicle Structural DynamicsAdding the unsteady aerodynamicsUnsteady Vortex Lattice Method (UVLM)Monolithic Coupling (linear problem)Flexible aircraft dynamics (linear/nonlinear)Flexible aircraft dynamics (linear/nonlinear)Stability of very light HALE UAV*Stability analysis of full aircraftDynamic stability vs. stiffnessClosing the loopClosing the loopDynamic aeroelasticity of manoeuvring aircraftDynamic aeroelasticity of manoeuvring aircraft*Load Alleviation for a HALE UAVWake Vortex Encounters (WVE)Are wake encounters important?Open-Loop results*Hybrid control for load alleviationHybrid control for load alleviationTowards Predictive ControlApplications to wind energy*Conclusions