Robust Nonlinear Control Based on Describing Function Methods

The robust control problem for nonlinear systems is discussed from the standpoint of the amplitude sensitivity of the nonlinear plant and final control system. Failure to recognize and accommodate this factor may give rise to nonlinear control systems that behave differently for small versus large input excitation, or perhaps exhibit limit cycles or instability. Sinusoidal-input describing functions (sidfs) are shown to be effective in dealing with amplitude sensitivity in two areas: modeling (providing plant models that achieve an excellent trade-off 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.