Optimization-based Design of Plant-Friendly Multisine Signals using Geometric Discrepancy Criteria Hans D. Mittelmann * and Gautam Pendse Department of Mathematics and Statistics Arizona State University, Tempe, Arizona 85287 Daniel E. Rivera and Hyunjin Lee Control Systems Engineering Laboratory Department of Chemical and Materials Engineering Arizona State University, Tempe, Arizona 85287-6006 Abstract. System identification is an important means for obtaining dynamical models for process control applications; experimental testing represents the most time-consuming step in this task. The design of constrained, “plant-friendly” multi- sine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for data-centric estimation methods, where uniform coverage of the output state-space is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear problem example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal displaying a desirable balance between high and low gain directions. The solution involves very little user intervention (which enhances its practical usefulness) and has great benefits compared to multisine signals that minimize crest factor. The constrained nonlinear optimization problems that are solved represent challenges even for high-performance optimization software. Keywords: system identification, process control, constrained optimization 1. Introduction Dynamic modeling is a critical task to many problems in the areas of simulation, prediction, and control of process systems. Given the complexity of most industrial plants, a sensible approach is to es- timate dynamic models from data generated through well-designed experiments; this is the problem of system identification (Ljung, 1999). Particular industries, such as the petrochemical and refining industries, rely almost exclusively on system identification as the principal means for obtaining dynamic models for advanced control purposes. * to whom all correspondence should be addressed; phone: (480) 965-6595, email:Hans.Mittelmann@asu.edu c  2005 Kluwer Academic Publishers. Printed in the Netherlands. Weylmultisinefinal3b.tex; 25/04/2005; 10:54; p.1