Model predictive control of an overhead crane using constraint substitution

This paper describes a real-time model predictive control (MPC) scheme for an overhead crane subject to state and input constraints. The constraints are taken into account by means of a transformation technique which transforms the system dynamics with the corresponding constraints into a new unconstrained representation. This method allows to reformulate the underlying optimal control problem (OCP) of the MPC scheme into an unconstrained counterpart. The unconstrained OCP is then solved by means of a fast MPC algorithm that uses a finite number of iterations per MPC step in order to ensure real-time feasibility. Simulation as well as experimental results demonstrate the computational performance of the MPC scheme.