Modified observer backstepping controller for a dynamic positioning system

• Conventional observer backstepping controllers are inadequate for DP systems.
• Estimation error and saturation of the actuators lead to on–off-like control signals.
• A smooth commanded thrust is achieved by adding two gain matrices in the controller.
• Proposed modifications improve overall controller performance.

A procedure for attenuating the control law of a vessel dynamic positioning system, based on the observer backstepping methodology, is proposed. The motivation is the appearance of an undesirable on–off behavior on the signal sent to the actuators when their saturation is considered and the control law is dependent on estimated state variables. Two gain matrices associated with the error variables are introduced to achieve the desired attenuation. Stability is proven through Lyapunov stability analysis. Numerical simulations confirm the effectiveness of the proposed controller to render the control law compatible with the limitations of the actuators.