Dynamic Modeling and Feedback Linearization Control of a 3-D Overhead Gantry Crane System

The overhead crane systems are important heavy-duty machines that are widely used, especially in construction and industry sectors to transport and lift heavy loads. This paper introduces the mathematical modeling of a 3-D overhead crane. The Euler-Lagrange equation is utilized to extract the dynamic equations of the crane system. The obtained nonlinear crane model has been linearized by applying the feedback linearization technique. Then, a PID controller has been developed and implemented to the obtained linearized crane model. The parameters of the designed PID controller have been tuned by implementing the Differential Evolution (DE) algorithm which significantly improved the performance of the PID controller. The simulation results have been performed using MATLAB/SIMULINK platform. The obtained simulation results clearly showed the impact of applying the Differential Evolution (DE) technique to tune the PID controller gains which provided better performance compared to the manually tuned PID controller gains.