Because of the complexity, non-linearity, and under-actuated features double pendulum overhead cranes, a control method based on linear active disturbance rejection (LADRC) differential flatness theory is proposed to realize accurate trolley positioning effective swing eliminating. Specifically, in order simplify system model, we introduce construct output. Based this method, uncertainty extern...

In crane automation systems, precise knowledge of the load position is a key factor for fulfilling positioning accuracy requirements. This contribution presents a nonlinear observer design for harbor cranes which makes use of gyroscope measurements. Both single-pendulum load configurations and more complex double-pendulum configurations are considered. The gyroscope sensors are attached to the ...

Various behavior types of reaction forces and Lagrange multipliers for the case mechanical systems with configuration space singularities are studied in this paper. The motion a one-dimensional double pendulum (or singular pendulum) transversal point or first order tangency is considered. Properties depends on constraint line which free vertex moves along. Configuration could be represented by ...

The phenomenon of dynamic stabilization of the inverted pendulum whose pivot is forced to oscillate with a high frequency in vertical direction is revisited. A simple physically meaningful explanation of the phenomenon is presented, followed by the derivation of an approximate quantitative criterion of stability. A computer program simulating the physical system is developed, which aids the ana...

This paper studies the stability and bifurcations of the relative equilibria of the double spherical pendulum, which has the circle as its symmetry group. This example as well as others with nonabelian symmetry groups, such as the rigid body, illustrate some useful general theory about Lagrangian reduction. In particular, we establish a satisfactory global theory of Lagrangian reduction that is...