Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback

• Published in: arXiv.org
• Main Authors: Pintelon, Rik, Schoukens, Maarten, Lataire, John
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 06.04.2020
• Subjects: Approximation; Closed loops; Computer Science - Systems and Control; Continuous time systems; Discrete time systems; Frequency response functions; Mathematical analysis; Noise; Noise measurement; Nonlinear response; Nonlinear systems
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2004.02579

In many engineering applications the level of nonlinear distortions in frequency response function (FRF) measurements is quantified using specially designed periodic excitation signals called random phase multisines and periodic noise. The technique is based on the concept of the best linear approximation (BLA) and it allows one to check the validity of the linear framework with a simple experiment. Although the classical BLA theory can handle measurement noise only, in most applications the noise generated by the system -- called process noise -- is the dominant noise source. Therefore, there is a need to extend the existing BLA theory to the process noise case. In this paper we study in detail the impact of the process noise on the BLA of nonlinear continuous-time systems operating in a closed loop. It is shown that the existing nonparametric estimation methods for detecting and quantifying the level of nonlinear distortions in FRF measurements are still applicable in the presence of process noise. All results are also valid for discrete-time systems and systems operating in open loop.