System identification and model validation

1. Photos placed in
horizontal position
with even amount
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and header
Photos placed in horizontal position
with even amount of white space
between photos and header
Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia
Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of
Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
Advanced WEC
Dynamics and
Controls
System Identification and
Model validation
Ryan Coe (rcoe@sandia.gov)
Giorgio Bacelli (gbacell@sandia.gov)
December 6, 2016

2. Outline
1. Project overview/overall motivation
2. Linear, frequency domain, non-
parametric models
3. Parametric models
4. Multi-input models
5. Model validation comparison
6. Ongoing/future work

3. Project motivation
 Numerous studies have shown large benefits of more advanced control of
WECs (e.g., Hals et al. showed 330% absorption increase)
 Most studies rely on significant simplifications and assumptions
 Availability of incoming wave
foreknowledge
 1-DOF motion
 Linear or perfectly know
hydrodynamics
 No sensor noise
 Unlimited actuator (PTO) performance
3
Project goal: accelerate/support usage of advanced WEC
control by developers

4. Project objectives
 Use numerical modeling and novel laboratory testing
methods to quantitatively compare a variety of control
strategies: system identification methods for richer results (better numerical
models and better controls)
 Produce data, analyses and methodologies that assist
developers in selecting and designing the best control
system for their device: provide developers with the information
needed to make informed decisions about their specific strategy on PTO control
 Use numerical modeling and testing to determine the
degree to which these control strategies are device
agnostic: broadly applicable quantitative results, methods and best practices
applicable to a wide range of devices
 Develop strategies to reduce loads, address fatigue and to
handle extreme conditions: reduce loads and high-frequency vibration
in both operational and extreme conditions
 Full wave-to-wire control: absorption, generation, power-electronics
and transmission considered in control design
 Develop novel control strategies and design
methodologies: leverage Sandia’s control expertise from aerospace,
defense and robotics to develop novel WEC control approaches
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5. Test hardware – WEC device
5
Weldment
Motor stators
Vertical carriages
Access ladder
6" down-tube
PCC tower
Motor sliders
Planar motion table
Ballast plates
U-Joint
Rotation lockout bars
Wave seal
Pressure
transducers

6. Test objectives
“Traditional” decoupled-system testing
• Radiation/diffraction
• Monochromatic waves
Multi-sine, multi-input, Open Loop testing
• Excite system w/ both inputs (waves and
actuator) w/o control (uncorrelated inputs)
• Band-width-limited multi-sine signals
“At-sea” testing
• Excite system w/ both inputs (waves and actuator)
• Idealized wave spectra
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Control performance is
directly dependent on
model performance

7. Control models
What is the objective?
Control system design
Steps
1. Identify available measurements (𝑦)
2. Study quality of the measurements (𝑦)
(e.g. noise)
3. Design state estimator/observer
 E.g.: Kalman filter and Luenberger observer are
model based
4. Design control system
 Many control algorithms require a model of the
plant (e,g. MPC, LQ)
(Control Input) (Plant Output)
State estimator
Control
System
Plant
𝑢 𝑦
𝑥
(Estimates state of the plant)

8. Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
function
Frequency
response
function
(WAMIT)
 Many types of
models to choose
from
 “Correct” model
type dictated by
intended
application(s)

9. Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
function
Frequency
response
function
(WAMIT)
Frequency domain
models often provide
useful insight in system
dynamics and assist in
analytic tuning

10. Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
function
Frequency
response
function
(WAMIT)
Non-parametric
models directly
produced by numerical
and empirical methods
(no fitting necessary)

11. Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
function
Frequency
response
function
(WAMIT)
State space models
often used in linear
control (e.g. MPC, LQ)

12. Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
function
Frequency
response
function
(WAMIT)
Description of
dynamics in terms of
poles and zeros

13. Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
function
Frequency
response
function
(WAMIT)
Black-box w/ actuator (𝐹𝑎) and wave elevation (𝜂)
Radiation-diffraction model
Black-box w/ actuator (𝐹𝑎) and pressure (𝑝)

14. Linear vs. Nonlinear models
 Non Linear:
 Pro
 More accurate description of system dynamics over
broader region of operation
 Better performing control
 Cons
 More difficult to identify
 More difficult for control design
 May be less “robust” (good interpolators, but may not be good extrapolators)
 Linear
 Pro
 Identification is much easier (plenty of tools and theory available)
 Control design is easier (plenty of tools and theory available)
 Can have many “local model” and controllers (e.g. Gain scheduling )
 Cons
 Local approximation (models are good only around a region of operation)
 Certain systems cannot be approximated by linear models
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Nonlinear
Linear
1
Linear
2
Linear
4
Linear
3
Linear
5
Linear
6 Linear
7
𝑯 𝒔
𝑻 𝒑
Linear
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15. LINEAR, FREQUENCY DOMAIN,
NON-PARAMETRIC MODELS
System Identification and Model validation

