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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
Ryan Coe ([email protected])Giorgio Bacelli ([email protected])December 6, 2016
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 ()
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
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
WECInputsignalgenerator
19
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Frequency (Hz)
0
10
20
30
40
50
60
Mag
nitu
de
Spectrum of the input force
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Frequency (Hz)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Mag
nitu
de
Spectrum of the velocity
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Frequency (Hz)
0
5
10
15
20
25
30
Mag
nitu
de
Spectrum of the input force
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Frequency (Hz)
0
0.002
0.004
0.006
0.008
0.01
0.012
Mag
nitu
de
Spectrum of the velocity
Intrinsic impedance FRFW
hite
inpu
tPi
nk in
put
Force Velocity
Input signals Output signals
0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5000
10000
15000
Mag
nitu
de
ExperimentalExperimental (smoothed)WAMIT
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1frequency (Hz)
-2
-1
0
1
2
Pha
se (r
ad)
Intrinsic impedance FRF
Results Comparison with WAMIT Verification of local linearity
(damping depends on the input power/amplitude) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Frequency (Hz)
0
5
10
15
20
25
30
Mag
nitu
de
Spectrum of the input force
0.2 0.4 0.6 0.8 10
5000
10000
15000Magnitude of Zi
0.2 0.4 0.6 0.8 1f (Hz)
-2
-1
0
1
2Phase of Zi
0.2 0.4 0.6 0.8 10
500
1000
1500
2000Real part of Zi
0.2 0.4 0.6 0.8 1f (Hz)
-2
-1
0
1104 Imaginary part of Z i
Experimental
WAMIT
Intrinsic impedance FRF Results: comparison over multiple experiments
Comparison with WAMIT Verification of local linearity
(damping depends on the input power/amplitude)
Radiation FRF
Radiation impedance
Radiation impedance
Radiation FRF
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000Radiation damping B( )
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1f (Hz)
500
1000
1500
2000Added Mass A( )
Experimental
Experimental
WAMIT
WAMIT
• Consistency over different experiments
• For each experiment,linear friction has been estimated by best fitting withWAMIT
Excitation force FRF
Design of experiment
WEC(locked)
Excitation forceFrequency Response Function
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
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6Frequency (Hz)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
S(
)
Pseudo-randomAveraged pseudo-randomPeriodicTheoretical
Excitation force FRF
Results
Input signals:Pink-type multisine waves
Wave probes
Buoy
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Frequency (Hz)
0
0.5
1
1.5
2
2.5
3
Am
plitu
de (m
)
10-3
0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49Frequency (Hz)
0
0.5
1
1.5
2
2.5
Am
plitu
de (m
)
10-3
NO spectrum leakage
Top view of thewave tank
0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
Mag
nitu
de
104 Excitation FRF H( )
Staff1Staff2Staff3Staff4WAMIT
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (Hz)
-200
-100
0
100
Pha
se (r
ad)
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
Mag
nitu
de
104 Excitation FRF
Pink spectra wavesSinusoidal wavesWAMIT
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (Hz)
-4
-2
0
2
4
Pha
se (r
ad)
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)
Excitation force FRF w/o locking device
0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
Mag
nitu
de
104 Excitation FRF H( )
DynamicDiffractionWAMIT
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (Hz)
-200
-100
0
100
Pha
se (r
ad)
PARAMETRIC MODELSSystem Identification and Model validation
200 205 210 215 220 225 230 235 240 245 250Time (s)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Velo
city
(m/s
)
Measured vs. Simulated Velocity
MeasuredSimulated
Parametric model for radiation impedance
FDI toolbox for radiation model
100 101
Frequency [rad/s]
500
1000
1500
2000
Add
ed M
ass Experimental (smoothed)
Parametric modelWAMIT
100 101
Frequency [rad/s]
0
1000
2000
Dam
ping
Validationbroadband flat (white) multisine
Identificationbroadband pink multisine
1-NRMSE = 0.893
Parametric model for intrinsic impedance
N4ID for intrinsic impedance
1.5 2 2.5 3 3.5 4 4.5 5 5.5 60
2
4
6
Mag
nitu
de
10-4 Intrinsic Impedance
Non-parametricParametric
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6Frequency (Hz)
-2
-1
0
1
2
Pha
se (r
ad)
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.
34
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
35
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)
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
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
http://www.nationalhydroconference.com/index.html
41
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.
Project team:Alison LaBonte (DOE)Jeff Rieks (DOE)Bill McShaneGiorgio 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.