Max-Plus Algebraic Modeling and Control of High-Throughput Screening Systems

In this paper, we present a max-plus algebraic model for cyclically operated high-throughput screening plants. A max-plus algebraic representation of the system, derived directly from a discrete-event systems model of the predetermined globally optimal solution, contains negative order arcs, forcing certain events in previous cycles to occur after events in the current cycle. With respect to the cycle index, though of course not in terms of time, the model is acausal. However, the model can be transformed into a system representation without negative order arcs. The obtained max-plus algebraic model can then be applied as a controller to handle unexpected deviations from the predetermined cyclic operation during runtime.