A Discretized Optimization Strategy for Rest-to-Rest Maneuvers of Overhead Cranes Considering the Effect of Damping Available to Purchase

An optimization strategy to reduce residual vibration of rest-to-rest maneuvers of overhead cranes is proposed. The proposed technique is based on generating shaped acceleration commands for a simple harmonic oscillator with damping included. Furthermore, the proposed technique solves the problem of discrete signal commands that result from using slow digital to analog convertors on real cranes. A discretized acceleration profile is derived analytically using finite step segments. These segments are integrated into a matrix, which is then coupled with a system response matrix through the system’s equations of motion. The resulting input acceleration matrix is then optimized to satisfy rest-to-rest maneuver conditions. The profile designer can control many parameters such as maneuver duration, discrete time step, hoisting speed, damping ratio, maximum velocity and acceleration. Unlike traditional command shapers, the proposed shaped profiles are independent of the natural period of the system, i.e., the acceleration profile duration is designer selectable. Through several examples, the performance of the proposed controller is validated numerically. Results show that the proposed shaping technique can effectively eliminate residual vibrations in rest-to-rest maneuvers of damped single-degree-of-freedom systems.