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.

The purpose of this study was to compare ankle joint loads (Linear and Angular Impulses) while descending the stairs and ramp. Ten young male subjects participated in this study. Stairs and ramp of identical slope (30 degrees) were custom-made to include force plates in the middle of pathways. Subjects descended the stairs and ramp at a comfortable speed and posture. The stance period was divided into three phases, weight acceptance (WA), single limb stance, and pre-swing. Three-directional impulses and their sum were derived from the reaction forces and moments at the ankle joint. Differences in impulse sums (Both Linear and Angular) between stairs and ramp were significant only in the early (WA) phase, whereas those of stairs were greater than the ramp. All subjects adopted forefoot strike strategy for the stairs and 80% of the subjects adopted rearfoot strike strategy for the ramp. An increase in the GRF and moment arm of the GRF at the ankle joint in case of forefoot strike may have contributed to the increase in the linear and angular impulse in the early phase of stair descent compared to ramp descent. The results are in agreement with the preference of ramp in the elderly.