A transparent experimental modelling method for linear multiple-input multiple-output systems

Abstract

This paper presents a transparent technique that simulates processes using input and output measurement data without the use of any complex optimization or iterative algorithms. The method is very simple and easy to understand as it comprises only of linear ordinary differential equations, Laplace transformations and least squares technique. The solution can be expressed only in two linear matrix equations. The main aim is to provide bachelor students of engineering with a tool to formulate transfer functions.

The method is validated with artificially generated erroneous measurement data as well as using measurements obtained from a practical application at the university. Inclusion of dead times and estimation of initial conditions make it ideal to be used for various range of applications such as stable and unstable systems with and without damping, open and closed loop systems. Over-integration, normalizing and/or zeroing of different coefficients add more degrees of freedom to improve the model quality.