Comparing Combinations of Linear and Nonlinear Feedback Terms for Ship Motion Control

In this article, combinations of linear and nonlinear feedback terms are investigated for 3 degrees-of-freedom pose and velocity control of ships. Nonlinear control algorithms that are found in the literature often have linear feedback terms, which result in nice globally exponential stability properties when assuming no actuator constraints. However, considering that all actuators have saturation constraints, such stability properties are not feasible in practice. Applying nonlinear feedback terms can be a step to handle such constraints. As a result, this article explores nonlinear feedback terms for both the kinematic and kinetic control loops. Specifically, three controllers based on a cascaded backstepping control design are implemented and compared through simulations and model-scale experiments in an ocean basin. Stability properties and tuning rules for all the controllers are also provided. Interestingly, the use of nonlinear feedback terms gives the ability to constrain the feedback control inputs globally while simultaneously being able to change the convergence rates locally. The price to be paid is the introduction of additional tuning parameters. The three controller types are compared using performance metrics which consider both control accuracy and energy use.