Abstract||This thesis is concerned with robust control of an offshore steel jacket platform
subject to nonlinear wave-induced forces. Since time delay and uncertainty are
inevitably encountered for an offshore structure and their existence may induce instability, oscillation and poor performance, it is very significant to study on how the
delay and uncertainty affect the offshore structure. In this thesis, a memory robust
control strategy is, for the first time, proposed to reduce the internal oscillations
of the offshore structure under wave-induced forces, so as to ensure the safety and
comfort of the offshore structure.
Firstly, when the system's states are adopted as feedback, memory state feedback
controllers are introduced for the offshore structure. By using Lyapunov-Krasovskii
stability theory, some delay-dependent stability criteria have been established, based
on which, and by combining with some linearization techniques, memory state feedback controllers are designed to control the offshore structure. The simulation results show that such controllers can effectively reduce the internal oscillations of the
offshore structure subject to nonlinear wave-induced forces and uncertainties. On
the other hand, a new Lyapunov-Krasovskii functional is introduced to derive a less
conservative delay-dependent stability criterion. When this criterion is applied to
the offshore structure, an improved memory state feedback controller with a small
gain is obtained to control the system more effectively, which is sufficiently shown
by the simulation.
Secondly, when the system's outputs are adopted as feedback, memory dynamic
output feedback controllers are considered for the offshore structure. By employing
a projection theorem and a cone complementary linearization approach, memory
dynamic output feedback controllers are derived by solving some nonlinear minimization problem subject to some linear matrix inequalities. The simulation results
show that the internal oscillations of the offshore structure subject to nonlinear
wave-induced forces are well attenuated.
Finally, robust H control is fully investigated for the offshore structure. By employing Lyapunov-Krasovskii stability theory, some delay-dependent bounded real
lemmas have been obtained, under which, via a memory state feedback controller or
a dynamic output feedback controller, the resulting closed-loop system is not only
asymptotically stable but also with a prescribed disturbance attenuation level. The
simulation results illustrate the validity of the proposed method.