Nonlinear optimal control of overhead cranes for installing sea-submerged water-supply tubes

In this article, a new nonlinear optimal control method is proposed for 3-DOF overhead cranes with variable hoisting payload, used in berthing and installing sea-submerged water-supply tubes for arid islands. The dynamic model of this robotic crane undergoes first approximate linearization around a temporary operating point that is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of Jacobian matrices. For the approximately linearized model of the overhead crane with variable hoisting and water-submerged payload an H-infinity feedback controller is designed. For the computation of the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. Global stability is proven through Lyapunov analysis.