Discrete event systems, also known as DES, are class of system that can be applied to systems having an event that occurred instantaneously and may change the state. It can also be said that a discrete event system occurs under certain conditions for a certain period because of the network that describes the process flow or sequence of events. Discrete event systems belong to class of nonlinear systems in classical algebra. Based on this situation, it is necessary to do some treatments, one of which is linearization process. In the other hand, a Max-Plus Linear system is known as a system that produces linear models. This system is a development of a discrete event system that contains synchronization when it is modeled in Max-Plus Algebra. This paper discusses the production system model in manufacturing industries where the model pays the attention into the process flow or sequence of events at each time step. In particular, Model Predictive Control (MPC) is a popular control design method used in many fields including manufacturing systems. MPC for Max-Plus-Linear Systems is used here as the approach that can be used to model the optimal input and output sequences of discrete event systems. The main advantage of MPC is its ability to provide certain constraints on the input and output control signals. While deciding the optimal control value, a cost criterion is minimized by determining the optimal time in the production system that modeled as a Max-Plus Linear (MPL) system. A numerical experiment is performed in the end of this paper for tracking control purposes of a production system. The results were good that is the controlled system showed a good performance.
Analysis and control of max-plus linear discrete-event systems: An introduction
