Operator-based robust right coprime factorization design for planar gantry crane

In this paper, a nonlinear robust control scheme is considered for a planar gantry crane system. The influence of motion friction and viscous friction of the linear motor and viscous friction of the cable is investigated under different operating conditions. Then, the Lagrange motion equation of the planar gantry crane is setup, which can be described as a nonlinear dynamic model. For this system, there exist one input force and two outputs including the displacement distance of the linear motor and the swing angle of the cable, that is, it is a nonlinear underactuated system. In this paper, the swing angle is regarded as variable parameter, which is calculated approximately using the force and the displacement distance. As a result, it leads some uncertainties in the considered model, which is unknown but bounded. To avoid the influence of the unknown uncertainties, operator-based robust right coprime factorization approach is considered for the nonlinear system. The stability of the control system is guaranteed by robust right coprime factorization condition. The nonlinear robust controller makes the linear motor move to the desired position and the swing of the cable go to zero nonoscillatory. Numerical simulation is given to show the effectiveness of the proposed method.