Harmonic Disturbance Rejection with Applications to the Control of Offshore Cranes
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The research proposed in this dissertation has been conducted from a theoretical as well as an applicative point of view. From a theoretical standpoint, the scope of the thesis falls within the field of the nonlinear output regulation theory, and, more specifically, within a variant of the latter known as the harmonic disturbance rejection theory. Within such a framework, techniques such as internal model-based (IMC), external model-based (EMC) and adaptive feedforward-based (AFC) control have been investigated. Some of the theoretical findings have also been applied to the problem of controlling cranes employed in marine offshore lowering operations. The specific, applicative problem consists in preventing the damaging effects originating as a result of a possibly violent interaction between the payload and the waves at water-entry. The experiments, performed on a scale-model of an offshore crane and carried out at the Marine Cybernetics Laboratory at NTNU, have shown that the proposed strategies have been effective in improving the performances of previous approaches present in the literature. The structure of this dissertation is based upon the material of three distinct journal papers which have been, either published or submitted for publication in international journals. In the first one, the aforementioned crane-control problem was addressed by resorting to a re-interpretation in a linear output-regulation setting of a previous, feedforward control strategy present in the literature. A major challenge involved in the application of the internal model-based design to the problem under consideration, was that the regulation error was not available for feedback, thereby distancing the actual setting from a canonical one. A certainty equivalence design was then pursued by relying on observers of fixed structure in order to reconstruct the unavailable tracking error. In doing so, a certain number of simplifying assumptions were made, such as knowledge of both the plant parameters and the frequencies of the harmonics of the wave-induced disturbances; moreover, a linear model of the hydrodynamic force was employed. In spite of such limitations, the experiments showed improvements with respect to the previous control strategy. In the second contribution, all the restrictive assumptions upon which the previous work relied, were removed. In doing so, a nonlinear robust design was pursued; while the unavailable states were reconstructed by means of a canonical adaptive observer, the far more challenging task involving the reconstruction of the wave-induced disturbances, was accomplished by resorting to a hybrid, adaptive external model-based strategy. Moreover, the nonlinearities originating from the hydrodynamic forces were fully taken into account, resulting in a highly nonlinear setting. The overall design, not only enhances the robustness properties as compared to the previous approach, but also leads to remarkable improvements of the experimental results. In the third contribution proposed in this thesis, the problem of the adaptive feedforward compensation for the case of nonlinear systems, was addressed, to the best of the author’s knowledge, for the first time. Restricting the attention on those nonlinear systems possessing a unique, T-periodic steady-state whenever forced by a disturbance with the same period, it was shown how, under suitable assumptions, the proposed scheme succeeds in achieving disturbance rejection with a semi-global domain of convergence. The effectiveness of the proposed solution was demonstrated by combining results from averaging analysis with techniques for semi-global stabilization.