Twofold quantization in digital control: deadzone crisis and switching line collision

Abstract

Quantization, sampling and delay may cause undesired oscillations in digitally controlled systems. These vibrations are often neglected or replaced by random noise (Widrow and Kollár in Quantization noise: roundoff error in digital computation, signal processing, control, and communications, Cambridge University Press, Cambridge, 2008); however, we have shown that digital effects may lead to small amplitude deterministic chaotic solutions-the so-called microchaos (Csernák and Stépán in Int J Bifurc Chaos 5(20):1365-1378, 2010). Although the amplitude of the micro-chaotic oscillations is small, multiple chaotic attractors can appear in the state space of the digitally controlled system-situated far away from the desired state-causing significant control error (Csernák and Stépán in Proceedings of the 19th mediterranean conference on control and automation, 2011). In this paper, we are interested in the analysis of a digitally controlled inverted pendulum with both input and output quantizers along with sampling. We show that this twofold quantization creates patterns in the state space corresponding to different control effort (force or torque) values for a simple PD control. We also highlight how

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