Because of the complexity, non-linearity, and under-actuated features of double pendulum overhead cranes, a control method based on linear active disturbance rejection control (LADRC) and differential flatness theory is proposed to realize accurate trolley positioning and effective swing eliminating. Specifically, in order to simplify the system model, we introduce the differential flatness theory to construct system output. Based on this method, the uncertainty and system external disturbance become total disturbance. The control method of the crane is designed according to LADRC. Then, we use the bird swarm algorithm (BSA) to optimize controller's parameters. Finally, the double-pendulum crane control method based on the LADRC can better accomplish the crane's anti-swing and location in the real environment according to simulation and experimental results, which confirms its effectiveness and robustness in existing system.

Heat pumps are widely investigated for their versatile use in a wide range of applications. In this study, three types of heat pumps were experimentally compared. These heat pumps include an one-stage without injection vapor heat pump, an one-stage injection vapor heat hump and a two-stage injection vapor heat pump with an economizer. The results showed that the heating capacity of all three variants of heat pumps decreases with the decrease of the evaporation temperature. However, the attenuation ratio of the heating capacity is found to be different from one pump to another. On the one hand, the largest attenuation rate is found to be 68.84% for evaporating temperatures ranging from −1 °C to −23 °C and for the case of one-stage heat pump. On the other hand, the smallest attenuation rate is found to be 31% for the two-stage injection vapor heat pump in the same temperature range. It is worth noting that the heating efficiency is improved by the amount of vapor injection, nevertheless, there is a maximum value due to the limitations of the economizer. The two-stage injection vapor heat pump can exhibit an enhanced heating efficiency of 127% compared to the one-stage without injection vapor heat pump and 13% compared to the one-stage injection vapor heat pump for an evaporating temperature of −23 °C.