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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. SAND2017-3754 PE

StateestimationAdvancedWECDynamicsandControls

GiorgioBacelli,RyanCoeApril122017

Projectmotivation

§ NumerousstudieshaveshownlargebenefitsofmoreadvancedcontrolofWECs(e.g.,Halsetal.showed330%absorptionincrease)

§ Moststudiesrelyonsignificantsimplificationsandassumptions§ Availabilityofincomingwave

foreknowledge§ 1-DOFmotion§ Linearorperfectlyknow

hydrodynamics§ Nosensornoise§ Unlimitedactuator(PTO)

performance

2

Project goal: accelerate/support usage of advanced WEC control by developers

Controlstrategycomparison

3

Initial comparison completed and published (METS and SAND report)• Multiple novel strategies applied to WECs• Relative power improvement offered by 8

control strategies• “Cost-to-implement” metrics• Roadmap to WEC control w/ in-depth

discussion/instructions for implementation

http://energy.sandia.gov/wordpress/../wp-content/uploads/dlm_uploads/2016/06/SAND2016-4293.pdf

Testingandsystemidentification

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Wave tank testing results and analysis• Raw data available for download (MHK-DR)• Experimental design for wave tank testing of

WECs• System identification methods• Model formulation and validation• Pressure-based model for excitation

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Scatter+

+ +G⌘

r

HZi

1Zi

WEC

+

+

⌘

Fa

v

⌘tot

⌘s

⌘r

B(!) +Bf + i

✓! (M +A(!))� K

!

◆!V = H(!) ⌘ + Fa

Fe = H(!) ⌘

Zi(!) = B(!) +Bf + i (! (M +A(!))�K/!)

V =H(!)

Zi(!)⌘ +

1

Zi(!)Fa.

v =1

Zi

Fa

+H

Zi

⌘

=1

Zi

Fa

+H

Zi

(⌘tot � ⌘r)

=1

Zi

Fa

+H

Zi

(⌘tot �G⌘

r

v)

v =1

Zi

+HG⌘

r

Fa

+H

Zi

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⌘r!0

⇡ 1

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Zi

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WEC

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⌘rG⌘

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HZi

1Zi

WEC

+

+

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v

⌘tot HZi+HG⌘

r

1Zi+HG⌘

r

Dual SISO

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Local linear models

0.2 0.4 0.6 0.8 10

2

4

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10

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(Ns/

m)

×103 |Zi|

0.2 0.4 0.6 0.8 1

Frequency (Hz)

-1.5

-1

-0.5

0

0.5

1

1.5

(rad)

Zi

081

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086

087

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WAMIT

0.2 0.4 0.6 0.8 10

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(Ns/

m)

×103 Re [Zi]

0.2 0.4 0.6 0.8 1

Frequency (Hz)

-15

-10

-5

0

5

10

(Ns/

m)

×103 Im [Zi]

0.2 0.4 0.6 0.8 10

2

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(Ns/

m)

×103 |Zi|

0.2 0.4 0.6 0.8 1

Frequency (Hz)

-1.5

-1

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1

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(rad)

Zi

081

082

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085

086

087

089

090

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WAMIT

0.2 0.4 0.6 0.8 10

1

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(Ns/

m)

×103 Re[Zi]

0.2 0.4 0.6 0.8 1

Frequency (Hz)

-15

-10

-5

0

5

10

(Ns/

m)

×103 Im[Zi]

Results depend on test amplitude, nonlinear?

0 0.05 0.1 0.15 0.2 0.25 0.3

1/||v||2

0

200

400

600

800

1000

1200

Beq

Pink multisine

White multisine

Beq = ↵1

kvk2+ �

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Pressure based models

250 255 260 265 270 275 280 285 290 295 300

t (s)

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(m/s

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Validation

Simulation

Experimental

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WEC

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MISO

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+

Fe

Dual SISO

Dual SISO vs. MISO MISO vs. experiment

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

(N/m

)

×104 |H|

Lock OFF

Lock ON

WAMIT

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Frequency (Hz)

-200

-150

-100

-50

0

50

(ra

d)

H

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At-sea modeling

1. Execute forced oscillation experiments in calm water to obtain a model of the intrinsic impedance and obtain either a parametric or nonparametric model for Zi.

2. Execute the forced oscillation experiment in presence of waves. In this case, the available measurements are the actuator force (Fa), the buoy velocity (v) and the surface elevation (η). By using the frequency-domain equation of motion it is possible to write the excitation FRF as function of the known quantities as:

Fe(!) + Fa(!) = Zi(!) V (!), with Fe(!) = H(!)⌘(!)

H(!) =Zi(!) V (!)� Fa(!)

⌘(!)

