Decoupled linear model and S

Overhead cranes with double-pendulum effect seem more practical than those with single-pendulum effect. However, in this case, it is difficult to find an applicable controller for such systems. Hence, a linearized and decoupled double-pendulum overhead crane dynamic model is derived by adopting a disturbance observer and modal analysis technique. The S-shaped trajectory is planned by solving algebraic equations, and the stability of the system is confirmed by the Routh–Hurwitz stability theory. Experimental results and simulations demonstrate the effectiveness of the proposed method. It could be realized to operate the crane accurately without sensor systems for measuring load sways by using the proposed method