Analysis and control of nonlinear systems with DC terms

Although nonlinear systems with a DC term are quite often found, very little work has been done about the important effects that the DC term produces on the nonlinear system response. Some work can be found based on NARMAX model identification-this work identifies the system by NARMAX models and from them obtains the Higher-order Frequency Response Functions (HFRFs). From the HFRFs, the effects of the DC term on the nonlinear system can be predicted. This paper represents an extension of such a work; but here, other parametric models are used: the Associated Linear Equations (ALEs). This allows identification of the system directly from the frequency domain and the direct observation of the effect of the DC term. Because the model is parametric, it arguably allows one to explain the nonlinear system behaviour in a physical way. Also in this paper, the ALE-based identification scheme is extended to systems with DC, and it is explained how to construct Volterra inverses for such systems with the objective of implementing an open-loop control of nonlinear systems. Unlike the situation for systems without DC, the pre-inverse and post-inverse Volterra systems differ from each other. In fact, the DC in the post-inverse cannot be eliminated in all the cases. The inverse strategies are tested on two simulated nonlinear systems: a Duffing oscillator and a Hammerstein model.