This paper presents an adaptive control approach using a model matching technique for 3-DOF nonlinear crane systems. The proposed control is linearly composed of two control frameworks: nominal PD control and corrective control. A nonlinear crane model is approximated by means of feedback linearization to design nominal PD control avoiding perturbation. We propose corrective control to compensate system error feasibly occurring due to perturbation, which is derived by using Lyapunov stability theory with bound of perturbation. Additionally, we achieve stability analysis for the proposed crane control system and analytically derive sufficient stability condition with respect to its perturbation. Numerical simulation is accomplished to evaluate our proposed control and demonstrate its reliability and superiority compared to traditional control method.

This paper presents a robust control approach for nonlinear uncertain crane systems with a three DOF framework. We deal with an overhead crane in which a trolley located on the top is moved to x-and y-axes independently. We first approximate the nonlinear system model through feedback linearization transformation to simply construct a PD control and then design a robust control system for compensating control deviation feasibly occurring due to modeling error or system perturbation in practice. An adaptive control rule is analytically derived by using Lyapunov stability theory given bounds of system perturbation. We accomplish numerical simulation for evaluating the proposed methodology and demonstrate its superiority by comparing with the traditional control strategy.

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