29Nonlinear(2)

29Nonlinear(2) - still well represents the cubic...

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Example : Identification of a cuber in nonlinear system shown below. ) ( f A Cuber ) ( 3 t y ) ( t x The input x is normal distributed with zero mean and ) ( t 7 . 2 = x σ as shown in Fig.A(a). Now we consider three different cases for the linear system . ) ( f A i) When ) f A , both the probability density estimate of , and, the input versus output plot clearly indicate the cubic nonlinearity in the system, as shown in Figs.A(a) and (b), respectively. 02 . 0 ( = = k ) ( 3 t y ii) When f A ) is a low-pass filter with filter frequency corresponding to 90% of the Nyquist cut-off frequency, the probability density estimate of y well represents the cubic nonlinearity of the system, whereas the input versus output plot indicates only the possibility of a cubic nonlinearity, as shown in Figs.A(c) and (d), respectively. k / ( ) ( 3 t iii) When f A is a low-pass filter with filter frequency corresponding to 50% of the Nyquist cut-off frequency, the probability density estimate of
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Unformatted text preview: still well represents the cubic nonlinearity of the system, but the input versus output plot completely fails in identifying the nonlinearity, as shown in Figs.A(e) and (f), respectively. k / ) ( ) ( 3 t y In conclusion, the zero-memory nonlinearity can be well identified from the probability density estimate of the output, and, the input versus output plot, when the input is normal distributed. However, as the dynamic system is followed after the zero-memory nonlinearity, the input versus output plot tends to fail in identifying the nonlinearity. MAE 591 RANDOM DATA C. W. Lee -10 10 1 PDF input output-10 10-10 10 INPUT OUTPUT (a) (b) -10 10 1-10 10-10 10 INPUT (c) (d) -10 10 1-10 10-10 10 INPUT (e) (f) Figure A. Nonlinear system with a cuber...
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29Nonlinear(2) - still well represents the cubic...

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