Limit cycles resulting from quantization in digital control systems.

The existence of quantizer-induced limit cycles in digital control systems is a well-known phenomenon. This paper reports the results of an investigation into the discrete describing function technique which is applicable not only to the quantizer nonlinearity but also to any nonlinearity in an otherwise linear discrete system. First a general expression is developed for the discrete describing function that is applicable to any nonlinearity. The describing function is then obtained for the quantizer nonlinearity. Finally, the use of the discrete describing function is illustrated by an example of a digital control system.