Nonlinear control systems with random inputs

Abstract

The describing-function method for the analysis of nonlinear systems with sinusoidal inputs is interpreted as a mean-square quasi-linearization technique and is generalized to apply to random signals.An amplitude-sensitive (or zero-memory) nonlinearity is interpreted as being approximately equivalent to a linear frequency-insensitive device, and a formula is derived for its equivalent gain.A simple rate-limited control system with a Gaussian input is analyzed as a specific application.Approximation of a general nonlinear element (containing memory) is considered next, and a relation between equivalent-system impulse response and the response of the actual nonlinearity is derived.

Random Vibration of Thin Elastic Plates and Shallow Shells

“…Because of difficulty in solving these simultaneous partial differential equations analytically, these equations will be solved numerically by a finite-difference method. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) which is the first desired equation. Substituting eqs.…”

“…Substituting eqs. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) into eq. (2-9) to get, We shall reduce eq.…”

“…(l-2) or (1-3) is possible. One approximate technique for this type of equation is the equivalent linearization technique which was originated by Krylov-Bogoliubov [17] in deterministic theory and was applied to problems of random vibrations by Booton [18] and Caughey [19]. Lin [20] investigated the single-mode response of a flat, plate undergoing moderately large deflections subject to stationary Gaussian excitation whose power spectrum is relatively flat.…”

Sixty years of stochastic linearization technique

“…15. Only in one oscillator, originally studied by Booton [3], Elishakoff and Colajanni [19] demonstrated that both techniques lead to coincident results. Thus, in balance one has to prefer, due to pragmatic reasons, Eq.…”

“…The reasons for this abrupt change are due to two causes: the opening of national frontiers, and a wave of enthusiasm for applied science, motivated by the technical achievements obtained in the production of new weapons''. The method of stochastic linearization technique was proposed more or less simultaneously on both sides of the Atlantic: by Booton [3] and Caughey [4] in the U.S. and by Kazakov [5] in the former S.U.…”