Adaptive fuzzy backstepping hierarchical sliding mode control for six degrees of freedom overhead crane

The Prescribed-Time Sliding Mode Control for Underactuated Bridge Crane

“…x 4 in Equation ( 10) and combine Model (7) with Equation (10), it is necessary to construct the following equation to hold:…”

“…The transformation of Model (7) into Model ( 14) is achieved by constructing auxiliary variables while transforming control Objective (3) into lim…”

“…The problem of positioning and swing elimination in bridge crane systems has been extensively researched. This research encompasses open-loop control methods such as input shaping [1] and trajectory planning [2,3], as well as closed-loop control methods, like PID control [4,5], backstepping control [6,7], fuzzy control [8], and sliding mode control [9][10][11][12]. The core idea of input shaping and trajectory planning is to design the acceleration of the trolley, so as to reduce the swing of the load as much as possible during the movement of the trolley.…”

Modeling and control of overhead cranes: A tutorial overview and perspectives

“…Several kinds of flexibilities, e.g., transversal deflection (see Fig. 2(c)) and length extension [194,128] can be taken into account in this category, leading to several different equations depending on the flexibility types. The models in this category lead to PDE-ODEs, e.g., linear wave equation [64,118,69,67] or semilinear wave equation [140], caused by the cart and cable dynamics, that need to be spatially discretized with finite-element methods (FEM) for simulation and for control application (for instance see [79]) and yield finite-dimensional Lagrange systems based on FEM approximations of the wave equation [71], and Rayleigh-Ritz discretization [62].…”