Boundary Output Feedback Control for A Class of Gantry Crane Systems via Backstepping Approach

In this paper, a boundary output feedback controller is addressed for a class of gantry cranes via the backstepping approach. The gantry crane is modeled into a dynamical system govern by partial differential equations (PDEs). Then, utilizing the backstepping technique, the dynamical PDE system can be transformed into a target system under the designed controller which only forces on the trolley. Besides, based on the operator semigroup theory and the Lyapunov stability theory, the solution to the target system is proven to be well-posed and exponentially stable. According to the inverse transformations and the stability of the target system, the dynamical system is confirmed to be exponentially stable. Finally, simulation and comparison are presented to verify the efficiency and the advantages of the proposed method.