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Distributed parameter systems (DPS) are formulated as partial differentialequations (PDE). Especially, under time-varying boundary conditions, PDEintroduce force coupling. In the case of the flexible stacker crane (STC),nonlinear coupling is introduced. Accordingly, online trajectory planning andtracking can be addressed using a nonlinear model predictive control (NMPC).However, due to the high computational demands of a NMPC, this paper discussesa possibility of embedding nonlinearities inside a linear parameter varying(LPV) system and thus make a use of a numerically low-demanding linear MPC. Theresulting mismatches are treated as parametric and additive uncertainties inthe context of robust tube-based MPC (TMPC). For the proposed approach, most ofthe computations are carried out offline. Only a simple convex quadraticprogram (QP) is conducted online. Additionally a soft-constrained extension wasbriefly proposed. Simulation results are used to illustrate the goodperformance, closed-loop stability and recursive feasibility of the proposedapproach despite uncertainties.

Tube-based Robust Model Predictive Control for a Distributed Parameter System Modeled as a Polytopic LPV (extended version)