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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Ole Jakob Sørdalen, PhD
Counsellor Science & Technology
The Royal Norwegian Embassy, Singapore
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
Assumption here: Thrusters are bi-directional
A(a) T = t , simple pseudo inversion can give high gains and high thrust
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
A+ = V S+ UT
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
s < 0.05
Ted = A+etc
Ad+ = V Sd+ UT T = V Sd+ UTtc
efficient ”geometrical” filtering of this noise