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-program 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 ControlsRyan Coe (rcoe@sandia.gov)Giorgio Bacelli (gbacell@sandia.gov)June 6, 2016

Outline1. Project overview/overall motivation2. Control comparison3. Control basics4. Testing overview5. Testing results6. Model validation7. Future work8. Questions/discussion

3

PROJECT OVERVIEWAdvanced WEC Dynamics and Controls

4

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 performance

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

5

Project objectives Use numerical modeling and novel laboratory testing

methods to quantitatively compare a variety of control strategies: advanced 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

6

WEC CONTROLS COMPARISONAdvanced WEC Dynamics and Controls

7

Control strategy comparison

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

Advanced WEC Control

What is the potential of control systems in WECs?

9

Buoy design

Final designAxisymmetric shapes

Absorption: comparison

10

Comparison of Control Strategies

Baseline (Resistive) Model Predictive Control (MPC) Dynamic Programming (DP) Shape Based (SB) Control Linear Quadratic (LQ) Control PDC3 Latching

11

Model Predictive Control

Optimization based control strategy Can be computationally expensive

The control signal is optimal for the predicted excitation force for a linear system. Requires estimator/predictor If the prediction is perfect, the control algorithm provides the

maximum energy absorption The control algorithm is capable including constraints

(motion, force) in the formulation of the optimization problem

Requires PTO capable of generating reactive power Requires energy storage

12

Dynamic Programming

It can be implemented for nonlinear systems Optimization based control strategy

Computationally very expensive The control signal is optimal for the predicted excitation force

for a linear system. Requires estimator/predictor If the prediction is perfect, the control algorithm provides the

maximum energy absorption The control algorithm is capable including constraints

(motion, force) in the formulation of the optimization problem

Requires PTO capable of generating reactive power Requires energy storage

13

Shape Based Control

It can be implemented for nonlinear systems Optimization based control strategy

Computationally very expensive, but more efficient than DP The control signal is optimal for the predicted excitation force

for a linear system. Requires estimator/predictor If the prediction is perfect, the control algorithm provides the

maximum energy absorption The control algorithm is capable including constraints

(motion, force) in the formulation of the optimization problem

Requires PTO capable of generating reactive power Requires energy storage

14

Linear Quadratic Control

Pure feedback control strategy Computationally inexpensive (matrix multiplication) Optimal feedback gain is obtained by offline optimization

Linear WEC model LQ feedback control is well known for good properties

(stability, robustness to parameters uncertainty,…) Requires PTO capable of generating reactive power

Requires energy storage NOT capable of dealing with constraints

15

PDC3 Potential to demonstrate actual realization of CC control design

Implementation will be fundamentally novel and first practical approximation (scheduled for next FY17)

Wave foreknowledge is not required Method is computationally fast and potentially easy to

implement Uses linear WEC model Fundamentally feedback control strategy (PD loops) Requires PTO capable of generating reactive power

Requires energy storage Expansion of strategy to multi-DOF’s and more nonlinear cases

is essential in order to understand how well strategy can work on real world systems

16

Latching

It is a switching control strategy It does not require model of the WEC for the calculation for

the control signal (in its simplest form)

It can be used also for nonlinear systems It may require prediction of wave elevation/excitation force to

improve performance It does not require PTO capable of generating reactive power

Does not require energy storage NOT capable of dealing with constraints

17

Sea states

18

Summary of results

All units in metric

19

Summary of results (Sample time-series)

Velocity vs Excitation force

20

Summary of results (Sample time-series)

Actuator force vs Excitation force

21

Summary of results (Sample time-series)

Instantaneous absorbed power and excitation force

22

Nonlinear WEC model

Nonlinear configurations CONFIG-D3:

Quadratic drag Actuator stroke length = 0.5m Actuator max force = 8.0 kN

CONFIG-D4: Quadratic drag Actuator stroke length = 0.5m Actuator max force = 2.7 kN

Controllers (linearized control model)

Resistive MPC LQ Latching

23

Nonlinear WEC model

Note: Plant (WEC) models are nonlinear; control models are linear

Linear controllers perform well with (mild) nonlinear devices

24

CONTROL BASICSAdvanced WEC Dynamics and Controls

25

Control systems design

WEC

EXAMPLE: CC conjugate controlIdeal case (simulation)

Wave excitation force ()

ControllerReference velocity

𝑣𝑟𝑒𝑓 𝑣

26

Control systems design

WEC

EXAMPLE: CC conjugate controlA more “Realistic” situation

Wave excitation force () (Unknown)

Noise

Sensors

ControllerState estimator

Reference velocity

�̂� 𝑒 �̂�𝑟𝑒𝑓

𝑣Velocity calc.

