Large amplitude oscillation of crane payloads is detrimental to safe and efficient operation. Under certain conditions, the problem is compounded when the payload creates a double-pendulum effect. Most crane control research to date has focused on single-pendulum dynamics. Several researchers have shown that single-mode oscillations can be greatly reduced by properly shaping the inputs to the crane motors. This paper builds on those previous developments to create a method for suppressing double-pendulum payload oscillations. The input shaping controller is designed to have robustness to changes in the two operating frequencies. Experiments performed on a portable bridge crane are used to verify the effectiveness of this method and the robustness of the input shaper.

Systems that exhibit flexible dynamics are widespread and present a very challenging control problem when their performance is pushed to the limit If there is some knowledge of the flexible modes, then command signals can be generated to negate the detrimental dynamics. These vibration-reducing commands are dependent on the feedback controller gains because the gains influence the flexible modes. This paper presents a method for concurrently designing a PD feedback controller and a command generator so that performance is optimized. The design method takes into account limits on allowable overshoot, residual vibration, and actuator effort. Furthermore, the structure of the method allows a wide range of performance requirements, such as disturbance rejection, to be integrated into the design. Results demonstrate that a PD controller cannot achieve the same performance as a PD controller augmented with a command generator.

Manipulating payloads with gantry cranes can be difficult given the inherent system flexibility. In fact, the payload cannot move until some deflection occurs in the support cable, thereby generating a horizontal force. Gantry crane dynamics can often be effectively modeled as a single linear flexible mode. However, if the crane is equipped with a large-mass hook and the payload is sufficiently light, then the dynamics can become complicated by double-pendulum effects. This paper presents a method for determining the contribution of the second pendulum mode to the overall dynamic response. Furthermore, an input shaping scheme is developed to reduce residual oscillations. This control method utilizes the double-pendulum dynamics to determine the parameters of the input shaping algorithm.

The dynamic behavior of a planar gantry crane with hoisting of the load is investigated. The command generation method of input shaping is proposed for reduction of the residual vibration. Several versions of input shaping are evaluated and compared with time-optimal rigid-body commands over a wide range of parameters. Input shaping provides significant reduction in both the residual and transient oscillations, even when the hoisting distance is a large percentage of the cable length. Experimental results from a 15-ton gantry crane at the Savannah River Technology Center are used to support the numerical results.

If the dynamic behavior of a flexible system is known, then commands can be generated to negate the detrimental dynamics. These commands are dependent on the feedback controller gains. The paper presents a method for concurrently designing the feedback controller and the command generator so that performance is optimized.

Manipulating payload with gantry cranes can be difficult given the inherent system flexibility. Gantry crane dynamics can often be effectively modeled as a single linear flexible mode. However, if the crane is equipped with a large-mass hook and the payload is sufficiently light, then the dynamics can become complicated by double-pendulum effects. This paper presents a method for determining the contribution of the second pendulum mode to the overall dynamic response. Furthermore, an input shaping scheme is developed to reduce residual oscillations. This control method utilizes the double-pendulum dynamics to determine the parameters of the input shaping algorithm

If the dynamic behavior of a flexible system is known, then commands can be generated to negate the detrimental dynamics. These commands are dependent on the feedback controller gains. This paper presents a method for concurrently designing the feedback controller and the command generator so that performance is optimized. The vibration of flexible systems often limits operational speed. If the system dynamics are known, commands can be generated that will negate the system's flexible modes. Input shaping is one such command generation scheme that is implemented by convolving a sequence of impulses with the command signal. Input shaping can be used in conjunction with any type of feedback controller. A block diagram for the case with an input shaper outside the loop and a Proportional-Derivative (PD) feedback controller is shown in Figure 1. A method is presented in this paper for formulating residual vibration and auxiliary performance constraints to simultaneously calculate

The performance of many mechanical systems is often limited by their flexibility. One method for counteracting the detrimental effects of flexibility is to generate commands that will not induce vibration. A system for which a moderately accurate dynamic model can be constructed is generally a good candidate for a type of command generation called input shaping. Traditional robust input shapers are designed based on anticipated deviations from the modeled natural frequencies. In this paper an input shaper is developed based on deviations from physical parameters, rather than from frequencies. A two-link robotic arm is used to demonstrate the effectiveness of the parameter-based shaper design method.