Analysis of oscillations in systems with polynomial-type nonlinearities using describing functions

Sufficient conditions for the existence of oscillations are obtained in the case of an autonomous single-loop feedback system when the nonlinear elements belong to a class of polynomials. Both a graphical procedure and an algebraic technique are presented for use with describing function analysis, and a graphical procedure is given for use with multiple input describing functions. Graphing is done in a parameter space of the solution, rather than in the complex plane.