Mathematical models based on spline functions for industrial applications

Abstract

There are several instances where samples of the controlled variable are the only data available to describe a process. In order to determine the performance of a plant, digital techniques are used to analyze the data. Then, the set of samples conforms the plant model. The main disadvantage of this approach is the poor predictive properties that the model has when changes in the process occur.

Spline functions are the tool of choice for the analytical representation of a plant based on the sampled data from a process. Once a plant model is described in spline form, the spline coefficients become the model parameters. These parameters are used for the adaptation of sample-based models.

Two practical applications are considered in this study: non-parametric plant models and systems excited with non-sinusoidal waveforms. Classical adaptive control techniques, such as projection algorithm and least square, can be used when non-parametric plant models are approximated by spline functions. Additionally, the spline approximation techniques extend the applicability of the non-parametric models to the area of multirate sampling control. The spline approximation of voltage and current signals is used in this work to predict the behavior of a nonlinear circuit at a different operating point. Instantaneous phasors are used in combination with spline functions to create a hybrid technique that takes advantage of both classical methods and spline models. Sampled data from electric arc furnaces are used to test the spline-base signal approximation techniques.