[PDF] An Equivalent Gain And Stochastic Analysis For Nonlinear Sampled Date Control Systems eBook

Author : Roi Francis Prueher (Jr)
Publisher :
Page : 147 pages
File Size : 30,7 MB
Release : 1956
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In this thesis, a generalized equivalent gain function for nonlinear sampled-data control systems is defined and is specified to be the ratio of the z-transform of the crosscorrelation function of the system input and output signals to the z-transform of the autocorrelation function of the system input signal. Although this definition can be used to derive the usual describing function when the input is sinusoidal, it is not restricted to the sinusoidal case. Consequently, it is fundamentally an equivalent gain function in the sense originally proposed by R.C. Booton, and it is a nonlinear element representation more general than the usual describing function. In the past, the techniques of describing function analysis have been helpful in nonlinear analysis and have furnished valid results. The applications of these techniques can be extended with the generalized equivalent gain function. The sinusoidal describing function and the discrete describing function become special cases of the equivalent gain function when the input is restricted to sinusoidal variations and a sampled-data system is studied. The equivalent gain function can be used for general deterministic input systems and can also be used for systems with stochastic input signals.

Author : Richard W. Troop
Publisher :
Page : 98 pages
File Size : 21,94 MB
Release : 1968
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The analysis of a nonlinear sampled-data(NLSD) system subjected to stochastic inputs is shown to be simplified by means of a generalized equivalent gain Keq(z), where Keq(z) is defined as the ratio of the z-transform of the cross-correlation function of the nonlinear element, and the z-transform of the auto-correlation function. Computations for the equivalent gain of five nonlinear elements are performed. Both the NLSD system and the quasi-linear sampled-data (QLSD) system are simulated on the analog computer and the results compared and analyzed by statistical means. An analytical solution for the QLSD system is also presented. (Author).