Download - Status of Nonlinear Model Reduction Framework in Py A. Da Ronch University of L iverpool , UK
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Status of Nonlinear Model Reduction Framework in Py
A. Da RonchUniversity of Liverpool, UK
Liverpool, 16 March 2012
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Target
• Nonlinear models for flexible aircraft (hierarchy)
• Nonlinear model reduction for control implementation
• Develop nonlinear control strategies
Py framework - data exchange to/from control people
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Where do we stand?
• Model caseo Nonlinear p/p aerofoilo ROM/NROM generationo Control - gust alleviation
• Extend approach along 2 pathso Introduce CFD to p/p aerofoil (with Nik)o Nonlinear beam + linear aerodynamics
• Combine models of varying fidelity UVLM++ to be included in Py
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Model reduction
n
Trfs
w
wwww
UwRdtdw
R
,,
, *
• Taylor expansion of R• Project onto a small basis of aeroelastic modes
• z is complex-valued
nmCz
zfuBuBAzdtdz
m
nlinddcc
FOM
ROM/NROM
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Where do we stand?
• Model caseo Nonlinear p/p aerofoilo ROM/NROM generationo Control - gust alleviation
• Extend approach along 2 pathso Introduce CFD to p/p aerofoil (with Nik)o Nonlinear beam + linear aerodynamics
• Combine models of varying fidelity UVLM++ to be included in Py
![Page 7: Status of Nonlinear Model Reduction Framework in Py A. Da Ronch University of L iverpool , UK](https://reader035.vdocuments.site/reader035/viewer/2022062812/568162ac550346895dd32fc1/html5/thumbnails/7.jpg)
Aerofoil section
12 states: p/p aerofoil + flap + gust
Nonlinear restoring forces (polynomial form)
Tfff
Ts
Tfss
www
hw
wwww
81 ,,
,
,,
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FOM/ROM gust response – linear structural model
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FOM gust response – linear/nonlinear structural model
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NFOM/NROM gust response – nonlinear structural model
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Linear control law on ROM - H∞ (with Y. Wang and A. Wynn)
CL
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Aerofoil section
Linear control done on linear ROM
but
issues with NROM data interpretation
Alternative way suggested (and implemented) to export
NROM coefficients
afternoon session
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Exporting NROM data for control
mm
m
CA
Cz
Azz
ia
iqpz
jk
jjj
)Im()Re(
zz
x
1) Complex-valued ROM system
2) Isolate real/imag parts
3) Real-valued variable
mj
xxx
xxx
kmkjm
kmkj
,,1
4) Real-valued system
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Exporting NROM data for control
ib
zzbz
jrs
srjrsj
Quadratic term in NROM
mj
xxxxxxxxx
xxxxxxxxx
smrsrmsmrmsrjm
smrsrmsmrmsrj
,,1
Real-valued system
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Exporting NROM data for control
Linear terms tensor of order 2Quadratic terms tensor of order 3Cubic terms tensor of order 4
in “easy to use” format for control applications - good
mmmm
mmm
mm
C
B
A
2222
222
22
ˆ
ˆ
ˆ
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Where do we stand?
• Model caseo Nonlinear p/p aerofoilo ROM/NROM generationo Control - gust alleviation
• Extend approach along 2 pathso Introduce CFD to p/p aerofoil (with Nik)o Nonlinear beam + linear aerodynamics
• Combine models of varying fidelity UVLM++ to be included in Py
![Page 17: Status of Nonlinear Model Reduction Framework in Py A. Da Ronch University of L iverpool , UK](https://reader035.vdocuments.site/reader035/viewer/2022062812/568162ac550346895dd32fc1/html5/thumbnails/17.jpg)
F90 routines
Py framework
Py script
• Beam code• Low-level programming
• Py-driven simulations• High-level programming
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F90 routines
Py framework
Py script
• Memory storage C/Fortran like• No derived types
• LAPACK/BLAS calls removed• Derived types
Wrapper in F90
Wrapper.f90
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F90 routines
Py framework
Py script
• Memory storage C/Fortran like• No derived types
• LAPACK/BLAS calls removed• Derived types• Dynamic library .so
Wrapper in F90
• 1d Py array to multi-dim F90 array• Assembly variables to derived types• Pass data back to Py
BeamLib.so
# Sample .py code - import shared librarylibso = cdll.LoadLibrary(“./BeamLib.so”)
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Wrapper.f90
Py F90: reconstruct derived typesF90 Py: disassemble derived types
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Wrapper.f90
Py F90: from 1d array to 2d/3dF90 Py: convert back to 1d array
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Static Aeroelastic Run, HALE wing - Py is LIN/NLN struct + STRIP
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Py framework
Static aeroelastic (linear/nonlinear trim) ok
but
work needed for dynamic aeroelastic analysis
afternoon session
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Py framework
FOM• Newmark for 2nd order ODEs (unconditionally stable)• rewrite aerodynamics as 2nd order system• expand size of system to solve
ROM/NROM• rewrite system as 1st order ODEs• ROM generation should apply without modifications
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lib/
src/ linux64/
fortran/
main/ install/ bin/ wrapper/
• Wrapper.f90• Makefile• BeamLib.so
Modified source code• LAPACK/BLAS removed• New routines *_clean.f90
Code integration
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lib/
src/ linux64/
fortran/
main/ install/ bin/ wrapper/
• Add flag -DNOLAPACK to use LU factorization• Default remains LAPACK calls• One single code (UL/IC), easiness to replace/update beam code
Conditional compilation
Code integration - suggestion
! Sample .f90 code#ifdef NOLAPACK
! LU factorization#else
! default solver#endif
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Project webpage
• cfd4aircraft new layout, dedicated sections to research
themes
• Flexflight page could haveo section for open-access documentso pswd-protected member area (meeting archives, etc.)
see current status
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Conclusionsp/p aerofoil• NROM generation demonstrated
• NROM data for control design
Py framework for beam code• dynamic solver to be completed
• model reduction for gust response
test approach to larger systems
(Suggestions for data exchange/code integration/...)