The "noise" induced by quantization in digitally controlled systems can be modelled as small amplitude chaotic behaviour described by a simple piecewise linear map, the micro-chaos map. The chaotic nature of certain micro-chaos maps was proved rigorously in the last 20 years. It was also pointed out that several disconnected strange attractors or repellers may coexist far from the desired state of the system. The control error is influenced by the number of these strange sets and the local behaviour of trajectories in their neighbourhoods. In the present paper we focus on the exploration of the possible attractor/repeller structures in the phase space of a PD-controlled system and estimate the expected control error by several methods.