Approximation of nonlinear dynamic plant by linear model under sinusoidal signal

The steady-state response of a nonlinear object, stimulated by sinusoidal signal, contains both the sinusoidal components of the same pulsation and higher harmonics. In the case of a linear plant with complex poles, working on the border of stability, a steady-state response of a sinusoidal input also contains the components with different pulsations. Their amplitude and phase shifts are dependent both on the system parameters, the excitation signal and the initial conditions. Can be expect that this property allows to approximate the steady-state behavior of nonlinear object by steady-state response of linear model. Probably, the parameters of this model depend strongly on the amplitude and phase of the sinusoidal excitation. The paper attempts to approximation of the steady-state behavior of the nonlinear object by the steady state response of the linear model. The specified sinusoidal excitation with typical zero initial conditions were used. A similar mechanism is used in the describing function methods, and the proposed method can be treated as a part of a class of harmonic linearization methods. The methodology of the method is illustrated in three examples. In two cases the behavior of linear models quite accurately resembles the actual waveforms of the plant. These results seem of interest, although usefulness of such models is difficult to predict.