Flatness based Control of a Gantry Crane

This contribution deals with flatness based control of a laboratory model of a gantry crane. The mechanical model has 3DOFs, where a trolley can be moved on a rail, the load is fixed at the end of a rope and can be lifted or lowered by coiling or uncoiling this rope on a cylinder. Under the assumption that the rope is always stretched, the underactuated system is not input to state linearisable but it is flat with the coordinates of the load as flat output. Since the flat output coincides with the variables to be controlled, a flatness based design for trajectory tracking and stabilisation is indicated. The design of the tracking control is accomplished in two steps. First, the system is exactly linearised by a quasi-static state feedback. Subsequently, for the linear system a feedback with integral parts is designed such that the motion of the load is stabilised about the reference trajectories. Moreover, the control law is extended by terms which approximately compensate for the friction occurring at the gantry crane. Finally, the setting of the controller parameters is discussed and measurement results are presented, which demonstrate an excellent tracking behaviour and disturbance attenuation.