Robust PID anti-swing control of automatic gantry crane based on Kharitonov's stability

PID (proportional+integral+derivative) control is known as simple and easy-to-implement controller. However, the robustness performance is often not satisfactory when dealing with parameter variations of the plant. In addition, its design procedure is not straightforward for the system which is non-SISO (Singe Input Single Output) system like a gantry crane. In this paper, a stable robust PID controller for anti-swing control of automatic gantry crane is proposed. The proposed method employs Genetic Algorithm (GA) in min-max optimization to find the stable robust PID. In the optimization, the robustness of the controller is tested using Kharitonov's polynomials robust stability criterion to deal with parametric uncertainty appears in gantry crane model. For practicality, the model is identified by conducting simple open-loop experiment in the beginning. The experimental results show that a satisfactory robust PID control performance can be achieved. The controller is able to effectively move the trolley of the crane in short time while canceling the swing of the payload for different conditions of payload mass and cable length variations.