Fixed-Time Adaptive Robust Synchronization with a State Observer of Chaotic Support Structures for Offshore Wind Turbines

The chaotic support structures for offshore wind turbines are often subjected to a severe environment. A robust control scheme needs to be considered to maintain them in a safe operational limit. Robust sliding mode control (SMC) scheme can provide an excellent robust controller against this severe and challenging environment for these chaotic structures. This paper proposes a novel fixed-time adaptive sliding mode control scheme with a state observer to synchronize chaotic support structures for offshore wind turbines in the presence of matched parametric uncertainties. The proposed controller is a new integration of adaptive control concept, SMC method, fixed-time stability concept and a state observer. A fixed-time stability concept is used to provide stability for the system within a presented time regardless of initial conditions. The adaptive concept is utilized to provide an online estimator of the uncertain upper bound. Also, a nonlinear observer is employed to provide an online estimator of an unmeasured state in the controller. Lyapunov stability theorem is used to analyze fixed-time stability of the system based on SMC methodology. The simulation results demonstrate that the proposed controller is able to ensure fixed-time synchronization along with providing precise means to estimate the unmeasured state as well as uncertainty upper bound.