This paper deals with the sliding mode control of a three-dimensional overhead crane. The model of the crane consists of five highly nonlinear second-order ordinary differential equations. The crane is an underactuated system, which makes the design of its controllers intricate. A sliding mode control scheme is proposed for the crane. This scheme, which guarantees the asymptotic stability of the closed-loop system, has two objectives: position regulation and anti-swing control. The performance of the closed-loop system is simulated using MATLAB. The simulation results indicate that the proposed control scheme works well. In addition, the robustness of the controller with respect to uncertainties in the crane parameters is investigated through simulations. It is found that the controller is robust to changes in the parameters. Moreover, since some of the states of the system are not measurable, a Luenberger-type observer is proposed. Simulation of the controlled system using the observer-based sliding mode controller produced good results.

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This paper investigates the sliding mode control of the Ball on a Beam system. A static and a dynamic sliding-mode controllers are designed using a simplified model of the system; the simplified model renders the system feedback linearizable. Then, a static and a dynamic sliding-mode controllers are designed using the complete model of the Ball on a Beam system. Simulation results indicate that the proposed controllers work well.The four proposed controllers are implemented using an experimental setup. Implementation results indicate that the proposed control schemes work well. As expected, it is found that the proposed two controllers which are designed using the complete model of the system gave better performance than the ones designed using the simplified model of the system. In addition, the experimental results indicate the two dynamic controllers greatly reduce the chattering usually associated with sliding-mode controllers.