Structures within the Quantization Noise: Micro-Chaos in Digitally Controlled Systems

Abstract

Abstract Quantization, sampling and delay in digitally controlled systems can cause undesired oscillations (Csernak and Stepan, 2011), which - depending on the nature of the uncontrolled system - may cause issues of various importance. In many cases, these oscillations can be treated as quantization noise (Widrow and Kollar, 2008), and can be handled elegantly with the corresponding quantization theory. However, we are interested in the structure and patters of quantization in case of a digitally controlled inverted pendulum with input and output quantizers and sampling. We show the patterns of control effort in case of a simple PD control and highlight how these patterns - along with the dynamics of the controlled system - lead to attractors or periodic cycles with superimposed chaotic oscillations.