Sinusoidal analysis of nonlinear control systems

EXTENSION OF SOME of the techniques of sinusoidal analysis familiar in linear-system theory to systems containing nonlinear elements provides much useful information concerning their design and performance. Most important is the ability to predict possible periodic behavior, both stable and unstable, of the unexcited systems. This ability allows nonlinearities to be accounted for in system synthesis so that the usually undesirable behavior implied by the periodic solutions can be prevented or at least controlled. Either linear or nonlinear correcting devices can be employed effectively for this purpose. Steady-state responses to external sinusoidal excitation, including the hysteretic frequency responses common in nonlinear systems, are determined readily when the response is of excitation frequency. The method is helpful also in obtaining a qualitative understanding of simple transient behavior.