Computation of the MIMO Volterra frequency response functions of nonlinear systems

• Published in: Mechanical systems and signal processing 2019-12, Vol.134, p.106323, Article 106323
• Main Authors: Peyton Jones, J.C., Yaser, K.S.A.
• Format: Article
• Language: English
• Subjects: Algorithms; Difference equations; Differential equations; Frequency response functions; Higher-order frequency response functions; Mathematical models; MIMO (control systems); MIMO Volterra series; Non-linear systems; Nonlinear response; Nonlinear systems; Parameters; Time domain analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2019.106323

•Automatic generation of MIMO Volterra frequency response functions (FRFs).•Applicable to MIMO Nonlinear Differential Equations and discrete time NARX models.•Relates parameters in the nonlinear time domain system equations to the resultant MIMO FRFs.•Reveals the structure of nonlinear MIMO Volterra frequency response functions.•Method is validated against previously published results. A new and efficient algorithm for computing the higher order Multiple-Input, Multiple-Output (MIMO) Volterra frequency response functions (FRFs) from nonlinear time domain parametric models is presented. Recently developed MIMO harmonic probing techniques are applied to a general class of nonlinear MIMO differential, or difference equation models in order to obtain algebraic expressions relating the parameters of the time-domain system to the desired MIMO Volterra FRFs. The FRFs for any specific system of interest can then be written directly by substitution of model parameters. The expressions also reveal the structure of the resultant MIMO Volterra FRFs providing insight into system behaviour. The method is readily automated in software, and results are illustrated by means of an example.