H∞ Output-Feedback Anti-Swing Control for a Nonlinear Overhead Crane System With Disturbances Based on T-S Fuzzy Model

In this paper, the
$H_{\infty }$
output-feedback controller for a nonlinear overhead crane system with external disturbances was developed. Firstly, the Takagi-Sugeno fuzzy model was used to represent the overhead crane system nonlinearity. A fuzzy-based state observer was then built to estimate the values of immeasurable variables. Secondly, a novel control design called virtual-desired variable synthesis was used to converting the tracking control into a stabilization problem. It was primarily used to define the internal desired states, making the design procedure clear and easy. The
$H_{\infty }$
performance criterion was used to attenuate external disturbances, and the closed-loop model stability was investigated using the quadratic Lyapunov function. Finally, three simulations were conducted to verify the feasibility and effectiveness of the proposed method. The results have shown that there is practically no positioning error and residual payload swing. Thus, in theory, any type of bounded external disturbances can be eliminated using the proposed method. Additionally, the convergence time is half of its model predictive control method counterpart and one-third of the standard
$H_{\infty }$
controller. Hence, it provides a reference for actual control of the overhead crane systems, mostly due to its good performance.