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465360 Tracking Control of Boundary Controlled Continuum Models of Production Systems

described by nonlocal spatially distributed continuous transport models, see [1] and [2].

This description is suitable, e.g., for a semiconductor factory which produces a large number

of items in a large number of steps. The considered continuum model satises conservation law,

and the appropriate mathematical variable representing the production flow is a products density.

Moreover, the production flow velocity of the conservative production system is given by

hyperbolic PDE depending only on the products density and it is constant cross the entire system

at a given time. Actually, this implies that in a real factory, all parts move through the factory with

same speed at a given time.

Controlling the production rate of a manufacture production system is an important goal in

manufacturing: producing too little of an item results in the lost sales and backlog costs while

producing too much leads to inventory and holding costs. In order to maximize protability, a

production system has to be able match its projected demand. Although demand is stochastic

over a given time period, a business typically generates a demand forecast for the next day,

week, month, etc and runs its production system to match this demand accordingly and this

demand can be modelled by a known signal process which is given by a so called exosystem.

In this work, we will develop a control law that controls the outflux of the continuum model

solely by regulating the influx to achieve demanded tracking of targeted production. In [3],

the theory about the output feedback stabilization of the considered continuum model has

been investigated and important results in [3] assist to construct the boundary control law in

such a way that the targeted demand tracking can be realized in the framework of internal

model control. Furthermore, the solvability of resulting regulator equations is discussed and

the solvability conditions is provided.

Finally, computer simulation will be presented to show the performance of the proposed

controller, in other words, the demanded tracking production can be achieved.

[1] Armbruster, D., Marthaler, D. E., Ringhofer, C., Kempf, K., and Jo, T. C. (2006). A contin-

uum model for a re-entrant factory. Operations research, 54(5), 933--950.

[2] Marca, M. L., Armbruster, D., Herty, M., and Ringhofer, C. (2010). Control of continuum

models of production systems. IEEE Transactions on Automatic Control, 55(11), 2511--2526.

[3] Coron, J. M., and Wang, Z. (2013). Output feedback stabilization for a scalar conservation

law with a nonlocal velocity. SIAM Journal on Mathematical Analysis, 45(5), 2646--2665.

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