Optimization-based design of plant-friendly multisine signals using geometric discrepancy criteria

The design of constrained, “plant-friendly” multisine 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 example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy (1980). 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 significant benefits compared to multisine signals that minimize crest factor.