A Simple Discretization Scheme for Gain Matrix Conditioning

TL;DR

This paper introduces a simple, non-iterative discretization method based on RGA for improving gain matrix conditioning in industrial MPC models, especially effective for large, complex systems.

Contribution

It presents a novel, efficient binning technique that quickly addresses 2x2 conditioning issues in gain matrices of any size, ensuring minimal gain adjustments.

Findings

Effective for large models with complex gain interactions

Guarantees gain adjustments below a specified threshold

Simplifies the process of improving matrix conditioning

Abstract

In industrial model predictive controllers (MPCs), models generated from regression-based system identification methods typically contain small or even physically non-existent degrees of freedom. Control issues can arise when the steady-state optimizer uses these small degrees of freedom to calculate targets for plant operation due to matrix ill-conditioning. Mathematical techniques like Relative Gain Array (RGA) and Singular Value Decomposition (SVD) are helpful for analyzing controller gain interactions and identifying conditioning issues, which can be corrected relatively easily in small models. However, these techniques are difficult and tedious to apply for larger, more complex models. This paper describes a novel, non-iterative, RGA-based, binning technique for discretizing the gain matrix and quickly solving 2x2 conditioning issues for any model size, while guaranteeing gain adjustments below a certain threshold. Higher order interactions are also discussed.