Low-oscillation command switch-times for relay-driven cranes with asymmetrical acceleration and deceleration

Cranes powered by relay-controlled circuits constitute an important set of industrial cranes used throughout the world. Due to their simplicity, ruggedness, and long service life, this type of crane can be found in older factories or in applications where precise motion control is not a strict requirement. However, controlling payload oscillations on this type of crane is challenging for two reasons: 1) Relays that can only be turned on or off allow for only limited control over the crane trolley velocity; and 2) These cranes typically have nonlinear asymmetrical acceleration and deceleration properties. This paper presents a method for determining the relay switch-times that move payloads with low residual oscillation. First, a closed-form equation for the residual oscillation given an arbitrary input motion is derived. Second, the relationship between crane trolley motion and switch-times is established. Finally, numerical searches are used to determine minimal-oscillation switch-times.