A 3D overhead crane is an underactuated system consisting of five outputs: trolley position, bridge translation, cable length, and two cargo swings. These outputs are controlled by three actuators for cargo hoisting, trolley motion, and bridge traveling. This study proposes the use of a nonlinear controller that performs five tasks concurrently: cargo hoisting, trolley tracking, bridge motion, payload vibration suppression during transport, and cargo swing elimination at the destination. The proposed algorithm is combined with two control components: (i) partial feedback linearization, which is a precursor to controller design, to suppress cargo vibration; and (ii) sliding mode method, which provides robust control in lifting the payload and driving trolley and bridge motions against model imprecision and uncertainty. These two control mechanisms are successfully merged into a combined controller because the kinematic relationships between the state variables are made apparent in the system dynamics. Simulation and experimental results show that the proposed controller asymptotically stabilizes all system responses.COMBINED CONTROL WITH SLIDING MODE AND PFL 3373 parameter-varying model, Giua [13] designed a controller-observer with state-feedback stabilization for time-varying systems. Park [14] proposed a nonlinear controller for a 2D container crane to suppress cargo swing, track the trolley, and lift the cargo. FLC was applied to the trolley and cargo hoisting dynamics to obtain one controller component; the antiswing component was obtained with an energy-based nonlinear control design. Cho [15] proposed a scheme linearly composed of two controls: nominal proportional-derivative (PD) control designed through feedback linearization and corrective control. Cho expanded this so-called PFL controller with an adaptive component in [16].Studies on SMC for crane systems have also been published. The general theory of SMC for a class of underactuated systems was first presented by Bergeman [17], developed by Lee [18], and completed by Ashrafiuon [19] and Sankaranarayanan [20]. Focusing on overhead crane control, Karkoub [21] introduced a variable structure controller in conjunction with state feedback control andţ-synthesis control. Bartolini [22] proposed a simple control scheme based on second-order sliding modes for a payload-cart system with constant cable length. In another study by Bartolini [23], two SMC laws were constructed: a proportional-integral controller and a linear, observer-based, time-varying feedback scheme. Liu [24] combined fuzzy logic with SMC for an overhead crane based on a linearized mathematical model. Lee [25] developed an SMC controller by analyzing sliding surface stability to concurrently control cargo swing and trolley motion. With the simplest crane model wherein cable length is constant, an adaptive fuzzy SMC control was proposed by Park [26] for cargo antiswing and trolley tracking. Almutrairi [27] adopted the SMC scheme developed by Lee [25] to develop a 3D crane control system. An ...

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This study constructs an original mathematical model of a shipboard container crane and proposes a nonlinear controller for the complicated operation duties in which the viscoelasticity of seawater and the flexibility of handling cable are taken into account. By using two inputs, namely, the pulling force of the trolley and the torque of the hoist, the controller simultaneously drives six outputs, including trolley motion, cable length, container swing, axial container oscillation, ship roll, and ship heave. The effects of elasticity factors and wave excitations on system performance are also investigated. The simulation and experiment results reveal that the controlled system responses remain stable and consistent despite disturbances.

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