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

¹ Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece
² Department of Industrial Engineering, University of Salerno, Fisciano, 84084, Italy
³ Department of Mechanical Engineering, University of Northumbria, NE1 8ST, Newcastle, UK
⁴ Department of ECS Engineering, Rensselaer Polytechnic Institute, 12065, Troy, New York, USA
⁵ Laboratoire de Robotique, Université de Tunis el Manar, Tunis 1068, Tunisia

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Abstract

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.