Combined hysteresis and nonlinear gains in complex control systems

The types and sources of hysteresis commonly found in mechanical systems, and some of the effects thereof, are discussed. The describing function technique as specifically applied to studying hysteresis-caused limit cycles is outlined. The use of an analog computer for studying hysteresis in servosystems is reviewed. Techniques are presented for determining active and passive compensation to eliminate or reduce hysteresis limit cycles. Finally, a method is given for analyzing hysteresis plus a single-valued nonlinearity when they occur together or apart in a single or multiloop control system. By this method it is possible to synthesize a nonlinear gain characteristic which eliminates or reduces a hysteresis limit cycle. The validity of the method is demonstrated by comparison with analog computer results.