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Research Papers

Application of Model Predictive Control to Control Transient Behavior in Stochastic Manufacturing System Models

[+] Author and Article Information
Alireza Fazlirad

Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB, T2N 1N4, Canada
e-mail: afazlira@ucalgary.ca

Theodor Freiheit

Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB, T2N 1N4, Canada
e-mail: tfreihei@ucalgary.ca

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received November 19, 2014; final manuscript received August 25, 2015; published online April 7, 2016. Assoc. Editor: Jianjun Shi.

J. Manuf. Sci. Eng 138(8), 081007 (Apr 07, 2016) (15 pages) Paper No: MANU-14-1617; doi: 10.1115/1.4031497 History: Received November 19, 2014; Revised August 25, 2015

Increasing complexity in manufacturing strategies and swift changes in market and consumer requirements have driven recent studies of manufacturing systems, with transient behavior being identified as a key research area. Till date, satisfying consumer demand has focused on steady-state planning of production, mostly using stochastic or deterministic optimal control methods. Due to the difficulty of obtaining optimal control for many practical situations, as well as in evaluating performance under optimal control, these studies have not been conducive to the analysis or control of transient behavior. This paper bridges this gap by applying model predictive control to a manufacturing system modeled as a discrete-time Markov chain. By modifying the initiation of production as probabilities within the Markov chain, a method is proposed to directly control the system to specific expected performance levels and improve its stochastic transient behavior.

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Figures

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Fig. 1

Markov chain model of the manufacturing system

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Fig. 2

Algorithm flowchart of sequence of calculations

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Fig. 3

Controlling system to inventory and service rate set-points: (a) controlling buffer levels to a set-point, (b) development of control variables when controlling buffer to a set-point, (c) controlling service rate to a set-point, and (d) development of control variables when controlling service rate to a set-point

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Fig. 4

Effect of control on buffer level at two demand rates: (a) controlled buffer, demand rate = 0.77, (b) uncontrolled buffer, demand rate = 0.77, (c) controlled buffer, demand rate = 0.53, and (d) uncontrolled buffer, demand rate = 0.53

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Fig. 5

Effect of eliminating the upstream failed state on output and control variables: (a) controlled buffer, system with a failed state, (b) controlled buffer, system without a failed state, (c) control variables, system with a failed state, and (d) control variables, system without a failed state

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Fig. 6

Settle times for controlled and uncontrolled systems: (a) buffer level and (b) service rate

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Fig. 7

Comparison of controlled and uncontrolled demand loss: (a) buffer level and (b) service rate

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Fig. 8

Controlled and uncontrolled average demand loss: (a) buffer level and (b) service rate

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Fig. 9

Comparison of average blockage and machine utilization with average demand loss in an inventory controlled system: (a) average demand loss and blockage, (b) average demand loss and machine utilization, and (c) settle times and demand rates

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Fig. 10

Controlled and uncontrolled cumulative service rate error when controlling service rate

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