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IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 55, NO. 11, NOVEMBER 2010 2511 Control of Continuum Models of Production Systems
 

Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 55, NO. 11, NOVEMBER 2010 2511
Control of Continuum Models of Production Systems
Michael La Marca, Dieter Armbruster, Member, IEEE, Michael Herty, and Christian Ringhofer
Abstract--A production system which produces a large number
of items in many steps can be modelled as a continuous flow
problem. The resulting hyperbolic partial differential equation
(PDE) typically is nonlinear and nonlocal, modeling a factory
whose cycle time depends nonlinearly on the work in progress.
One of the few ways to influence the output of such a factory is by
adjusting the start rate in a time dependent manner. We study two
prototypical control problems for this case: i) demand tracking
where we determine the start rate that generates an output rate
which optimally tracks a given time dependent demand rate and ii)
backlog tracking which optimally tracks the cumulative demand.
The method is based on the formal adjoint method for constrained
optimization, incorporating the hyperbolic PDE as a constraint
of a nonlinear optimization problem. We show numerical results
on optimal start rate profiles for steps in the demand rate and
for periodically varying demand rates and discuss the influence
of the nonlinearity of the cycle time on the limits of the reactivity

  

Source: Armbruster, Dieter - Department of Mathematics and Statistics, Arizona State University

 

Collections: Mathematics