On the analysis of bi-stable control systems

The basic theory of bi-stable oscillating loop control is first sumaarized using standard describing function concepts. The effective transfer characteristic of the hi-stable switch is defined in terms of the ratio of both amplitude and frequency of the control error signal to amplitude and frequency of the loop oscillation signal. The effect of variation in loop oscillation amplitude with low frequency control error amplitude is considered. The relationship between switch gain at control frequencies and switch gain at oscillation frequency is noted. The inherent insensitivity of the bistable oscillating system to variations in linear loop parameters is discussed. The effect of variation in loop gain of the bi-stable system is compared with the effect of equal variations in a similar linear system. The possibility of bi-stable loop oscillation at more than one frequency is considered. The conditions are defined which insure oscillation at the intended oscillation frequency. Analog simulation tests used to verify these loop oscillation criteria are outlined.