16. Intrinsic impedance FRF
Linear model of a WEC (Radiation-diffraction model)
EOM:
Intrinsic
impedance:

17. Intrinsic impedance FRF
Why focus on the intrinsic impedance?
 Models are used for:
 Design of the control system
 Design of estimator (e.g. Kalman filter)
 𝑍𝑖 describes the input/output behavior of the WEC
(not the only one, there )
WEC
1
𝑍 𝑖(Input) (Output)
State estimator
Control
System

18. Intrinsic impedance FRF
 Design of experiment :forced oscillations test set-up
 Open loop
WEC
Input
signal
generator

19. Intrinsic impedance FRF
19
WhiteinputPinkinput
Force Velocity
Input signals Output signals

20. Intrinsic impedance FRF
 Results
 Comparison with WAMIT
 Verification of local linearity
(damping depends on the input
power/amplitude)

21. Intrinsic impedance FRF
 Results: comparison over multiple experiments
 Comparison with WAMIT
 Verification of local linearity
(damping depends on the input power/amplitude)

22. Radiation FRF
Radiation impedance
Radiation impedance

23. Radiation FRF
• Consistency over
different experiments
• For each experiment,
linear friction 𝐵𝑓 has been
estimated by best fitting with
WAMIT

24. Excitation force FRF
 Design of experiment
WEC
(locked)
Excitation force
Frequency Response Function

25. Excitation force FRF
 Periodic vs non-periodic (pseudo periodic) waves
Periodic waves:
• Data collection: 10 minutes
• No need for frequency smoothing (avg)
• Higher frequency resolution
Pseudo-Periodic waves:
• Data collection:30 minutes
• Frequency smoothing (avg) required
• Lower frequency resolution

26. Excitation force FRF
Results
Input signals:
Pink-type multisine waves
Wave probes
Buoy
NO spectrum leakage
Top view of the
wave tank

27. Excitation force FRF (sinusoidal waves)
Sinusoidal waves
 Pros
 If input is a pure sinusoid
(very difficult in wave tank), it
may be possible to obtain
more accurate description of
nonlinearities
 Cons
 (Very) Time consuming
 Low frequency resolution
(Multisine signal with T=3 minutes has more than
200 frequencies between 0.25Hz and 1Hz)
 Some nonlinearities or time
varying behaviors may not be
excited with single frequency
input signals (e.g. nonlinear
couplings between modes)

28. Excitation force FRF w/o locking device

29. PARAMETRIC MODELS
System Identification and Model validation

30. Parametric model for radiation impedance
FDI toolbox for radiation model
Validation
broadband flat (white) multisine
Identification
broadband pink multisine
1-NRMSE = 0.893

31. Parametric model for intrinsic impedance
N4ID for intrinsic impedance
Identification
Band limited white noise (non periodic)
(initial 70% of the dataset)
Validation
Band limited white noise
(last 30% of the dataset)
1-NRMSE = 0.912

32. MULTI-INPUT SINGLE-OUTPUT
MODELS
System Identification and Model validation

33. Black box MISO models
 Identification procedure
 Uncorrelated inputs
 Design of experiment
 Bandwidth
 Periodic and non-periodic inputs
𝐺(𝑠)
𝑢1 = random signal
𝑢2 = random signal
𝑦
• For same frequency resolution and RMS value, the
signal-to-noise ratio is 2 smaller, or for the same signal-
to-noise ratio and RMS value, the measurement time is 2
times longer.
• The experiment do not mimic the operational conditions,
which may be a problem if the system behaves
nonlinearly.

34. MISO
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Actuator force + wave elevation to velocity

35. MISO
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Actuator force + pressure to velocity

36. MODEL VALIDATION COMPARISON
System Identification and Model validation

37. Comparison of MISO vs “dual-SISO”
(radiation/diffraction model)
Dual-SISO
(radiation/diffraction model)
MISO

38. Velocity comparison
Fit (1-NRMSE) = 0.672
Fit (1-NRMSE) = 0.870
Model order = 5
Model order = 2
MISO
(Force/wave elev. to velocity)
MISO
(Force/pressure to velocity)

39. Future work
 3-DOF system ID: obtain complex system models using efficient
system ID techniques
 Real-time closed-loop control: implement real-time control with
realistic signals/measurements
 Include power-electronics and structural modeling
 Industry partner for large-scale at-sea control
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40. Upcoming events
 Spring webinar
 Topic: state-estimation for FB control
 Date TBD, Jan-March
 METS Workshop
 In conjunction with METS 2017 (MAY 1 - 3, WASHINGTON D.C.)
 Extended technical presentations
 Invited speakers
 Roundtable discussion
 Networking and collaboration brainstorming
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http://www.nationalhydroconference.com/index.ht
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41. Thank you
This research was made possible by support from the Department of Energy’s Energy
Efficiency and Renewable Energy Office’s Wind and Water Power Program.
Sandia National Laboratories is a multi-mission laboratory managed and operated by
Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the
U.S. Department of Energy’s National Nuclear Security Administration under contract
DE-AC04-94AL85000.
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Project team:
Alison LaBonte (DOE)
Jeff Rieks (DOE)
Bill McShane
Giorgio Bacelli (SNL)
Ryan Coe (SNL)
Dave Wilson (SNL)
David Patterson (SNL)
Miguel Quintero (NSWCCD)
Dave Newborn (NSWCCD)
Calvin Krishen (NSWCCD)
Mark Monda (SNL)
Kevin Dullea (SNL)
Dennis Wilder (SNL)
Steven Spencer (SNL)
Tim Blada (SNL)
Pat Barney (SNL)
Mike Kuehl (SNL)
Mike Salazar (SNL)
Ossama Abdelkhalik (MTU)
Rush Robinett (MTU)
Umesh Korde (SNL)
Diana Bull (SNL)
Tim Crawford (SNL)

