Optimal Synergetic and Feedback Linearization Controllers Design for Overhead Crane Systems: A Comparative Study

This study presents a performance comparison between a synergetic controller (SC) and a feedback linearization based state feedback controller (FL-SFC) applied to overhead crane system. At first, the mathematical model of the system is formulated. Thereafter, the design of both SC and FL-SFC are elaborated, leading to the development of control laws for the proposed controllers. For the SC design, the Lyapunov function is employed to guarantee an exponential convergence of the tracking error to zero. In the FL-SFC approach, an equivalent transformation is used to convert the nonlinear system into a linear form, and then the state feedback controller (SFC) method is utilized to make the error function reach zero where accordingly the crane moves to the specified displacement with minimum sway angle. Taking the advantages of simulating the global pollination process, enabling effective exploration of the entire search space and reducing the risk of being trapped in local minima, the flower pollination algorithm (FPA) is used to tune the design variables of the controllers based on the integral absolute error (IAE) criterion. MATLAB software is used to perform the simulation of the two proposed methods into the crane system. The results show that the SC exhibits a good performance in normal operation and a robustness test involving system parameters’ changes than the FL-SFC.