Probabilistic uncertainty description for an ETFE estimated plant using a sequence of multi-sinusoidal signals

This paper generalizes a probabilistic frequency-domain uncertainty description for an Empirical Transfer Function Estimate (ETFE) model developed by Bayard by using an input signal that is composed of a sequence of distinct multi-sinusoidal signals, instead of a single fixed multi-sinusoidal signal. Each signal in the sequence may have different sinusoidal amplitudes, number of signal periods, and fundamental frequency. The corresponding aggregate ETFE plant estimate for the sequence of multi-sinusoidal signals is developed as well. Besides their usefulness for robust control design, the plant and uncertainty expressions enable the use of adaptive algorithms for input signal adjustment during experimental testing in system identification. The use of adaptive signal algorithms also allows the opportunity to improve plant estimates, shape the probabilistic uncertainty description, and reduce input signal duration based on information learned during identification testing. A series of illustrative examples are included to show the relationship between the properties of the multi-sinusoidal signals in the input sequence and the plant uncertainty description.