Stateobserversandstateestimators

§ WHY?§ Controlsystemdesignedtomakeuseofstateinformationhave

generallybetterperformance

9

Observer Estimator

�� = 𝐴𝑥 + 𝐵𝑢 + 𝑤𝑦 = 𝐶𝑥 + 𝐷𝑢 + 𝑣

WEC model�� = 𝐴𝑥 + 𝐵𝑢𝑦 = 𝐶𝑥 + 𝐷𝑢

WEC model

Observers

§ Basicstateobserver(Luenbergerobserver)§ Thedesignofanobserveristhedesignofastablecontrol

system:chooseLsothat(A-LC)isstable 10

𝑥-./ = 𝐴𝑥- + 𝐵𝑢-𝑦 = 𝐶𝑥- + 𝐷𝑢-

WEC model𝑥1-./ = 𝐴𝑥1- + 𝐿 𝑦- − 𝑦1- + 𝐵𝑢-

𝑦1- = 𝐶𝑥1- + 𝐷𝑢-

𝑒- = 𝑥1- − 𝑥- (observer error)

𝑒-./ = 𝐴 − 𝐿𝐶 𝑒- (observer error dynamic)

If stable 𝑒- → 0 and 𝑥1- → 𝑥-

Discrete time observer

Discrete time KF

Kalmanfilter(Estimator)

§ Optimalestimator:minimizethecovariancematrixoftheerroronthestate(undercertainconditions)

§ Thedesignofanobserveristhedesignofastablecontrolsystem

11

𝑥-./ = 𝐴𝑥- + 𝐵𝑢- + 𝑤-𝑦 = 𝐶𝑥- + 𝐷𝑢- + 𝑤-

WEC model𝑥1-./|- = 𝐴𝑥1-|-8/ + 𝐴𝐾- 𝑦- − 𝐶𝑥1-|-8/ + 𝐵𝑢-Similar structure to the observer but gain 𝐾- is optimized

𝐾- = 𝑃-|-8/𝐶; 𝐶𝑃-|-8/𝐶; + 𝑅8/

𝑃-|- = 𝐼 − 𝐾-𝐶 𝑃-|-8/

𝑃-./|- = 𝐴𝑃-|-𝐴; + 𝑄

Kalmanfilter(Estimator)

§ Muchsimplerimplementation§ Muchfastercomputation§ 𝐾? and𝑃? canbeprecomputedusingMATLAB“dare”function

12

Steady state Kalman filter

𝑥1-./|- = 𝐴𝑥1-|-8/ + 𝐵𝑢- + 𝐾? 𝑦- − 𝐶𝑥1-|-8/

𝐾? = lim-→?

𝐾-Measurements at time step k

Input at time step k

𝑥-./ = 𝐴𝑥- + 𝐵𝑢- + 𝑤-𝑦 = 𝐶𝑥- + 𝐷𝑢- + 𝑤-

WEC model

EstimationforWECs:objectives

§ Limitednumberofmeasurementsareavailablewhenatsea§ Forcontrolpurposes,itisusefultoknow:

§ statesoftheWECthatcannotbemeasureddirectly,e.g.velocityandloadsonthestructure

§ Forcesduetothewaves,e.g.excitationforce(excitationforceisanexternalforce)

13

EstimationforWECs:literature

§ Somegoodliteratureisavailable,butstrongassumptionsonavailablemeasurements.E.g.estimationofexcitationforcewhenfullstateisavailable(Position,velocity,…)

§ Thesemeasurementsarenotavailableforafloatingdevice.§ Velocitydifficulttomeasuredirectly.Ifdifferentiatedfrom

positionitcanbenoisy,andnoiseisnotindependentfromposition.

§ Excitationisassumedtobepartofthestateandthestatevectorisaugmented.Itworkswell,howeverthereisalagintheestimationandmodeldoesnotreflecttheactualphysics

§ B.A.LingandB.A.Batten,“RealTimeEstimationandPredictionofWaveExcitationForcesonaHeavingBody,”inProceedingsoftheASME201534thInternationalConferenceonOcean,OffshoreandArcticEngineering(OMAE2015),St.Johnś,Newfoundland,2015.

§ P.Kracht,S.Perez-Becker,J.B.Richard,andB.Fischer,“PerformanceImprovementofaPointAbsorberWaveEnergyConverterbyApplicationofanObserver-BasedControl:ResultsFromWaveTankTesting,”IEEETransactionsonIndustryApplications,vol.51,no.4,pp.3426–3434,Jul.2015.

§ M.Abdelrahman,R.Patton,B.Guo,andJ.Lan,“Estimationofwaveexcitationforceforwaveenergyconverters,”in20163rdConferenceonControlandFault-TolerantSystems(SysTol),2016,pp.654–659.

§ …

14

Realisticscenarios

§ WECconnectedtofixedreference§ Measurements:Positionandacceleration

§ FloatingWEC:§ Pressureandacceleration(noinformationonpositiononafloating

body)

15

Framework§ Simultaneousestimationofstateandunknowninputs

§ Excitationforceisconsideredanunknowninput§ ItisageneralizationoftheKalmanfilter

16

�� = 𝐴𝑥 + 𝐵𝑢 + 𝐺𝑑 + 𝑤𝑦 = 𝐶𝑥 + 𝐷𝑢 + 𝐻𝑑 + 𝑣

WEC model

𝑑 ≡ 𝐹H Unknown input (or disturbance)

𝑢 Control input 𝑦 measured outputs

[1] S. Z. Yong, M. Zhu, and E. Frazzoli, “A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems,” Automatica, vol. 63, pp. 321–329, 2016.

