Fuzzy-Model-Based Control of an Overhead Crane With Input Delay and Actuator Saturation

This paper investigates the problem of a Takagi–Sugeno (T–S) fuzzy-model-based control of a nonlinear overhead crane system with input delay and actuator saturation. The complex nonlinear dynamic system of the crane is modeled as a three-rule T–S fuzzy model with a saturated input. Based on the fuzzy model, a state-feedback controller is designed so that trajectories of the system that start from an ellipsoid will remain in it, where a decay rate is introduced to accelerate the response speed. Besides, since the input delay often appears in real equipment, the delayed feedback control is also considered with respect to the actuator saturation. Delay-dependent existence conditions of the fuzzy controller are established such that the load can be placed in a desired position by the crane with a much suppressed swing angle, where trajectories of the closed-loop system that start from a bounded set will asymptotically converge to a contractively invariant ellipsoid. The results are formulated in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Simulations on the true plant are illustrated to show the feasibility and effectiveness of the proposed control method.