Higher Order Sliding Mode Control Applied to Dynamic Positioning Systems

Abstract

This paper presents the application of Higher Order Sliding Mode Control (HOSM) theory to the problem of Dynamic Positioning (DP) of offshore vessels. Robustness aspects of Sliding Mode Control are suitable for DP design, since the vessels are subjected to several unmeasured environmental disturbances and there are also modeling uncertainties inherent to such a complex system. However, first-order sliding mode control presents chattering (high frequency oscillation) in the control action. Such effect is eliminated by changing the original formulation of the controller, replacing the sign function by a smooth transition function (such as sigmoid or saturation). Such replacement introduces a steady state error, that is then eliminated by the introduction of an integral action. The application of HOSM control naturally eliminates the chattering, since the order of the system is artificially increased and the control action is in fact the time-integral (low-pass filter) of a high-frequency oscillatory signal. So, there is no necessity of changing the original formulation of sliding mode control to obtain a smooth control action, while still keeping the good robustness and model-error insensibility properties of sliding mode control. Problems associated with the necessity of second order derivative of the position are discussed, and an exact-robust differentiator is then applied. A numerical simulator is used to assess the performance and robustness of the HOSM control applied to a typical DP shuttle tanker. Preliminary experimental analysis is also exposed.