Great amount of work has been dedicated to eliminate residual vibrations in rest-to-rest motion. Considerable amount of these methods is based on convolving a general input signal with a sequence of timed impulses. These impulses usually have large jumps in their profiles and are chosen depending on the system modal parameters. Furthermore, classical input shaping methods are usually used for constant cable length and are sensitive to any change in the system parameters. To overcome these limitations, polynomial command shapers with adjustable maneuvering time are proposed. The equation of motion of a simple pendulum with the effect of hoisting is derived, linearized, and solved in order to eliminate residual vibrations in rest-to-rest maneuvers. Several cases including smooth, semi-smooth and unsmooth continuous shapers are simulated numerically and validated experimentally on an experimental overhead crane. Numerical and experimental results show that the proposed polynomial command shaper eliminates residual vibrations effectively. The effect of linear hoisting is also included and discussed. To enhance the shaper performance, extra parameters are added to the polynomial function to reduce shaper sensitivity. Results show that the effect of adding these parameters greatly enhances the shaper performance.

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