On dynamic effects of quanization and overflow nonlinearities in digital feedback control systems

The stability of SISO digital feedback systems is considered. These systems contain a linear dynamic plant, a digital controller and suitable D/A and A/D connections. The design of such a system is normally accomplished by ignoring the nonlinear effects caused by quantization and overflow truncation. It is shown (by simulations of specific examples) that quantization can lead to loss of asymptotic stability. Instead, our results prove that one has convergence to a small neighborhood of the origin. For large initial conditions it is shown that overflow effects can lead to unbounded solutions.