LP methods in MPC of large‐scale systems: Application to paper‐machine CD control

Abstract

An application of a linear-programming based model-predictive control strategy to the paper-machine cross-direction (CD) control problem is presented. The objective of CD control is to maintain flat profiles of variables of interest by minimizing worst-case deviations from setpoints (defects). These control problems can have as many as 200 actuators (inputs) and 400 sensor measurements (outputs). This large size coupled with the stringent real-time requirement of computing a control moue in a few seconds poses a veiy challenging control problem. The LP-based strategy is particularly well suited for solving such classes of control problems. This strategy has demonstrated its ability to solve large-scale control problems (over 100 inputs and 100 outputs) in real time and exhibits robustness to model uncertainty.

Near time-optimal model predictive control using an L1-norm based cost functional

“…Most works in literature deal with quadratic cost functionals, but there are also a few works considering linear cost functionals, with a reduced computational complexity as the main reason [7], [10]. In this work, the advantage of a reduced complexity is combined with a smaller overshoot and a near time-optimal control behavior through a formulation using the 1 -norm.…”

Design sensor trajectory for control: Application to sheet‐forming processes

“…1987 . Various model predictive control MPC strategies for Ž such a large-scale system were also proposed Braatz et al, 1992;Laughlin et al, 1993;Rawlings and Chien, 1996;Dave . et al, 1997;Dave et al, 1999;Van Antwerp and Braatz, 2000 .…”

Design of cross-directional controllers with optimal steady state performance

“…But as we have separated the non-linearity from the dynamics it is straightforward to introduce any other choice of norm, without changing the dynamics away from the constraints. In particular both l 1 norm [7] and l ∞ norm [11] criteria have been recommended for certain cross-directional problems. Either may be substituted in this scheme, resulting in a linear program.…”

“…The usual approach for cross-directional control is to design an MPC (e.g. [17,27,7,21]). In this paper we have proposed a modification to an unconstrained IMC structure, based on [22].…”

“…If the latter strategy is adopted alone, the effects of integral action can lead to severe performance degradation [37,33]. Strategies for minimising l 1 norms [7] and l ∞ norms [11] have also been discussed. A number of control designs that seek approximate solutions to the quadratic cost have also been discussed-for example [4,35,5,16,29,13].…”