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Photos placed in
horizontal position
with even amount
of white space
between photos
and header
Photos placed in horizontal...
Outline
1. Project overview/overall motivation
2. Linear, frequency domain, non-
parametric models
3. Parametric models
4....
Project motivation
 Numerous studies have shown large benefits of more advanced control of
WECs (e.g., Hals et al. showed...
Project objectives
 Use numerical modeling and novel laboratory testing
methods to quantitatively compare a variety of co...
Test hardware – WEC device
5
Weldment
Motor stators
Vertical carriages
Access ladder
6" down-tube
PCC tower
Motor sliders
...
Test objectives
“Traditional” decoupled-system testing
• Radiation/diffraction
• Monochromatic waves
Multi-sine, multi-inp...
Control models
What is the objective?
Control system design
Steps
1. Identify available measurements (𝑦)
2. Study quality ...
Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
fun...
Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
fun...
Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
fun...
Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
fun...
Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
fun...
Types of models
Time domain
Frequency
domain
Parametric
State-space
Transfer
function
Non-
parametric
Impulse
response
fun...
Linear vs. Nonlinear models
 Non Linear:
 Pro
 More accurate description of system dynamics over
broader region of oper...
LINEAR, FREQUENCY DOMAIN,
NON-PARAMETRIC MODELS
System Identification and Model validation
Intrinsic impedance FRF
Linear model of a WEC (Radiation-diffraction model)
EOM:
Intrinsic
impedance:
Intrinsic impedance FRF
Why focus on the intrinsic impedance?
 Models are used for:
 Design of the control system
 Desi...
Intrinsic impedance FRF
 Design of experiment :forced oscillations test set-up
 Open loop
WEC
Input
signal
generator
Intrinsic impedance FRF
19
WhiteinputPinkinput
Force Velocity
Input signals Output signals
Intrinsic impedance FRF
 Results
 Comparison with WAMIT
 Verification of local linearity
(damping depends on the input
...
Intrinsic impedance FRF
 Results: comparison over multiple experiments
 Comparison with WAMIT
 Verification of local li...
Radiation FRF
Radiation impedance
Radiation impedance
Radiation FRF
• Consistency over
different experiments
• For each experiment,
linear friction 𝐵𝑓 has been
estimated by bes...
Excitation force FRF
 Design of experiment
WEC
(locked)
Excitation force
Frequency Response Function
Excitation force FRF
 Periodic vs non-periodic (pseudo periodic) waves
Periodic waves:
• Data collection: 10 minutes
• No...
Excitation force FRF
Results
Input signals:
Pink-type multisine waves
Wave probes
Buoy
NO spectrum leakage
Top view of the...
Excitation force FRF (sinusoidal waves)
Sinusoidal waves
 Pros
 If input is a pure sinusoid
(very difficult in wave tank...
Excitation force FRF w/o locking device
PARAMETRIC MODELS
System Identification and Model validation
Parametric model for radiation impedance
FDI toolbox for radiation model
Validation
broadband flat (white) multisine
Ident...
Parametric model for intrinsic impedance
N4ID for intrinsic impedance
Identification
Band limited white noise (non periodi...
MULTI-INPUT SINGLE-OUTPUT
MODELS
System Identification and Model validation
Black box MISO models
 Identification procedure
 Uncorrelated inputs
 Design of experiment
 Bandwidth
 Periodic and n...
MISO
34
Actuator force + wave elevation to velocity
MISO
35
Actuator force + pressure to velocity
MODEL VALIDATION COMPARISON
System Identification and Model validation
Comparison of MISO vs “dual-SISO”
(radiation/diffraction model)
Dual-SISO
(radiation/diffraction model)
MISO
Velocity comparison
Fit (1-NRMSE) = 0.672
Fit (1-NRMSE) = 0.870
Model order = 5
Model order = 2
MISO
(Force/wave elev. to ...
Future work
 3-DOF system ID: obtain complex system models using efficient
system ID techniques
 Real-time closed-loop c...
Upcoming events
 Spring webinar
 Topic: state-estimation for FB control
 Date TBD, Jan-March
 METS Workshop
 In conju...
Thank you
This research was made possible by support from the Department of Energy’s Energy
Efficiency and Renewable Energ...
References
[1] R. Coe, G. Bacelli, O. Abdelkhalik, and D. Wilson, “An assessment of WEC
control performance uncertainty,” ...
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Advanced WEC Dynamics and Controls: System Identification and Model Validation

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System identification and model validation

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Advanced WEC Dynamics and Controls: System Identification and Model Validation

  1. 1. Photos placed in horizontal position with even amount of white space between photos 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. 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. 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. 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 4
  5. 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. 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 6 Control performance is directly dependent on model performance
  7. 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. 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. 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. 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. 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. 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. 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. 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 14 Nonlinear Linear 1 Linear 2 Linear 4 Linear 3 Linear 5 Linear 6 Linear 7 𝑯 𝒔 𝑻 𝒑 Linear 8
  15. 15. LINEAR, FREQUENCY DOMAIN, NON-PARAMETRIC MODELS System Identification and Model validation
  16. 16. Intrinsic impedance FRF Linear model of a WEC (Radiation-diffraction model) EOM: Intrinsic impedance:
  17. 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. 18. Intrinsic impedance FRF  Design of experiment :forced oscillations test set-up  Open loop WEC Input signal generator
  19. 19. Intrinsic impedance FRF 19 WhiteinputPinkinput Force Velocity Input signals Output signals
  20. 20. Intrinsic impedance FRF  Results  Comparison with WAMIT  Verification of local linearity (damping depends on the input power/amplitude)
  21. 21. Intrinsic impedance FRF  Results: comparison over multiple experiments  Comparison with WAMIT  Verification of local linearity (damping depends on the input power/amplitude)
  22. 22. Radiation FRF Radiation impedance Radiation impedance
  23. 23. Radiation FRF • Consistency over different experiments • For each experiment, linear friction 𝐵𝑓 has been estimated by best fitting with WAMIT
  24. 24. Excitation force FRF  Design of experiment WEC (locked) Excitation force Frequency Response Function
  25. 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. 26. Excitation force FRF Results Input signals: Pink-type multisine waves Wave probes Buoy NO spectrum leakage Top view of the wave tank
  27. 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. 28. Excitation force FRF w/o locking device
  29. 29. PARAMETRIC MODELS System Identification and Model validation
  30. 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. 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. 32. MULTI-INPUT SINGLE-OUTPUT MODELS System Identification and Model validation
  33. 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. 34. MISO 34 Actuator force + wave elevation to velocity
  35. 35. MISO 35 Actuator force + pressure to velocity
  36. 36. MODEL VALIDATION COMPARISON System Identification and Model validation
  37. 37. Comparison of MISO vs “dual-SISO” (radiation/diffraction model) Dual-SISO (radiation/diffraction model) MISO
  38. 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. 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 39
  40. 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 40 http://www.nationalhydroconference.com/index.ht ml
  41. 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. 41 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. 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. 42

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