A step-by-step method for transient analysis of feedback systems with one nonlinear element

An analytical-numerical-graphical method is presented for the transient analysis of nonlinear feedback systems. The method is applicable to systems of any number of linear elements and one nonlinear element whose characteristic may be represented by y = φ(x), where x and y are its instantaneous input and output. The techniques employed are operational mathematics, numerical integration, and a graphical solution of two algebraic relations. Several examples, including both electric networks and a feedback control system, illustrate the procedure. Experimental results and theoretical considerations relating to the accuracy of the method are given.