27

Control systems design

Control model: If control algorithm is based on a model of the system

(i.e. model based control), then: First principle model --> from theory System identification --> from data

𝐹 𝑜𝑝𝑡=𝑍𝑖❑

❑∗=[𝑅 (𝜔 )+𝐵+𝑖 (𝜔 (𝑀+𝑀𝑎 (𝜔 ) )− 𝑘𝜔 )]

∗

EXAMPLE: CC conjugate control

28

Control systems design

Measurements: Available measurements

May not be possible to measure all the quantities we want (e.g. excitation force, velocity)

State estimator design Noise in the measurements

Filter Frequency domain control design

29

Control Structure Interaction (CSI)

What happens when you close the loop? Even with a simple linear damping, the closed loop system behaves

differently

Root locus example: when increasing the damping the poles moves towards RHP zeros -> system unstable

𝑦𝑢=

𝐺 (𝑠)  1+𝐺 (𝑠)𝐵

𝐺 (𝑠 )

𝐵

𝑦𝑢

-5 -4 -3 -2 -1 0 1 2 3 4 5

-1.5

-1

-0.5

0

0.5

1

1.5

Root Locus

Real Axis (seconds -1)

Imag

inar

y A

xis

(sec

onds

-1)

30

Control Structure Interaction (CSI) Example: WEC / bridge interaction

31

Control Structure Interaction (CSI)

Closing the loop on velocity using position measurements

0 1 2 3 4 5 6 7time

-1.5

-1

-0.5

0

0.5

1

1.5posvel

0 50 100 150 200 250 300 350 400# harmonic component

0

0.05

0.1

0.15

velocity FFT

𝑢 (𝜔 )=𝑖 𝜔 𝑧 (𝜔 )When differentiating the position,The noise is amplified by “”i.e. linearly increasing with frequency

32

Control Structure Interaction (CSI)

Sensitivity function and “waterbed effect”

Feedback Systems: An Introduction for Scientists and EngineersBy Karl Johan Aström, Richard M. Murray

33

Control Structure Interaction (CSI)

Bottom line: Even the implementation of a “simple” linear damping is not trivial

One simple approach Low-pass filter

CAREFUL ABOUT THE PHASE!

-40

-30

-20

-10

0

Mag

nitu

de (d

B)

10-2 10-1 100 101 102-90

-45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/s)

𝐺 (𝑠 )= 11+𝑠

Cut-off frequency is 1rad/sPhase is ~5degree at 0.1rad/s

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WAVE TANK TESTINGAdvanced WEC Dynamics and Controls

35

Test objectives

“Traditional” decoupled-system testing• Radiation/diffraction• Monochromatic waves

Multi-sine, multi-input testing• Excite system w/ both inputs (waves and actuator)• Band-width-limited multi-sine signals

“At-sea” testing• Excite system w/ both inputs (waves and actuator)• Idealized wave spectra

36

Test objectives

“Traditional” decoupled-system testing

Multi-sine, multi-input testing

“At-sea” testing

Can the approach used in other fields for system

identification provide better results for WECs?

Can tests that can be conducted at-sea (i.e. cannot control incoming waves) provide sufficient data to

model the dynamic system (e.g. to update the model intermittently)?

What subtleties specific to WECs need to be

considered for designing a better wave tank test?

