Control of manufacturing systems using state feedback and linear programming

Eekelen, J.A.W.M. van; Lefeber, Erjen; Roset, B.J.P.; Nijmeijer, Henk; Rooda, J.E.

doi:10.1109/cdc.2005.1582896

Cited by 4 publications

(8 citation statements)

References 11 publications

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“…Note that similar to maxplus model (6), min-plus model (10) is also scalable: adding more workstations makes the model grow proportionally.…”

Section: Min-plus Model: Time Domainmentioning

confidence: 99%

“…As discrete state variables we introduce the number of lots in the buffer, x 1 (t) ∈ {0, 1, 2}, the number of lots on the machine, x 2 (t) ∈ {0, 1} and the number of finished lots, x 4 (t) ∈ Z. This way of defining the state of a manufacturing system (with these variable types) was first introduced in [6]. We define the state of the workstation as:…”

Section: Hybrid Model In χ Formalismmentioning

confidence: 99%

“…In event domain, no state exists as a function of time, which makes real-time control difficult, if not impossible. In [6] we developed a new characterization of the state as a function of time for manufacturing systems (which by nature are event driven), which works very intuitively. This characterization is well suited for incorporating initial conditions of a manufacturing system.…”

Section: Introductionmentioning

confidence: 99%

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Coupling event domain and time domain models of manufacturing systems

Eekelen

Lefeber

Rooda

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-Manufacturing systems are often characterized as discrete event systems (DES) and consequently, these systems are modeled with discrete event models. For certain discrete event modeling paradigms, control theory/techniques have been developed in event domain. However, from a control or performance perspective, a lot of notions are time related, like stability, settling time, transient behavior, throughput, flow time, efficiency, etc. Moreover, if we also consider market/customer requirements, almost all requirements are within time perspective: due dates, deliverability, earliness, tardiness, etc. Therefore, it is also useful to have time driven models of manufacturing systems. To combine the insights in modeling and control obtained in both time and event domain, it is useful to create a coupling between those two domains. This paper describes modeling techniques in both time domain and event domain for a class of manufacturing systems and establishes a generic coupling between two model descriptions. The coupling exists of two maps between the models' states, enabling real-time control of manufacturing systems.

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“…Note that similar to maxplus model (6), min-plus model (10) is also scalable: adding more workstations makes the model grow proportionally.…”

Section: Min-plus Model: Time Domainmentioning

confidence: 99%

Section: Hybrid Model In χ Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coupling event domain and time domain models of manufacturing systems

Eekelen

Lefeber

Rooda

2006

Proceedings of the 45th IEEE Conference on Decision and Control

Self Cite

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“…The problem of scheduling several jobs on a set of machines with infinite queues is covered extensively in Pinedo (2005). Other models include a method of treating manufacturing systems as continuous systems in time and controlling them using linear programming is given in van Eekelen et al (2005), and the so-called "hot ingot" problem, or continuous processing flowshop, which requires a scheduled job to move to the next machine in its route with no delay. The "hot ingot" problem is shown to be equivalent to a single machine with sequence dependent setup times in Reddi and Ramamoorthy (1972).…”

Section: Introductionmentioning

confidence: 99%

“…Many different objectives are specified in Pinedo (2005); these objectives introduce ideas such as minimum makespan, maximum throughput, minimum (weighted) tardiness, minimum lead time, and so on. In van Eekelen et al (2006) and Boccadoro and Valigi (2003) an optimal 2-product cyclical schedule is determined for a single machine with setup costs. A natural extension to this problem is that of scheduling a job shop with multiple machines.…”

Section: Introductionmentioning

confidence: 99%

Model approximation for batch flow shop scheduling with fixed batch sizes

Weyerman

Rai

Warnick

2014

Discrete Event Dyn Syst

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Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these "t-step" approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.

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