Fine tuning of a PID controller with inlet derivative filter using Pareto solution for gantry crane systems

Abstract

Gantry cranes are widely used in transporting heavy loads in construction projects and critical industries such as petrochemical industry and nuclear power stations. Their mission should be accomplished with as high accuracy for the trolley positioning, and minimum values of sway oscillation angles as possible. So, the control strategies aim to achieve high productivity (through transporting the trolley with good precision) while considering safety precautions (through eliminating sway oscillations). One of the linear closed loop control methods is using PD and PID controllers. This research provides a non-linear mathematical model for single-pendulum gantry crane with two stable control schemes that depend on PID and PD controllers equipped with inlet derivative filter for every scheme. The two control schemes utilize a PID controller for positioning the trolley and a PD controller for eliminating undesired sway angles of the payload. In the second scheme, the input voltage control signal is always saturated to be positive to preserve the direction of rotation of the driving DC motor. The controllers include up to five gains and two inlet derivative filter coefficients which are tuned using Multi-Objective Genetic Algorithm (NSGA-II) with four different fitness functions and one weighted function to choose a suitable solution from other Pareto solutions. The simulation results are presented to show the superiority of the second scheme precision in trolley transporting with minimum payload sway oscillations.

Keywords

• Optimal Pareto solutions
• PID controller
• Multi-Objective Genetic Algorithm (NSGA-II)
• Optimization
• Saturated input control signal
• Gantry Crane system