Explicit model predictive control of an automated storage retrieval system

This thesis is written with the objective to research the possibilities of explicit Model Predictive Control applied to a practical implementation. In particular, in this work the realistic example of an Automated Storage / Retrieval System has been considered and a control-oriented model has been derived. This model has allowed the design and implementation of an Explicit Model Predictive Control law, from which the advantages and disadvantages can be researched. The project has been developed in partnership with the Politecnico di Milano and the Consiglio Nazionale delle Ricerche. The first step of the project focused on the analysis of a generalized description of the Automated Storage / Retrieval System and on the study of the physical equations describing its behavior. In particular, in view of the design specifications, the dynamics of the system have been identified and the manipulated and controlled variables have been defined. Subsequently, the physical equations describing the system have been analyzed, and a non-linear hybrid model has been obtained. After the derivation of the model, dedicated software has been used to explore possibilities to convert the non-linear hybrid model into a linear and easily optimizable form. Subsequently, the steps to compute an explicit control law using these linear hybrid models have been explained. Additionally, a custom-made program has been written to compute the explicit Model Predictive Control law for Automated Storage / Retrieval Systems based on the non-linear system. The generalized form has been used in two test cases from which the benefits and the advantages of applying an explicit Model Predictive Control in industrial systems are concluded. The main findings are that the explicit law is feasible for systems with a limited amount of inputs and states, due to the fact that the online and offline computation of the control law in the explicit form correlate significantly with these parameters.