Efficient control of a nonlinear double

This paper proposes an efficient proportional–integral–derivative (PID) control of a highly nonlinear double-pendulum overhead crane without the need for a payload motion feedback signal. Optimal parameters of the PID controllers are tuned by using an improved particle swarm optimization (PSO) algorithm based on vertical distance oscillations and potential energy of the crane. In contrast to a commonly used PSO algorithm based on a horizontal distance, the approach resulted in an efficient performance with a less complex controller. To test the effectiveness of the approach, extensive simulations are carried out under various crane operating conditions involving different payload masses and cable lengths. Simulation results show that the proposed controller is superior with a better trolley position response, and lower hook and payload oscillations as compared to the previously developed PSO-tuned PID controller. In addition, the controller provides a satisfactory performance without the need for a payload motion feedback signal