Explicit GPC Control Applied to an Approximated Linearized Crane System

This paper proposes a MIMO Explicit Generalized Predictive Control (EGPC) for minimizing payload oscillation of a Gantry Crane System subject to input and output constraints. In order to control the crane system efficiently, the traditional GPC formulation, based on online Quadratic Programming (QP), is rewritten as a multiparametric quadratic programming problem (mp-QP). An explicit Piecewise Affine (PWA) control law is obtained and holds the same performance as online QP. To test effectiveness, the proposed method is compared with two GPC formulations: one that handle constraints (CGPC) and another that does not handle constraints (UGPC). Results show that both EGPC and CGPC have better performance, reducing the payload swing when compared to UGPC. Also both EGPC and CGPC are able to control the system without constraint violation. When comparing EGPC to CGPC, the first is able to calculate (during time step) the control action faster than the second. The simulations prove that the overall performance of EGPC is superior to the other used formulations.