The mode of oscillation resulting from the instability of a system in self-oscillatory, as exemplified by limit cycling.
This paper presents a method for predicting whether or not certin kinds of nonlinear sampled-data feedback systems can oscillate, and verifying the existence of the predicted oscillation.
Mainly the existence of quantizer-induced limit cycles is investigated. The describing function is obtained for the nonlinear block containing a quantizer, a sampler and a zero-order hold circuit.
For the sub-harmonics of the sampler frequency, a systemtic method is developed to determine the smallest region of the complex plane in which the describing function can be asserted to lie.
Drawing the inverse Nyquist diagram of the linear part in the same plane, the sequence of limit cycle is predicted by the well-known graphical method.
Verifying the result, a numerical method is used. The D.F. procedure is most suitable for prediction and a numerical method is more advantegeous for verifying.
For a setter nonlinearity, with or without memory, the smallest region in which the D.F. can be asserted to line is also shown. It seems to have some deeper significance.
No report of this type of study has been published to date.