Dynamic Positioning using Integrator Backstepping: a non-linear Lyapunov stable observer-based approach

Abstract

Dette projekt dokumenterer udviklingen af en ikke-lineær controller, estimator samt model, til brug i dynamis positionering af en shuttle tanker. State-of-the-art metoder udviklet af [FG98], gør brug af backstepping metoder til kontrol af et forsynings skib. Denne rapport er baseret på dette arbejde, og foreslår en metode hvormed de forstyrrelser bølgerne inducerer på skibet kan inkluderes. Estimatoren er baseret på [FS99], der har udviklet en bølgefiltrerende estimator der både udviser Lyapunov stabilitet samt passivitet. Estimatoren er baseret på den kendte ikke-lineære model af skibet, og gennem denne, udregnes estimater af skibets attitude til brug i controlleren. Estimatoren viser at kunne forbedre på GPS samt kompas målinger. Estimatoren vises at være eksponentielt global stabil, og vil derved give estimater der over tid konvergerer mod den sande måling. Stabilitets egenskaben samt tuningen af filtret sker ved brug af Kalman-Yakubovich-Popov lemmaet. Slut resultatet er en uniform global eksponentiel stabil controller, der kan holde fartøjets position under indflydelse af eksterne forstyrrelser. Sammenligningsgrund- laget for controlleren er det lineære system der i øjeblikket anvendes hos FORCE TECHNOLOGY . Dette system bruges til at teste thruster-konfigurationer under en række givne forstyrrelser. Resultater viser at den ikke-lineære controller er bedre end dens lineære modstykke, og foreslåes derfor som udskiftning til det system der bruges hos FORCE TECHNOLOGY . Udover controlleren, er start skridtet taget til at udvikle et on-line thrust allokerings modul, der løser en kvadratisk ligning, og gennem dette giver en optimal løsning på hvorledes de enkelte thrusters skal agere for at opnå den ønskede thrust. Store udsving i kontrol signalet har desværre vist at den foreslåede algoritme ikke kan håndtere store udsving i reference signalet. Kompleksiteten af problemet stammer fra de 2 azimuth thrustere der er monteret på skibet. Disse kan både producere en kraft i x- og y-retningen samt et moment omkring z-aksen, og allokeringen har således svært ved at finde en endelig løsning. Umiddelbart er der ikke nogen der tidligere har forsøgt at inkludere den bølge baserede bevægelses parameter i stabilitets analysen for skibe, og dette forsøg lægger op til en større undersøgelse af ikke-lineær kontrol af skibe og andre off-shore fartøjer. Forslag der kan gøre systemet bedre bliver diskuteret i slutningen af rapporten.

This project documents the development of a non-linear controller, estimator and model to be used for dynamic positioning of a shuttle tanker. State-of-the-art methods have been developed by [FG98], which employs a backstepping framework for the control of a supply ship. This project is based on this work, and fosters to improve on the outcome, by including the wave induced motions in the stability analysis. The estimator is based on the works of [FS99] who develops a wave filtering estimator that is both stable and passive in a Lyapunov sense. The estimator is based on the known non-linear model of the vessel, and through this, provides the controller with an estimate of the position that is better than using raw GPS and compass measurements. The estimator is shown to be exponentially globally stable, and will thus provide an estimate that over time converges to the true measurement. The stability properties and tuning of the filter is achieved using the Kalman-Yakubovich-Popov lemma. The end result is a uniform globally exponential stable controller that is able to maintain the vessels position whilst under the influence of disturbances. The benchmark of the controller is the linear system used at FORCE TECHNOLOGY to test if various thruster configurations of ships are able to maintain the position under specified disturbances. Results have shown that the non-linear controller outperforms the linear counterpart, and as such could replace the system used at FORCE TECHNOLOGY . Besides the controller, initial steps to develop an on-line thrust allocating module by solving a quadratic equation have been developed and tested, however, large jumps in the control signal makes the allocating module unstable. The complexity of the optimization problem is evident by the two azimuth thrusters mounted on the vessel, which both requires an angle and an input force, and through this, can be used to produce a force in the x- and y-direction as well as a moment about the z-axis. To the authors knowledge, no one have included the wave induced motion pa- rameter in the stability analysis of ships - and these findings make way for a deeper investigation into non-linear control of ships and other off-shore vehicles. Proposals to make the system even more robust are discussed in the report.

A master thesis from Aalborg University

Dynamic Positioning using Integrator Backstepping: a non-linear Lyapunov stable observer-based approach