advanced wec dynamics and controls: system identification and model validation

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

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

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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


domain

Parametric


Non-parametric



Frequency domain models often provide

useful insight in system dynamics and assist in

analytic tuning

Types of models


domain

Parametric


Non-parametric



Non-parametric models directly

produced by numerical and empirical methods (no fitting necessary)

Types of models


domain

Parametric


Non-parametric



State space models often used in linear

control (e.g. MPC, LQ)

Types of models


domain

Parametric


Non-parametric



Description of dynamics in terms of

poles and zeros

Types of models


domain

Parametric


Non-parametric



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:


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


Design of experiment :forced oscillations test set-up Open loop

WECInputsignalgenerator

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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


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)


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


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


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


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.

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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

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


Time (seconds)

Velo

city

(m/s

)

250 255 260 265 270 275 280 285 290 295 300-0.5

0

0.5v

MeasuredSimulated


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

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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.

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)

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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.