“…When an emergency stop is required, the non-zero initial state of the crane can introduce strong residual vibrations to the payload, that is, velocity, swing angle or angular velocity are not zero. Although many works have been proposed to solve the stable control problem of the overhead crane, most of them assume that the cranes have zero initial states, for example, proportional-integral-derivative (PID) control, 8,9 fuzzy control, [10][11][12] optimal control, [13][14][15] sliding-mode control, [16][17][18][19] model predictive control (MPC), [20][21][22][23] trajectory planning control, 24,25 and command shaping control. [26][27][28] To handle the non-zero initial velocity issue, Joaquim Maria Veciana et al introduced a method that considered the initial states for the control inputs, which were obtained from a feedback sensor and this method could be processed with a reasonable time delay.…”