Flatness-Based Control in Successive Loops of an H-Type Gantry Crane with Dual PMLSM

Abstract

Gantry cranes of the H-type with dual electric-motor actuation are widely used in industry. In this article the control problem of an H-type gantry crane which is driven by a pair of linear permanent magnet synchronous motors is considered. The integrated system that comprises the H-type gantry crane and its two PMLSMs is shown to be differentially flat. The control problem for this robotic system is solved with the use of a flatness-based control approach which is implemented in successive loops. To apply flatness-based control in successive loops, the state-space model of the H-type gantry crane with dual PMLSM is separated into subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. The state variables of the preceding (i-th) subsystem become virtual control inputs for the subsequent (i+1-th) subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves stabilization of the H-type gantry crane with dual PMLSM without the need of diffeomorphisms and complicated state-space model transformations.