Objective function selection of GA-based PID control optimization for automatic gantry crane

Gantry cranes are widely used in various applications to transfer a payload from one position to desired position. Gantry crane system is an underactuated system where the number of inputs is less than the number of outputs. When the input signal is given to the actuator, the trolley starts to accelerate whilst causing a swing of payload hanging on a flexible cable. Many researchers have proposed anti-swing controls of gantry crane using PID+PD structure where PID controller is used for trolley positioning control and PD controller is used to dampen the swing oscillation. This is because of the simplicity of PID control structure. Some have combined intelligent methods such as fuzzy and neural networks to improve the performance of the proposed PID control structure. This paper discusses GA-based PID+PD controller tuning for automatic gantry crane system. The discussion is emphasized on the selection of the objective function since the objective function is the key to use the GA (genetic algorithm). The optimized PID gains would be mainly due to the appropriate objective/fitness function. The simulation results show that a good anti-swing control performance can be obtained from the proposed objective function.