42. References
[1] R. Coe, G. Bacelli, O. Abdelkhalik, and D. Wilson, “An assessment of WEC
control performance uncertainty,” in International Conference on Ocean,
Offshore and Arctic Engineering (OMAE2017), in prep. Trondheim, Norway:
ASME, 2017.
[2] G. Bacelli, R. Coe, O. Abdelkhalik, and D. Wilson, “WEC geometry
optimization with advanced control,” in International Conference on Ocean,
Offshore and Arctic Engineering (OMAE2017), in prep, Trondheim, Norway.
ASME, 2017.
[3] O. Abdelkhalik, R. Robinett, S. Zou, G. Bacelli, R. Coe, D. Bull, D. Wilson,
and U. Korde, “On the control design of wave energy converters with wave
prediction,” Journal of Ocean Engineering and Marine Energy, pp. 1–11, 2016.
[4] O. Abdelkhalik, R. Robinett, S. Zou, G. Bacelli, R. Coe, D. Bull, D. Wilson,
and U. Korde, “A dynamic programming approach for control optimization of
wave energy converters,” in prep, 2016.
[5] O. Abdelkhalik, S. Zou, G. Bacelli, R. D. Robinett III, D. G. Wilson, and R.
G. Coe, “Estimation of excitation force on wave energy converters using
pressure measurements for feedback control,” in OCEANS2016. Monterey,
CA: IEEE, 2016.
[6] G. Bacelli, R. G. Coe, D. Wilson, O. Abdelkhalik, U. A. Korde, R. D.
Robinett III, and D. L. Bull, “A comparison of WEC control strategies for a
linear WEC model,” in METS2016, Washington, D.C., April 2016.
[7] R. G. Coe, G. Bacelli, D. Patterson, and D. G. Wilson, “Advanced WEC
dynamics & controls FY16 testing report,” Sandia National Labs, Albuquerque,
NM, Tech. Rep. SAND2016-10094, October 2016.
[8] D. Wilson, G. Bacelli, R. G. Coe, D. L. Bull, O. Abdelkhalik, U. A. Korde,
and R. D. Robinett III, “A comparison of WEC control strategies,” Sandia
National Labs, Albuquerque, New Mexico, Tech. Rep. SAND2016-4293, April
2016 2016.
[9] D. Wilson, G. Bacelli, R. G. Coe, R. D. Robinett III, G. Thomas, D. Linehan,
D. Newborn, and M. Quintero, “WEC and support bridge control structural
dynamic interaction analysis,” in METS2016, Washington, D.C., April 2016.
[10] O. Abdelkhalik, S. Zou, R. Robinett, G. Bacelli, and D. Wilson, “Estimation
of excitation forces for wave energy converters control using pressure
measurements,” International Journal of Control, pp. 1–13, 2016.
[11] S. Zou, O. Abdelkhalik, R. Robinett, G. Bacelli, and D. Wilson, “Optimal
control of wave energy converters,” Renewable Energy, 2016.
[12] J. Song, O. Abdelkhalik, R. Robinett, G. Bacelli, D. Wilson, and U. Korde,
“Multi-resonant feedback control of heave wave energy converters,” Ocean
Engineering, vol. 127, pp. 269–278, 2016.
[13] O. Abdelkhalik, R. Robinett, G. Bacelli, R. Coe, D. Bull, D. Wilson, and U.
Korde, “Control optimization of wave energy converters using a shape-based
approach,” in ASME Power & Energy, San Diego, CA, 2015.
[14] D. L. Bull, R. G. Coe, M. Monda, K. Dullea, G. Bacelli, and D. Patterson,
“Design of a physical point-absorbing WEC model on which multiple control
strategies will be tested at large scale in the MASK basin,” in International
Offshore and Polar Engineering Conference (ISOPE2015), Kona, HI, 2015.
[15] R. G. Coe and D. L. Bull, “Sensitivity of a wave energy converter
dynamics model to nonlinear hydrostatic models,” in Proceedings of the ASME
2015 34th International Conference on Ocean, Offshore and Arctic
Engineering (OMAE2015). St. John’s, Newfoundland: ASME, 2015.
[16] D. Patterson, D. Bull, G. Bacelli, and R. Coe, “Instrumentation of a WEC
device for controls testing,” in Proceedings of the 3rd Marine Energy
Technology Symposium (METS2015), Washington DC, Apr. 2015.
[17] R. G. Coe and D. L. Bull, “Nonlinear time-domain performance model for a
wave energy converter in three dimensions,” in OCEANS2014. St. John’s,
Canada: IEEE, 2014.
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