Nonlinear Optimal Control for Underactuated Offshore Cranes

There is wide use of boom cranes in ports and on vessels for ships' loading and unloading. In this article a nonlinear optimal control approach is proposed for the model of offshore boom cranes. The dynamic model of the boom cranes undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the system. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the boom cranes, under model uncertainties and external perturbations. For the computation of the controller's feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the boom cranes, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.