Quantizer-induced digital controller limit cycles

Limit-cycle oscillations can occur in recursive digital controllers, due to the finite resolution of the computational data word. Controllers are usually formed from first- and second-order structures, arranged in parallel, in cascade, or in a combination of these. A first-order structure cannot sustain a stable limit cycle, but a second-order structure can. A simple criterion, based on the describing function of a quantizer, is developed and presented for predicting the amplitudes and frequencies of quantizer-induced limit-cycle oscillations in second-order digital filter structures.