Dynamic Positioning using Integrator Backstepping: a non-linear Lyapunov stable observer-based approach
Author
Christensen, Rasmus Lundgaard
Term
4. term
Education
Publication year
2014
Submitted on
2014-06-04
Pages
87
Abstract
Dette speciale udvikler en ikke-lineær regulator, en estimator og en skibsmodel til dynamisk positionering af en shuttletanker (automatisk fastholdelse af position med thrustere). Arbejdet bygger på tidligere backstepping-baseret kontrol for forsyningsskibe og forbedrer den ved eksplicit at indarbejde bølgeinducerede bevægelser i stabilitetsanalysen. Estimatoren kombinerer den kendte ikke-lineære skibsmodel med et bølgefiltrerende design, der er stabilt og passivt i Lyapunov-forstand. I praksis sammenfletter den GPS- og kompasdata med modellen og giver dermed mere præcise positionsestimater end rå målinger alene. Estimatoren er bevist eksponentielt globalt stabil, hvilket betyder, at estimatet over tid konvergerer mod den sande position uanset startpunkt. Kalman–Yakubovich–Popov-lemmaet bruges til at indstille og verificere filterets stabilitet. Den resulterende regulator er ensartet globalt eksponentielt stabil og kan holde positionen trods forstyrrelser. Ydelsen benchmarkes mod det lineære testsystem, som FORCE TECHNOLOGY anvender til at evaluere skibes thrusterkonfigurationer; den ikke-lineære regulator overgår den lineære og kan potentielt erstatte det nuværende system. Specialet præsenterer også de første skridt mod et on-line kraftallokeringsmodul formuleret som en kvadratisk optimering. Test viser, at store spring i det pålagte styresignal kan gøre allokeringen ustabil. Problemet er komplekst, fordi to azimuth-thrustere (drejelige propeller) hver skal vælge retning og kraft og tilsammen skabe kræfter i x- og y-retning samt et drejemoment omkring z-aksen. Efter forfatterens bedste viden indgår en bølgeinduceret bevægelsesparameter ikke tidligere i stabilitetsanalyser af skibe; resultaterne åbner for videre forskning i ikke-lineær kontrol af skibe og offshore-fartøjer. Rapporten diskuterer desuden forslag til at gøre systemet endnu mere robust.
This thesis develops a nonlinear controller, an estimator, and a vessel model for dynamic positioning of a shuttle tanker (automatic station-keeping using thrusters). It builds on earlier backstepping-based control for supply ships and improves on it by explicitly including wave-induced motions in the stability analysis. The estimator combines a known nonlinear model of the vessel with a wave-filtering design that is stable and passive in a Lyapunov sense. In practice, it fuses GPS and compass data with the model to provide more accurate position estimates than raw sensors alone. It is proven exponentially globally stable, meaning its estimate converges to the true position over time from any starting point. The Kalman–Yakubovich–Popov lemma is used to tune and verify the filter’s stability. The resulting controller is uniformly globally exponentially stable and can maintain position in the presence of disturbances. Performance is benchmarked against the linear test system used at FORCE TECHNOLOGY to evaluate ship thruster configurations; the nonlinear controller outperforms the linear counterpart and could replace the current system. The thesis also reports initial work on an online thrust-allocation module formulated as a quadratic optimization. Tests show that large jumps in the commanded control signal can make this allocator unstable. The allocation problem is challenging because two azimuth thrusters must each choose a direction and a thrust level, together generating forces in the x and y directions and a yawing moment about the z-axis. To the author’s knowledge, no previous ship stability analysis explicitly includes a wave-induced motion parameter; these results point to further research opportunities in nonlinear control for ships and offshore vehicles. The report also discusses proposals for making the system more robust.
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