NAFEMS_RB_presentation

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3DS.COM©DassaultSystèmes|ConfidentialInformation|6/8/2015|ref.:3DS_Document_2012
Simulation and Validation of Active Control of Limit
Cycle Oscillation in Aeroelastic Systems (Cyber-
Physical Systems)
Ron-Bin Cheng
Technical Specialist, Dassault Systemes SIMULIA Corp.

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What is L-C-O in Aeroelastic Systems?
It’s a vibration issue of airfoil structure coupling with aerodynamics.
In certain circumstance there exists a consistent vibration
phenomenon called Limit-Cycle-Oscillation that causes the “Angle of
Attack”(torsion) and “Plunge”(bending) harmonically oscillating
motions of a wing structure during cruising within a range of speed.
In general, LCO is induced by structural and aerodynamic
nonlinearities, and is triggered by angle of attack.

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LCO of Wing Structure
--> Physical phenomenon: Limit-Cycle-Oscillation induced by wing structure coupling
with aerodynamics. (ref. to Strganac’s paper)

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 Theoretical Background and Control Key (Ideal lumped 2-D model)
 Design Process and Co-Sim Models (from low to high fidelity)
 Hydraulic Actuators and PIDs Performance Study
Brief Overview
 Simulation Results and Controller Data Extracted from FSI Simulations
Objective of this Work
 Model Co-Simulation to reproduce LCO and achieve the effective control
result comparable to experimental data.
 Workflow Summary and a Derivative Design
 Ultimate goal of Co-Simulation model: detailed FEM structure + CFD
simulation + Flap control algorithm + Hydraulic servo actuator
 Develop a reliable design workflow

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Theoretical Background and Control Key (2-D Lumped)
a controller changes flap surface for generating lift force/moment against the airflow force/ moment.
Structural dynamics
Aerodynamic lift force and drag moment
Three-Way Physics Coupling:
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hChKC
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Ug
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Flap angle feedback control

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hChKC
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state-space representation of 3-way coupling:
According to the control idea, flap angle can be designed as follows:
Where these terms are used to cancel out the
nonlinearity of f(x) for ‘alphaDot’ equation , i.e.
Therefore, the ‘alphaDot’ equation is ideally:
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  21 

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Linear Equation of “alpha”(ideal case):
  21 
By designing v1 and v2, “alpha” may be controlled in a good performance!
Example, v1 = 250 ; v2 = 25 (Controller turned on @ 5s in Dymola): Performance can be
designed by selecting
values of v1 and v2 with
good damping effect.

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Design Process and Co-Sim Models (from low to high fidelity)
 In addition to 3-way coupling, a hydraulic actuator driving flap surface is added for higher fidelity.
 4-code Co-Simulation
Avionics
Target flap angle
Measured
flap angle
Aerodynamic loading
Structure
Measured
plunge &
pitch
Measured
plunge &
pitch
Aerodynamic
loads
Torque
Hydraulic Actuator
(Abaqus/Standard)
(Abaqus/CFD)
Dymola

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Avionics
Aerodynamic loading
Structure
Hydraulic Actuator
 General Design Procedure

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Dymola
(Monolithic
Solution)
Low Fidelity
(Lumped)
Mixed Fidelity
test geometry
Mixed Fidelity
final geometry
High Fidelity
(FSI)
structure ODE Point mass/rotary inertia
(low-fi)
Coarse mesh
(medium-fi)
Finer mesh
(high-fi)
Finer mesh
(high-fi)
aeroloads ODE Equations
(low-fi)
Nodal traction
(Medium-fi)
Nodal traction
(Medium-fi)
CFD
(high-fi)
controller ODE Discrete
(high-fi)
Discrete
(high-fi)
Discrete
(high-fi)
Discrete
(high-fi)
actuator K+1PID, 2PIDs 2PIDs
(high-fi)
2PIDs
(high-fi)
2PIDs
(high-fi)
2PIDs
(high-fi)

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Hydraulic Actuators and PIDs Performance Study
 Actuator performance in non Co-sim doesn’t guarantee a good performance in Co-sim
 2 unit feedback closed-loop: Beta & Torque
K+PID 2 PIDs
Torque loop (P, I, D) = (1, 1, 0.15) (P, I, D) = (5, 10, 0.5)
Beta loop K= 10 (P, I, D) = (1, 0.05, 0.01)
K+PID
2PIDs

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 Failure case: Actuator Performance Downgrade from Dymola to lumped Co-Sim
2 PIDs actuator with (J, c, d) = (0.1, 1, 1)
Dymola
Co-Sim (failed)
Dymola
FlapAngle

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 Failure case : Know-how study to avoid actuator failure in Co-Sim
Good 2PID hydraulic: (J, c, d) = (0.1, 0.01, 0.01)
Bad 2PID hydraulic: (J, c, d) = (0.1, 1, 1)
Stepresponse
Stepresponse
Big oscillation characteristics of
actuator will cause Co-Sim model
fail !

