Estimation of Multi‐Order Spectra for Nonlinear Closed‐Loop Systems

In this paper, a multi‐order spectra estimation method is proposed for a nonlinear closed‐loop system based on the Volterra series. Owing to the correlation between the noise and the input, the estimation accuracy is poor when the nonlinear spectra of the plant is obtained using the traditional estimation method. In order to overcome this problem, a two‐step scheme is used to estimate the multi‐order spectrum of a nonlinear system operating in closed‐loop. Firstly, the generalized frequency response functions (GFRFs) from the reference signal to the input of the plant are estimated, and they are used to simulate the noise‐free input spectra of the plant. Secondly, the GFRFs of the controlled plant are estimated using the noise‐free input spectra and the output spectra. Because the GFRFs are multidimensional functions, the required amount of calculation for the estimation is very large. To reduce computational complexity, a simplified GFRF model is adopted to estimate the multi‐order nonlinear spectrum of the plant. In this model, the GFRF is transformed to a one‐dimensional function. Two simulation experiments are provided to illustrate the proposed approach.