Computational and Applied Math Proseminar

Department of Mathematics and Statistics
Arizona State University

Thursday, September 26, 2002, 12:15 p.m. in GWC 604

Daniel A. Rivera

Department of Chemical and Materials Engineering

Identification of Chemical Process Systems using
Constrained Minimum Crest Factor Multisine Inputs

Abstract System identification is the preferred method for creating the dynamic models needed to build control systems in the chemical process industries. The input signal design and execution stage of system identification represents the most time-consuming and expensive task in the model building process. This has motivated the need for so-called "plant-friendly" identification. A plant-friendly identification test will produce data leading to a suitable model within an acceptable time period, while keeping the variation in both input and output signals within user-defined limits.

In this presentation, the use of minimum crest factor multisine inputs as a means for accomplishing plant-friendly identification will be described. Multisine signals are deterministic, periodic signals whose power spectra can be directly specified by the user. The crest factor (defined as the ratio of the infinity norm over the 2-norm of the signal) provides a measure of how well distributed the signal values are over the input span. Lowering the crest factor of an input signal can significantly improve the signal to noise ratio of the resulting plant output, improving plant-friendliness during experimental testing. In the formulation that will be described in this presentation, a priori knowledge regarding the process is used to specify a frequency band of emphasis in the input signal.

An optimization problem is then solved which seeks to find the optimal phases in the multisine signal (and additionally, the Fourier coefficients in frequency bands not specified by the user) that directly minimize the crest factor. The optimization problem is solved in the presence of explicit time-domain constraints on upper/lower limits, move sizes, and rate of change in either (or both) input and output signals. The constrained time-domain formulation is appealing to process control engineers, who tend to think more in terms of maintaining high/low limits, move size constraints, and test duration during identification testing and less in terms of norm criteria that are typically used in the classical optimal input design formulations.

A series of examples meaningful to process control will be presented to demonstrate the usefulness of the proposed approach.
This is joint work with Hans Mittelmann.

For further information please contact: mittelmann@asu.edu