Input shaping and command shaping control techniques are the subject of large body of research in the past several decades. Most of the research is dedicated to time invariant single-mode systems. For a double pendulum hoisting system, hoisting results in a complex system of equations of motion. For rest-to-rest maneuvers, it is a common practice in research to split maneuvers into three consecutive independent stages; hoisting up the payload from an initial position, moving it horizontally, and finally lowering it to a final location. Input shaping is used is the horizontal travel motion stage to eliminate inertia excited vibrations. Although, this approach is effective, significant time penalties are involved due to the split motion approach. Further, traditional input shaping techniques involve significant jerks in the motion commands. To overcome these drawbacks, a new smooth waveform command shaping technique is proposed to enable concurrent hoisting and travel actions. The equations of motion including time varying coefficients are derived and used to determine the coefficients of an optimum waveform shaped command profile. Genetic algorithm optimization technique is used to find the optimal values of the command parameters. The initial values of these parameters are determined assuming a constant cable length. The effectiveness of the shaped command is demonstrated through numerical simulations and experiments on a scaled model of double pendulum using different maneuvers involving simultaneous travel and linear hoisting.

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