Case1:positionandacceleration

§ Measurements§ Position(encoder,potentiometer..)§ acceleration(accelerometer)

17

Models have been identified from experimental data

Case1:positionandacceleration

18

Case1:positionandacceleration

19

A short note on filters:

Accelerometers are affected by drift, but power in waves is band limited

Band pass filter for accelerometer

Case1:positionandacceleration

20

Cutoff frequency should be at least 10x max frequency of the waves

Cutoff frequency > 10x excitation frequencyCutoff frequency = 2x excitation frequency

Absorbed power with linear damper and velocity filtered trough a LPF

Case1:positionandacceleration

21

Algorithm: steady state

Much simpler and 10x faster than time-varying version

𝑥1-|-8/ = 𝐴𝑥1-|- + 𝐵𝑢- + 𝐺𝑑I-8/

𝑥1-|- = 𝐴𝑥1-|-8/ + 𝐿? 𝑦- − 𝐶𝑥1-|-8/ − 𝐷𝑢-

𝑑I-8/ = 𝑀? 𝑦- − 𝐶𝑥1-|- − 𝐷𝑢-

Similar structure to Kalman fiter

Case1:positionandacceleration

22

Case1a:positiononly

23

Show sample results: very sensitive to noise

Case1b:positiononly

24Very sensitive to noise, but a bit better than case 1a

Velocity obtained by differentiating position

Case1

25

Summary:• Adding redundant measurement

makes the estimation more robust.• Accelerometers are relatively

inexpensive

Case2:pressureandacceleration

§ Measurements§ Pressure§ Acceleration(accelerometer)

26

Models have been identified from experimental data

Case2:pressureandacceleration

§ Statespacemodel

27

Models have been identified from experimental data

��H = 𝐴H𝑥H + 𝐵H𝑃H𝐹H = 𝐶H𝑥H + 𝐷H𝑃H

𝐺H:

��L = 𝐴L𝑥L + 𝐵L𝐹M + 𝐵L𝐹H𝑦L = 𝐶L𝑥L + 𝐷L𝐹N + 𝐷L𝐹H

𝐺L:

�� = 𝐴𝑥 + 𝐵𝐹M + 𝐺𝑃H𝑦 = 𝐶𝑥 + 𝐷𝐹N + 𝐺𝑃H

Unknown input form

𝐴 = 𝐴L 𝐵L𝐶H0 𝐴H

𝐵 = 𝐵L0 𝐺 = 𝐵L𝐷H

𝐵H𝐶 = 𝐶L 𝐷L𝐶H

𝐻 = 𝐷L𝐷H +01

𝐷 = 𝐷L

Case2:pressureandacceleration

§ Sampleresults:

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Case2:pressureandacceleration

§ Sampleresults:§ Systemstates

29

Case2:pressureandacceleration

§ Sampleresults:

30

In-progress

§ WillreleasethecodeshortlyonMHKDRwebsite§ Caneasilybeextendedto

§ Multipledegreeoffreedom/multi-body/multi-device§ Multi-sensordatafusiontoimproveestimation

31

METSWorkshop

§ May3rd 1-5PM(inconjunctionwithMETSinWashington,DC)

§ Extendedtechnicalpresentations

§ Invitedspeakers§ Roundtablediscussion§ Networkingandcollaboration

brainstorming

32http://www.nationalhydroconference.com/index.html

Line 1

Line 2

Line NLine N

Linear actuator

Rotary actuator

Hydraulic machinery

Control system

Reference signal

Test PTO 1

Test PTO 2

Test stand

• A mobile test lab is being developed by Sandia National Labs for the testing of WEC power take-offs (PTOs)

• Linear and rotational PTOs• Multiple degrees-of-freedom, with independent control• Test stand will simulate dynamics (inertia, damping,

stiffness) of full scale WEC, as well as input from waves• This system will allow for PTO studies including

• System identification• Real-time control• Reliability• Grid interface simulations

• $1.2M of internal (Sandia) funding• Planned completion: October 2017• Planned specs.

• 5 to 500 kW • 0 and 2 Hz

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.

SAND2017-3300 M

Sandia Power Take-Off Test Stand

ThankyouThis research was made possible by support from the Department of Energy’s EnergyEfficiency and Renewable Energy Office’s Water Power Program.

Sandia National Laboratories is a multi-mission laboratory managed and operated bySandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for theU.S. Department of Energy’s National Nuclear Security Administration under contractDE-AC04-94AL85000.

34

Project team:Jeff Rieks (DOE)Bill McShane (DOE)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 (MTU)Diana Bull (SNL)Tim Crawford (SNL)