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# Thrust Allocation - PowerPoint PPT Presentation

Thrust Allocation. Ole Jakob Sørdalen, PhD Counsellor Science & Technology The Royal Norwegian Embassy, Singapore. Controller architecture. Sensor signal processing Signal QA Filtering and weighting Vessel Model Separate LF/WF model Kalman filter estimator Mooring model Optimal Control

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### Thrust Allocation

Ole Jakob Sørdalen, PhD

Counsellor Science & Technology

The Royal Norwegian Embassy, Singapore

• Sensor signal processing

• Signal QA

• Filtering and weighting

• Vessel Model

• Separate LF/WF model

• Kalman filter estimator

• Mooring model

• Optimal Control

• Positioning and damping

• Reduce fuel, tear and wear

• Mooring line break compensation

• Feedforward control

• Reference model tracking

• Optimal thrust allocation

Given desired forces and moment from the controller, tc =[txc, tyc, tyc]T.

Determine thrusts T=[T1, T2,..., Tn]T and azimuth angles a=[a1, a2,..., an]T so that

• ||A(a) T - tc|| is minimal to minimize the error

• ||T|| is minimal to minimize fuel consumption

• ai(t) is slowly varying to reduce wear and tear

Assumption here: Thrusters are bi-directional

• Singularities: the singular values of A(a) can be small;

A(a) T = t ,  simple pseudo inversion can give high gains and high thrust

• An azimuth thruster cannot be considered as two independent perpendicular thrusters since the rotation velocity is limited

• If the thruster is not symmetric, how should the azimuth respond to 180o changes of desired thrust directions?

• Forbidden zones

3

t

t

T

y

x

1

T

t

2

y

Singularities

There is an azimuth angle where det A(ais) = 0

A(ais) cannot be inverted

Example of a singular configuration:

Any m x n matrix A can be factored into

A = U S VT

Where U snd V are orthogonal matrices.

S is given by

• Coloumns of U: orthonormal eigen vectors of AAT

• Coloumns of V: orthonormal eigen vectors of ATA

• si = sqrt (eig(ATA) i)

• Pseudo inverse of A:

A+ = V S+ UT

• The least square solution to Ax = y is

x = A+y

i.e. either min ||Ax – y||2 or min ||x|| 2 Can use weighted LS.

Bow azimuth fixed 90o. Aft azimuts rotate

Area where s < 0.05

Area where s < 0.015

Fixed angle between aft azimuths

s < 0.05

• Consider azimuth thrusters as two perpendicar fixed thrusters

• New (expanded) relation: AeTe = t

• desired ”expanded” thrust vector Ted:

Ted = A+etc

• Note: T = A+(af)tc large T close to singular configurations!

• Modified pseudo inverse:

Ad+ = V Sd+ UT  T = V Sd+ UTtc

• Commanded thrust in directions representing small singular values are neglected

• This is GOOD

• Azimuth angles are always oriented towards the mean environment forces & torques

• Other commanded forces typically due to noise

 efficient ”geometrical” filtering of this noise

• Automatic azimuth control

• Automatic avoidance of forbidden sectors: not shown here

• Optimal direction control

• Smooth turning

• Optimal singularity handling

• Avoidance of unnecessary use of thrust

• Reduced wear and tear of propulsion devices

• Optimal priority handling

• Among thruster devices

• Among surge, sway, yaw