Broaching-to prevention in real-time using momentary state feedback control focusing on the saddle point in the system

For realizing real-time broaching-to prevention in regular waves, the momentary state feedback control in the vicinity of the saddle point of the dynamical system is newly proposed, based on the previous work (Maniyappan in J Mar Sci Technol, 2020, https://doi.org/10.1007/s00773-020-00743-4 ). This is an extension of the concept of OGY (Ott, Grebogi, and Yorke) (Ott in Phys Rev Lett 64:1196–1199, 1990) algorithm by applying momentary state feedback using the linear-quadratic regulator (LQR) only when the ship approaches a saddle point. It was numerically confirmed in regular waves that controlling the surging in a wave downslope during broaching-to enables to change the broaching to a periodic motion at lower Froude number. At higher Froude numbers, broaching-to prevention is achieved by undergoing stable surf-riding near the wave trough in lower heading angles. The robustness of the controller towards modeling uncertainties and limitation of the observed variables are also confirmed by using a controller model that ignores the nonlinear terms in the calm-water manoeuvring forces and the longitudinal position of the ship to waves.