37

Test hardware – WEC device

• Designed as WEC controls test-bed

• Not intended for full-scale

• Platform to implement, validate

and assess control strategies

• Multiple configurations

• 1-DOF, 3-DOF, 5-DOF

• De-ballast for increased hydro

nonlinearity

• ~1/17th scale

• Displacement: 858 kg

38

Test hardware – WEC device

39

Test hardware – sensors

• Acquired at 50 Hz• NI cRIO system coupled to

separate wave probe systems via TTL trigger and GPS timestamping

40

Test hardware – wave basinManeuvering and Seakeeping (MASK) basinNaval Surface Warfare Center, Carderock Division (NSWCCD)• Built 1962• Dimensions: 106x76x6m deep• Updated wavemakers in 2013

• 216 individual flaps• Peak wave power is approximately 1MW

41

Test hardware – basin layout

𝝀

𝑥𝑦

𝑧

brid

ge

Design factors:• Advanced radiation modeling• Hardware-in-the-loop wave

propagation/prediction• Directional seas

42

Test hardware – wave probes

Sonic probes (green) Tough Senix TSPC-30S1 20 Hz

Capacitive probes (magenta) OSSI Wave Staffs 50 Hz

Resistive probes (red) EDL wave-wires 50 Hz

43

TESTING RESULTSAdvanced WEC Dynamics and Controls

44

Testing

Excitation force model Device locked;

Radiation force model No waves;

System identification 2 inputs / 1 output system

Multisine force on actuator / Multisine wave spectra Band limited white noise on actuator / Bretschneider wave spectra

Why did we use periodic signals? Leakage Better signal to noise ratio – averaging over periods Smoother spectrum (no dips) Nonlinearity detection

45

Testing

System identification

References:• Davidson, J., Giorgi, S. and Ringwood, J.V.. Identification of wave tank models from numerical wave tank data – Part 1:

NWT identification tests. IEEE Trans. on Sustainable Energy, in press., 2016• Giorgi, S., Davidson, J. and Ringwood, J.V.. Identification of wave tank models from numerical wave tank data – Part 2:

Data-based model determination. IEEE Trans. on Sustainable Energy, in press., 2016

Plant(WEC)

Multi Input Single Output (MISO) system

Output:

Input 1: FPTO

Input 2: waves

46

Testing Repeating vs non-repeating spectra

Water surface elevation: Bretschneider spectrum, repeat period Trep= 5minutes

0 5 10 15

time (min)

-4

-3

-2

-1

0

1

2

3

4

5

(in)

NOTE: Measurements from acapacitive wave probe 185 190 195 200 205 210 215 220 225

time (s)

-4

-3

-2

-1

0

1

2

3

4

(in)

first periodsecond periodthird period

Detailed view of the overlapped time series

47

Testing results Repeating vs non-repeating spectra

Bretschneider

No Spectrum leakage for period signals Detailed view

# harmonic component

Pow

er

48

Testing results Repeating vs non-repeating spectra

Period T=5min, total time 15 min

Period T=2hrs, total time 30 min

Bretschneider

“Smoother” spectrum (smaller dips in the spectral density) Better S/N ratio

• Measurements from a capacitive wave probe• spectra have not been smoothed, filtered, averaged, etc,..

NOTEs:

𝜔

𝑆(𝜔

)

49

Testing Excitation FRF:

�̂� (𝜔 )

𝜂 (𝑡 )

𝐹 𝑙𝑜𝑐𝑘(𝑡) �̂� 𝑙𝑜𝑐𝑘 (𝜔 )

�̂� (𝜔 )

DFT (FFT)

trimmed at integer multiple of period

500.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Frequency (Hz)

0

0.5

1

1.5

2

2.5

3

|H(

)| (N

/m)

104

ExperimentalWAMIT

Testing Excitation FRF:

51

Testing Radiation FRF:

𝑍𝑟 (𝜔 )=�̂� (𝜔 )+𝑖 𝜔 �̂�𝑎 (𝜔 )=�̂� 𝑃𝑇𝑂 (𝜔 )�̂� (𝜔 )

−𝐵−𝑖(𝜔𝑀 − 𝐾𝜔 ) = Radiation damping = Added mass = velocity = PTO force= linear friction/dissipation= mass = hydrostatic restoring coeff

𝑍𝑟 (𝜔 )

𝑢 (𝑡 )

