Error Bounds for General Describing Function Problems

The describing function method is widely used without much attention being paid to the error analysis so vital in any approximate method. One reason for this is the lack of a straightforward user-oriented method for checking error bounds except when the nonlinear element characteristic is single valued and of bounded slope. This paper attempts to eliminate that defect. A far wider range of nonlinear elements is now amenable to straightforward, usually graphical treatment; discontinuities, hysteresis, and backlash characteristics are included. In addition, previous results for slope-bounded single-valued nonlinear characteristics may be substantially improved with a small additional computational effort.