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Structural Data Strganac’s/lumped
Chord span 0.6
Chord length 0.27
b 0.135
a -0.6847
r.p. location N.A.
c.g. location 0.0873
X_alpha 0.3313667
I_alpha 0.0558004
total mass 12.387
wing mass 2.049
k_alpha_k1 6.833
k_alpha_k2 9.967
k_alpha_k3 667.685
k_alpha_k4 26.569
k_alpha_k5 -5087.931
K_h 2844.4
C_h 27.43
C_alpha 0.036
Aeroload Data Strganac’s/lumped
b 0.135
a -0.6847
Cl_alpha 6.28
Cl_beta 3.358
Cm_alpha -1.15992
Cm_beta -1.94
Uair 16
PlungePitch
-- target Beta
-- flap Beta
Angle
Simulation Results and Controller Data Extracted from FSI Simulation
 Dymola Results (non Co-sim)

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 Co-sim results (lumped model)
Plunge
Pitch
-- target Beta -- flap Beta

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 Co-sim results (3D test geometry model)

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 3D final geometry model
 Resize the structure span from 0.6m to 0.01m for saving computational cost.
 2 FSI jobs to get CFD lift/moment and estimate associated parameters compatible with aerodynamic equations.
Structural Data 3D model, final
geometry
Chord span 0.01
Chord length 0.27
b 0.135
a -0.6277
r.p. location 0.05027
c.g. location 0.123
X_alpha 0.53878
I_alpha 0.00111
total mass 0.21
wing mass 0.03809
k_alpha_k1 0.11388
k_alpha_k2 0.16612
k_alpha_k3 11.1281
k_alpha_k4 0.44282
k_alpha_k5 -84.8
K_h 47.407
C_h 0.45717
C_alpha 0.0006
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 1st FSI job for reproducing LCO behavior without activation of flap surface
 By using Abaqus STD/CFD post-processing tools, Cl_alpha and Cm_alpha can be estimated.
Aeroload Ext. from CFD
b 0.135
a -0.6277
Cl_alpha 0.055
Cl_beta 0.042
Cm_alpha -0.0141
Cm_beta -0.018
Uair 16
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 = 0
= 0

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 The LCO behavior due to the aerodynamics equation with estimated parameters doesn’t agree well with one from FSI
 Enrich aerodynamic equations to get a better agreement with CFD’s LCO (using Dymola tool)
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Non-Enriched Enriched
factor A 1 1.025
factor B 1 1.75
factor C 1 0.8
factor D 1 5.0
A B
C D
= 0
= 0
Dymola Plunge non-Enriched
Dymola Pitch non-Enriched
FSI LCO Plunge
FSI LCO Pitch
Dymola Plunge Enriched
Dymola Pitch Enriched

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 2nd FSI job for generating flap surface response in CFD (applying moment on flap hinge connector.)
 By using Abaqus STD/CFD post-processing tools, Cl_beta and Cm_beta can be estimated from governing equations
Aeroload 3D with wrap
b 0.135
a -0.6277
Cl_alpha 0.055
Cl_beta 0.042
Cm_alpha -0.0141
Cm_beta -0.018
Uair 16
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C D

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 Co-sim results (high fidelity model with enriched and non-enriched controller )
Uctrl 16
sampling period 0.0025
Nu1 250
Nu2 25
b 0.135
a -0.6847
X_alpha 0.3313667
I_alpha 0.0558004
total mass 12.387
wing mass 2.049
k_alpha_k1 6.833
k_alpha_k2 9.967
k_alpha_k3 667.685
k_alpha_k4 26.569
k_alpha_k5 -5087.931
K_h 2844.4
C_h 27.43
C_alpha 0.036
Non-Enriched Enriched
factor A 1 1.025
factor B 1 1.75
factor C 1 0.8
factor D 1 5.0
--- enriched controller
--- non-enriched controller

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 Create lower fidelity model for further investigation or tuning with less computational cost before submitting a refined
Co-sim FSI analysis
--- 3D test geometry
--- 3D FSI
Test geometry (few hours computation)
Final FSI (few days computation)

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 Comparison with published data

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Workflow Summary and a Derivative Design
 Workflow steps
Step1. Develop Dymola, Abaqus/STD and CFD models at different levels of fidelity
Step2. Run 2 FSI jobs for preliminary investigating the fluid coefficients in
aerodynamic formulations
Step3. Compare the LCO results from FSI to low-fidelity models and iteratively refine
the aerodynamic formula with enriched factors
Step4. Run 3D FSI co-simulation to confirm the performance of entire system, and
refine the key parameters iteratively if needed.

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Workflow Summary and a Derivative Design
 derivative design
Structrual Data
Chord span 0.01
Chord length 0.674
b 0.337
a -0.3946
r.p. location 0.204
c.g. location 0.291
X_alpha 0.25816
I_alpha 0.011
total mass 0.52
wing mass 0.195
k_alpha_k1 1.42354
k_alpha_k2 2.0765
k_alpha_k3 139.1
k_alpha_k4 5.53521
k_alpha_k5 -1060
K_h 118.5175
C_h 1.142925
C_alpha 0.0075
Aeroload
b 0.337
a -0.3946
Cl_alpha 0.066
Cl_beta 0.039
Cm_alpha -0.032
Cm_beta -0.018
Uair 20
Enriched
factor A 1.025
factor B 1.75
factor C 0.35
factor D 0.35
Controller
Nu1 20
Nu2 100

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