Control of Time-Constrained Dual-Armed Cluster Tools Using (max, +) Algebra

International audienceThe problem studied in this paper is the control of discrete event systems subject to strict temporal constraints using (max, +) algebra. Initially we sought necessary and sufficient conditions for the existence of a causal control law guaranteeing the respect of the temporal constraints. Subsequently, a method for calculating the control law, if any, is proposed. The application which we are interested in is the control of a manufacturing semiconductor wafers process subject to strict temporal constraints

Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formul{\ae} expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

Control of Discrete Event Systems with Respect to Strict Duration: Supervision of an Industrial Manufacturing Plant

26 pagesInternational audienceIn this paper, we propose a (max,+)-based method for the supervi- sion of discrete event systems subject to tight time constraints. Systems under consideration are those modelled as timed event graphs and repre- sented with linear (max,+) state equations. The supervision is addressed by looking for solutions of constrained state equations associated with timed event graph models. These constrained state equations are derived by reducing duration constraints to elementary constraints whose con- tributions are injected in the system's state equations. An example for supervisor synthesis is given for an industrial manufacturing plant subject to a strict temporal constraint, the thermal treatment of rubber parts for the automotive industries. Supervisors are calculated and classified ac- cording to their performance, considering their impact on the production throughput

SIZING, CYCLE TIME AND PLANT CONTROL USING DIOID ALGEBRA

Using an industrial process from the car sector, we show how dioid algebra may be used for the performance evaluation, sizing, and control of this discrete-event dynamic system. Based on a Petri net model as an event graph, max-plus algebra and min-plus algebra permit to write linear equations of the behavior. From this formalism, the cycle time is determined and an optimal sizing is characterized for a required cyclic behavior. Finally, a strict temporal constraint the system is subject to is reformulated in terms of inequalities that the (min, +) system should satisfy, and a control law is designed so that the controlled system satisfies the constraint

Design of real-time periodic control systems through synchronization and fixed priorities

Control systems are often designed using a set of co-operating periodic modules running under control of a real-time operating system. A correct behaviour of the closed-loop controller requires that the system meets timing constraints like periods and latencies, which can be expressed as deadlines. The control system timing requirements are captured through a partition in control paths by which priorities are assigned according to their relative urgency. Latencies are managed through precedence constraints and more or less tight synchronization between modules. The implementation uses the fixed-priority based pre-emption service of an off-the-shelf real-time operating system. Such a system can be modelled with timed event graphs, and its temporal behaviour can be analysed using the underlying (max, plus) algebra. Examples coming from a uni-processor robot controller are provided

On Max-Plus Linear Dynamical System Theory: The Regulation Problem

A class of timed discrete event systems can be modeled by using Timed-Event Graphs, a class of timed Petri nets that can have its firing dynamic described by using an algebra called “Max-plus algebra”. For this kind of systems it may be desirable to enforce some timing constraints in steady state. In this paper, this problem is called a “max-plus regulation problem”. In this context we show a necessary condition for solving these regulation problems and in addition that this condition is sufficient for a large class of problems. The obtained controller is a simple linear static state feedback and can be computed using efficient pseudo-polynomial algorithms. Simulation results will illustrate the applicability of the proposed methodology

Knowledge Representation Concepts for Automated SLA Management

Outsourcing of complex IT infrastructure to IT service providers has increased substantially during the past years. IT service providers must be able to fulfil their service-quality commitments based upon predefined Service Level Agreements (SLAs) with the service customer. They need to manage, execute and maintain thousands of SLAs for different customers and different types of services, which needs new levels of flexibility and automation not available with the current technology. The complexity of contractual logic in SLAs requires new forms of knowledge representation to automatically draw inferences and execute contractual agreements. A logic-based approach provides several advantages including automated rule chaining allowing for compact knowledge representation as well as flexibility to adapt to rapidly changing business requirements. We suggest adequate logical formalisms for representation and enforcement of SLA rules and describe a proof-of-concept implementation. The article describes selected formalisms of the ContractLog KR and their adequacy for automated SLA management and presents results of experiments to demonstrate flexibility and scalability of the approach.Comment: Paschke, A. and Bichler, M.: Knowledge Representation Concepts for Automated SLA Management, Int. Journal of Decision Support Systems (DSS), submitted 19th March 200