Stabilizing position of the overhead crane with the weight suspended on a flexible cable
For the overhead crane with the weight suspended on a flexible cable, stabilization in the desired position is considered. The motion of the system is regarded as planar. The mathematical model of the entire system involves a partial differential equation with boundary conditions. The law of crane control is a linear feedback including information about the position of the crane carrier, its speed angle between the cable and the carrier at the point of their connection, the speed of variation of this angle, and the deformation of the cable. The feedback also involves an integral term. Therefore, three of the six addends in the control law correspond to the traditional PID-controller. The delay in the feedback is also taken into account. The problem of asymptotic stability of the desired crane position is reduced to studying the spectrum of a boundary problem and determining the necessary and sufficient conditions for which all infinitely numerous eigenvalues of the system lie in the left-hand plane of the complex plane. The results are formulated in terms of the domains of asymptotic stability constructed in the space of feedback coefficients. The stability domains with and without regards for cable flexibility are compared.
scientific article; zbMATH DE number 2108573