The determination method of the transfer function at which the gain characteristics of bode diagram present spontaneous attenuoation characteristics

The asymptote of the gain characteristics at the bode diagram of linear control system is gradient of 20N db/dec (N is an integral number) where the angular frequency is higher than break point frequency. Control system in which the asymptote is not gradient of 20N db/dec or in which the response wave is not a sin wave is called nonlinear control system. At the result of the frequency response experiment in the recorder of industrial-instruments, the gain characteristics of bode diagram presented spondaneous attenuation characteristics. Generally these transfer function separate into linear element and nonlinear element, the nonlinear element is analyzed by describing function. but we studied the equivalent transfer function on these characteristics and gained the next function. G(S, X)={1+T(X)S}^<K(X)>/1+2ζ(X)S/ω_n(X)+S^2/ω_n(X) List of symbols G(S, X)=equivalent transfer function X=input amplitude K(X)=equivalent exponent (K is not an integral number) T(X)=equivalent time constant ζ(X)=damping ratio ω_n(X)=break point frequency S=parameter of Laplace transformation We investigated the figured decision method of the coefficients in the above function gained from bode diagram of the nonlinear control system.