CONTROLBASED ON DESCRIBING FUNCTION METHODSJames

The robust control problem for nonlinear systems is discussed from the standpoint of the amplitude sensitivity of the nonlinear plant and nal control system. Failure to recognize and accommodate this factor may give rise to nonlinear control systems that behave diierently for small versus large input excitation, or perhaps exhibit limit cycles or instability. Sinusoidal-input describing functions (sidfs) are shown to be eeective in dealing with amplitude sensitivity in two areas: modeling (providing plant models that achieve an excellent trade-oo between conservatism and robustness) and nonlinear control synthesis. In addition , sidf-based modeling and synthesis approaches are broadly applicable. Several practical SIDF-based nonlinear compensator synthesis approaches are presented and illustrated via application to a position control problem.