The tower crane is widely used in construction and transportation engineering. To improve working efficiency and safety, input shaping methods have been applied. Input shaping is a method of reducing residual vibration of flexible systems by convolving a sequence of impulses with unit step command. However, input shaping is based on the linear system theory in which its control performances are degraded, in case of nonlinearity and unmatched dynamics of the control systems. In this paper, a new optimal reference input shape design method based on minimizing cost function is suggested and applied, to a simple cart-pendulum system which is a simplified model of tower cranes. Since pendulum dynamics is nonlinear, analytic solution does not exist. To overcome this problem, in this paper, a machine learning approach is suggested to find optimal reference input shape for the cart position control. The feasibility of the proposed design method is verified through some simulation examples by using MatLab.

This paper presents an improved input shaping method to eliminate vibration during circular interpolation of a flexible 2-axis positioning system. Due to the time delay introduced by input shaping, simultaneous 2-axis positioning with circular interpolation results in a certain amount of errors from the intended track or trajectory. This study investigated the track errors associated with circular interpolation caused by input shaping for a flexible 2-axis positioning system. The following three strategies for reducing such errors were proposed: velocity reduction in circular interpolation, adjustment of the time delay between 2 axes commands, and employment of a velocity profile compensation function. Simulations were performed to discuss the pros and cons of the three proposed strategies. Experiments were also performed to validate the results. Simulation and experiments showed that the track errors due to input shaping can be sufficiently reduced by combined use of the proposed strategies.