Algorithms for cable-suspended payload sway damping by vertical motion of the pivot base

Abstract

The solution of a case study problem of suspended payload sway damping by moving a pivot base in vertical direction is presented. Unlike for the classical problem of anti-sway control for moving the base in the horizontal direction, implemented e.g. in cranes, a direct solution by using control feedback theory for linear systems is not possible. Once the model is linearized, it becomes uncontrollable. Thus, a derivation of a nonlinear controller is needed to solve the task. In this context, two solutions are proposed. The first solution is based on imposing harmonic motion of the base with double frequency of the payload natural frequency. Synchronization of the base and the payload deflection angle is done either by proportional time-delay controller or by proportional-derivative delay free controller. Secondly, the Lyapunov's second method is directly applied to derive a nonlinear controller. For both cases, balancing the dissipated energy, rules for determining equivalent damping are explicitly derived. After discussing and solving the corresponding implementation aspects, both simulation and experimental validations are performed. The experimental validation is performed on a simplified problem, where only horizontal motion is possible. The simulation based validation is performed on a nonlinear two dimensional model of a quadcopter carrying a suspended payload.

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

“…In [28], the authors solve a problem of damped sway of a suspended payload that was achieved by moving a pivot base in vertical direction, as it can be seen in Figs. 2, 3, 4.…”

“…The numerical solutions are presented in Figs. 28,29,30,31,32,33,34,35,36,37,38,39. The value of = 2 is kept constant with zero initial velocities in all cases, but the value of m varies in time.…”

“…The Figs. 28,29,30,31,32,33,34,35,36,37,38,39 show the SAM mass's nonsingular orbits under swinging, that is, no physical contact between the swinging assembly and the pulley. It can be seen that the SAM is integrable when m = 3 , and from the results, the system is not integrable for m ∈ (0, 1) ∪ (3, ∞) .…”

“…Fig. 28 An orbit of the SAM for m = 2.0 , = 2 , and initial velocity equal to zero. In the radial direction, we measure l(t) ; in direction, we measure (t) Fig.…”

Controlling the variable length pendulum: Analysis and Lyapunov based design methods

“…Let us also point to an analogous problem, recently examined in [28], where the pendulum length is kept fixed and its angular motion is damped by up and down motion of the pivot. In this case, damping is achieved through the momentum effect of the difference between the gravitational and inertia forces on the pendulum bob.…”