Photos placed in horizontal position with even amount of white space
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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
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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
+HG⌘
r
⌘tot
�����G
⌘r!0
⇡ 1
Zi
Fa
+H
Zi
⌘tot
+
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WEC
+
+⌘
Fa
v
⌘tot
⌘rG⌘
r
HZi
1Zi
WEC
+
+
Fa
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
082
084
085
086
087
089
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091
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]
0.2 0.4 0.6 0.8 10
2
4
6
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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
082
084
085
086
087
089
090
091
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+ �
Systemidentification
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Pressure based models
250 255 260 265 270 275 280 285 290 295 300
t (s)
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-0.4
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0
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(m/s
)
Validation
Simulation
Experimental
+
�
WEC
+
+pe
Fa
v
p
pr
1Zi
WEC
+
+
Fa
v
p Gpe
Zi+GpeG
pr
1Zi+Gp
eGpr
Gpe
Zi
Ger
MISO
p
1Zi
Gpe
Fav+
+
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
Systemidentification
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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
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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)
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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)
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Models have been identified from experimental data
Case1:positionandacceleration
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Case1:positionandacceleration
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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
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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
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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
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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
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Case2:pressureandacceleration
§ Sampleresults:
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In-progress
§ WillreleasethecodeshortlyonMHKDRwebsite§ Caneasilybeextendedto
§ Multipledegreeoffreedom/multi-body/multi-device§ Multi-sensordatafusiontoimproveestimation
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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.
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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)