A new optimization technique is developed to generate a step-input acceleration function for an input shaping harmonic system. This approach is integrated into an overhead crane model for a rest-to-rest maneuver with standard and nonstandard maneuver settings. The proposed method guarantees the satisfaction of the system constraints and desired final conditions, while it minimizes the system sensitivity to crane cable-length variations. The minimal system sensitivity is achieved through an optimization algorithm that provides zero vibration and a minimum integral of system sensitivity over a continuous range of crane cable length. Numerical simulations are conducted to demonstrate the feasibility of the proposed shaper in eliminating the residual vibration at the end of a programmed maneuver. Sensitivity analyses are also performed to verify the robustness of the new shaper. In comparison to the previous shapers, the new methodology is significantly less sensitive and can effectively handle different arbitrary maneuver times.

This article presents a modified zero vibration (ZV) input shaping technique to address the sensitivity and flexibility limitations of the classic ZV shapers commonly implemented in overhead crane applications. Starting with the classical ZV formulation, new parameters are introduced to optimize the control system performance according to a versatile objective function. The new shaper enhances the design flexibility and operational domain of the shaper, while it inherits the robustness properties and computational efficiency of the ZV scheme. Unlike the original ZV shaper, the proposed shaper allows for the point-to-point maneuver time to be fixed. The sensitivity analysis of the controller confirms that the new shaper effectively reduces the ZV sensitivity to the cable length variations.

The residuals of liquid free-surface wave oscillations induced by a rest-to-rest crane maneuver of a suspended liquid container are eliminated using a command-shaped profile. The dynamics of liquid sloshing are modeled using an equivalent mechanical model based on a series of mass-spring damper systems. The proposed model considers the excited frequencies of the container swing motion and liquid sloshing modes. The objective is to design a discrete-time shaped acceleration profile with a variable command length, that controls the moving crane-jib, while suppressing the sloshing modes. Simulations are conducted to illustrate the command effectiveness in eliminating liquid sloshing with a wide variation range of system and command-designing parameters; liquid depth, cable length, command duration, and the employing of higher sloshing modes in representing the sloshing dynamics. The command sensitivity of the input command to changes of the system parameters are treated as well. A refined and smooth input command based on suppressing the residuals of multi-modes is also introduced. Furthermore, the command effectiveness was supported by a comparison with the time-optimal flexible-body control and multi-mode zero vibration input shaper.

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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