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 Advanced WEC Dynamics and Controls System Identification and Model validation Ryan Coe ([email protected]) Giorgio Bacelli ([email protected]) December 6, 2016
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Advanced WEC Dynamics and Controls: System Identification and Model Validation
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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 ControlsSystem Identification and Model validation
Outline1. Project overview/overall motivation2. Linear, frequency domain, non-
parametric models3. Parametric models4. Multi-input models5. Model validation comparison6. 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
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
5
Test hardware – WEC device
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
Control performance is directly dependent on
model performance
Control modelsWhat is the objective?
Control system design
Steps1. Identify available measurements ()2. Study quality of the measurements ()
(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
ControlSystem Plant𝑢 𝑦
�̂�(Estimates state of the plant)
Types of models
Time domainFrequency
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)
Types of models
Time domainFrequency
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
Types of models
Time domainFrequency
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)
Types of models
Time domainFrequency
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)
Types of models
Time domainFrequency
domain
Parametric
State-space Transfer function
Non-parametric
Impulse response function
Frequency response function (WAMIT)
Description of dynamics in terms of
poles and zeros
Types of models
Time domainFrequency
domain
Parametric
State-space Transfer function
Non-parametric
Impulse response function
Frequency response function (WAMIT)
Black-box w/ actuator () and wave elevation ()
Radiation-diffraction model
Black-box w/ actuator () and pressure ()
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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
Nonlinear
Linear 1
Linear 2
Linear 4 Linear
3
Linear 5
Linear 6 Linear
7
𝑯 𝒔
𝑻 𝒑
Linear 8
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 Design of estimator (e.g. Kalman filter)
describes the input/output behavior of the WEC(not the only one, there )
WEC
1𝑍 𝑖(Input) (Output)
State estimator
ControlSystem
Intrinsic impedance FRF
Design of experiment :forced oscillations test set-up Open loop
IdentificationBand limited white noise (non periodic)(initial 70% of the dataset)
ValidationBand limited white noise(last 30% of the dataset)
1-NRMSE = 0.912
MULTI-INPUT SINGLE-OUTPUT MODELS
System Identification and Model validation
Black box MISO models
Identification procedure Uncorrelated inputs Design of experiment
Bandwidth Periodic and non-periodic inputs
𝐺 (𝑠 )
= random signal
= random signal
𝑦
• For same frequency resolution and RMS value, the signal-to-noise ratio is 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.
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MISO
-60
-40
-20
0
To: v
From: eta
10-4 10 -2 100 102-90
0
90
180
270
To: v
From: F
10 -4 10-2 100 102
Bode Diagram
Frequency (Hz)
Mag
nitu
de (d
B) ;
Pha
se (d
eg)
Actuator force + wave elevation to velocity
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MISO
-40
-30
-20
-10
0
To: v
From: F
10-2 10 -1 100 101-135
-90
-45
0
To: v
From: P
10 -2 10-1 100 101
Bode Diagram
Frequency (Hz)
Mag
nitu
de (d
B) ;
Pha
se (d
eg)
Actuator force + pressure to velocity
MODEL VALIDATION COMPARISONSystem 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
250 255 260 265 270 275 280 285 290 295 300-0.5
0
0.5v
MeasuredSimulated
Measured vs. Simulated Velocity
Time (seconds)
Velo
city
(m/s
)
250 255 260 265 270 275 280 285 290 295 300-0.5
0
0.5v
MeasuredSimulated
Measured vs. Simulated Velocity
Time (seconds)
Velo
city
(m/s
)
MISO(Force/wave elev. to velocity)
MISO(Force/pressure to velocity)
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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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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
http://www.nationalhydroconference.com/index.html
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Thank youThis 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.
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.