Flatness-Based Model Predictive Control with Linear Programming for a Single Mast Stacker Crane

Abstract This paper deals with a trajectory tracking model predictive control for a single mast stacker crane, which is used for automatic storage or retrieval of payloads in automated warehouses. The mathematical model of the plant is a distributed parameter one, but it admits an excellent approximation by a flat lumped parameter system. The approximate nonlinear system is simplified further and the resulting linear time-varying system is implemented to design a model predictive controller. To provide an efficient formulation of an optimization task for the controller, the LTV-model is parametrized by a special flat output. Then, the model predictive control is formulated in the form of a linear program. For solving the derived linear program, an open-source optimal solver LP_SOLVE is chosen. To reduce a mechanical stress at clamping of a mast and an overall accessibility time, a special optimal trajectory calculated offline is chosen for the tracking by the designed controller. Finally, the simulation results of the nonlinear approximate model, subjected to model uncertainties and external disturbances, with the designed model predictive controller are presented.