𝐹 𝑃𝑇𝑂(𝑡 ) �̂� 𝑃𝑇𝑂 (𝜔 )

�̂� (𝜔 )

DFT (FFT)

trimmed at integer multiple of period

52

Testing Radiation FRF:

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000

0

1000

2000

3000

Rad

iatio

n D

ampi

ng

Radiation

ExperimentalWAMIT

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1frequency (Hz)

0

500

1000

1500

2000

Add

ed M

ass

53

Testing Models comparison from different experiments

�̂� 𝑃𝑇𝑂 (𝜔 )�̂� (𝜔 )

= �̂�𝑖=�̂� (𝜔 )+𝐵+𝑖(𝜔 (𝑀+ �̂�𝑎 (𝜔 ) )− 𝐾𝜔 )Intrinsic impedance

Experiments at different values of inputpower and spectra give same model

Sample Input force spectra

54

Testing

Pressure based frequency response functions Why use pressure?

Pressure relatively easy to measure Pressure sensors located on the device Excitation pressure to force TF is causal

12.3 12.4 12.5 12.6 12.7 12.8 12.9 13Time (min)

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

forcepressure

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

Mag

nitu

de

Radiation FRF (pressure/velocity)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1frequency (Hz)

-2

0

2

4

Pha

se

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

Mag

nitu

de

Excitation FRF (Force/Pressure)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1frequency (Hz)

-200

-100

0

100

200

Pha

se

55

Testing At sea system identification

It is not possible to use periodic waves at sea Still have control on the PTO force, depending on PTO capabilities

Band limited white noise BLWN Multisine Modulate PTO damping …

Plant(WEC)

Output:

Input 1: FPTO(Multisine, BLWN)

Input 2: (real) waves

BLWN = band limited white noise

56

Testing

Waterline in conical section nonlinear modeling: In progress

0 200 400 600 800 1000 1200 1400time (s)

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

z (m

)

Radiation: stepped sine

𝑧

Asymmetric response:nonlinear

57

FUTURE WORKAdvanced WEC Dynamics and Controls

58

Testing results State estimator

Using wave tank experiments At sea

WEC

𝐺𝑟𝑃𝑒

𝐹 𝑒

𝑧

𝐺𝑒

𝐹𝑃𝑇𝑂+

+

+

+ 𝑃

Model set-up:

= excitation pressure = measured pressure = exc pressure to Force TF = rad velocity to pressure TF

= Unknown input

59

Out-years Real-time control Expand study to

Nonlinear modeling/control Additional degrees-of-freedom

Include power-electronics and structural modeling Dynamics and control of 2nd device (considering WEC-Sim

validation device, “FOSWEC)

60

Publications/disseminations Control strategy development [3,4,5,6] Control-structure interaction [2] Control strategy comparison [3,4] Wave tank test report w/ testing data (in-prep) Model development [7,8] Updated control comparison, based on model from tank testing (in-prep) Pressure-excitation state-estimator (in-prep) Proposed: 2017 METS WEC dynamics and controls workshop

61

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 multiprogram 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)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 (SNL)Diana Bull (SNL)Tim Crawford (SNL)

62

References[1] ——, “Estimation of excitation force on wave energy converters using pressure measurements,” in OCEANS2016, submitted. Monterey,

CA: IEEE, September 2016.

[2] D. Wilson, G. Bacelli, R. G. Coe, R. D. R. 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.

[3] D. Wilson, G. Bacelli, R. G. Coe, D. L. Bull, O. Abdelkhalik, U. A. Korde, and R. D. R. III, “A comparison of WEC control strategies,” Sandia

National Labs, Albuquerque, New Mexico, Tech. Rep. SAND2016-4293, April 2016 2016.

[4] G. Bacelli, R. G. Coe, D. Wilson, O. A. U. A. Korde, R. D. R. III, and D. L. Bull, “

A comparison of WEC control strategies for a linear WEC model,” in METS2016, Washington, D.C., April 2016.

[5] 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.

[6] ——, “A dynamic programming approach for control optimization of wave energy converters,” in Ocean Engineering, in review, 2016.

[7] 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.

[8] 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.

[9] 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.

[10] 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.