Computer-aided Simplification of High-order Linear Models

Abstract

Models of many chemical processes are of high order. In order to simplify control laws for these systems and for practical implementation of the designed controllers, reduced-order or simplified models are sought. Many of the existing model reduction algorithms are computationally tasking, limited to rational systems, are fixed-parameter models, and involve a series of solution stages to the optimisation problem. This paper presents a very simple and effective computer-aided simplification (CAS) approach, the method of inequalities (MOI). For the past three decades, MOI has been applied to closed loop control system design, but not for solving model reduction problem. Hence, this work can be considered the first of its kind. A general multi-objective model reduction method is formulated for uncertain systems. The performance indices, which are defined as a set of algebraic inequalities, are defined as the sum of the squared errors between the output responses of the high-order uncertain systems and simplified uncertain systems. The simultaneous solution of these inequalities using moving boundaries process (MBP) in MATLAB environment yields stable optimal simplified models parameters. There is no need to monitor the stability of the reduced-order models during the course of iteration since the algorithm guarantees this. The effectiveness of the proposed approach is illustrated by means of three examples from the literature.

Keywords:

• Optimal simplified models
• Sum of squared errors
• Method of inequalities
• Computer-aided simplification
• Rational systems
• Uncertain systems