Reference
T. J. J. van den Boom and B. De
Schutter, "Model predictive control of manufacturing systems with max-plus
algebra," Chapter 12 in
Formal Methods in Manufacturing
(J. Campos, C. Seatzu, and X. Xie, eds.),
Industrial
Information Technology, CRC Press, ISBN 978-1466561557, pp. 343-378,
Feb. 2014.
Abstract
Manufacturing systems can often be modeled as max-plus-linear (MPL) systems.
MPL systems are discrete-event systems with synchronization but no choice and
they are linear in the so-called max-plus algebra, which has addition
maximization as its basic operations. In this chapter we present an in-depth
account of the model predictive control (MPC) framework for MPL systems. MPC is
an on-line model based controller design method that is very popular in the
process industry and that can also be extended to MPL systems. A key advantage
of MPC is that it can accommodate constraints on the inputs and outputs of the
controlled system. In MPC the optimal control signal is obtained by an
optimization over all possible future control sequences. In general, the
resulting MPL-MPC optimization problem is nonlinear and nonconvex. However, we
show that if the control objective is piecewise affine, the constraints are
linear, and if the control objective and the constraints depend monotonically
on the outputs of the system, which is a frequently occurring situation for
manufacturing systems, the MPL-MPC optimization can be recast into a linear
programming problem, which can be solved very efficiently. Subsequently we
focus on implementation and timing aspects, closed-loop behavior, and tuning
rules for MPL-MPC. We derive sufficient conditions for stability and formulate
a closed-loop expression for the unconstrained MPL-MPC controller. In the case
of perturbed operation due to modeling errors and/or noise we need a robust
MPL-MPC controller. We show that under quite general conditions the resulting
optimization problems can be solved very efficiently. For the bounded error
case we also derive an MPL-MPC controller by optimizing over feedback policies,
rather than open-loop input sequences. In general, this results in increased
feasibility and a better performance. Finally we discuss robust MPC for MPL
systems with stochastic uncertainty.
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BibTeX
@incollection{vanDeS:14-002,
author = {van den Boom, Ton J. J. and De Schutter, Bart},
title = {Model Predictive Control of Manufacturing Systems with Max-Plus
Algebra},
chapter = {12},
booktitle = {Formal Methods in Manufacturing},
series = {Industrial Information Technology},
editor = {Campos, Javier and Seatzu, Carla and Xie, Xiaolan},
publisher = {CRC Press},
pages = {343--378},
month = feb,
year = {2014}
}