A Procedure for Obtaining Multi Input Multi Output Volterra Models From Port-Based Nonlinear Differential Equations

Abstract

Physical nonlinear dynamic systems have traditionally been modeled using nonlinear ordinary differential equations (ODEs). One solution technique for single-input, single-output (SISO) nonlinear ODEs is obtained through a Volterra transfer function. Applying this solution technique for multi-input, multi-output (MIMO) nonlinear ODEs is complicated due to the difficulty of analytically determining MIMO Volterra kernels. In this work a procedure to obtain frequency domain MIMO Volterra models from external port-based nonlinear ODEs is presented. In a port-based model the number of system inputs is equal to the number of system outputs. Port-based models are important because any physical system can be modeled using ports. An example of a two-port nonlinear ODE is presented and different truncated MIMO Volterra transfer function models are obtained. The truncated Volterra model responses are then compared to the nonlinear ODE model response.