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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

Thrust Allocation

Ole Jakob Sørdalen, PhD

Counsellor Science & Technology

The Royal Norwegian Embassy, Singapore


Controller architecture
Controller architecture

  • 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

    • Wind load compensation

    • Reference model tracking

  • Optimal thrust allocation

  • Adaptive control



Problem statement
Problem statement

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


Challenges
Challenges

  • 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


Singularities

T

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:


Singular value decomposition
Singular Value Decomposition

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


About svd
About SVD ...

  • 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.


Example plot of smallest singular value
Example: plot of smallest singular value

Bow azimuth fixed 90o. Aft azimuts rotate


Area where s 0 05
Area where s < 0.05


Area where s 0 015
Area where s < 0.015


Fixed angle between aft azimuths
Fixed angle between aft azimuths

s < 0.05



How to determine angles a
How to determine angles a?

  • Consider azimuth thrusters as two perpendicar fixed thrusters

  • New (expanded) relation: AeTe = t

  • desired ”expanded” thrust vector Ted:

    Ted = A+etc


How to determine thrust t
How to determine thrust T?

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

  • Modified pseudo inverse:

    Ad+ = V Sd+ UT  T = V Sd+ UTtc


Geomtrical interpretation
Geomtrical interpretation

  • 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




Features
Features

  • 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


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