Quantization improves stabilization of dynamical systems with delayed feedback

Stépàn, Gábor; Milton, John; Insperger, Tamás

doi:10.1063/1.5006777

Cited by 16 publications

(24 citation statements)

References 35 publications

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“…In some cases one can even arrive to an unnatural conclusion, that using lower-resolution output quantizer or larger sampling time will actually result in lower control error. Similar results were found in [15,16], where the quantization improved the stability properties of the controlled system.…”

Section: Resultssupporting

confidence: 84%

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

Gyebrószki

Csernák²

2019

Nonlinear Dyn

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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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Section: Resultssupporting

confidence: 84%

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

Gyebrószki

Csernák²

2019

Nonlinear Dyn

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“…The model of inverted pendulum has a great significance in this area, as well, during the analysis of stick-balancing [6] which can provide important results to understand the control strategy implemented by the human brain when compared with measurements. As it was presented in [7], quantization can contribute to the stabilization of unstable dynamical systems in the presence of feedback delay in neural control.…”

Section: Introductionmentioning

confidence: 89%

“…, the state vector at the next sampling instant can be expressed by substituting T = 1 in Eq. (7). Thus, the following map is obtained:…”

Section: The Hybrid Micro-chaos Mapmentioning

confidence: 99%

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The Hybrid Micro-chaos Map: Digitally Controlled Inverted Pendulum with Dry Friction

Gyebrószki

Csernák²

2019

Period. Polytech. Mech. Eng.

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Digital effects (quantization, sampling and delay) can lead to small amplitude chaotic oscillations, called micro-chaos [1, 2]. Often, these vibrations are neglected due to their small amplitude or replaced by random noise, but doing so one might be unable to capture some important behavior of the digitally controlled system.One notable example is the PD-controlled inverted pendulum with quantization at the calculated control effort. Taking digital effects into account leads to separated chaotic attractors in the state space. While the amplitude of the chaotic oscillations is indeed small, these attractors are situated rather far from the desired position, introducing considerable control error. Micro-chaos is undoubtedly present in ideal models of computer-controlled mechanical systems, however an important question is still open: does it persist if a more complex model of reality is used? For instance, does it survive in the presence of dry friction?This paper answers the latter question analyzing the micro-chaos in a system with Coulomb friction. We introduce the so-called hybrid micro-chaos map that describes the behavior of a digitally controlled system with dry friction. Then, the theoretical analysis of this map is presented and numerical results are provided that were acquired using a new mathematical tool, the Clustered Simple Cell Mapping method.Lastly, we conclude, that the phenomena of micro-chaos can withstand the presence of Coulomb friction and chaotic attractors can coexist with sticking zones in the state space.

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“…The use of acceleration feedback gain was proposed in [4] where several stability charts were constructed in the space of control parameters P, D and A for the biophysically plausible time delay and system parameters of human balancing. 21 (for details see [6]).…”

Section: Linear Stability Of Quiet Standing and Parameter Selectionmentioning

confidence: 99%

Saturation limits the contribution of acceleration feedback to balancing against reaction delay

Zhang

Stépàn

Insperger

2018

J. R. Soc. Interface.

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A nonlinear model for human balancing subjected to a saturated delayed proportional–derivative–acceleration (PDA) feedback is analysed. Compared to the proportional–derivative (PD) controller, it is confirmed that the PDA controller improves local stability even for large feedback delays. However, it is shown that the saturated PDA controller typically introduces subcritical Hopf bifurcation into the system, which can also lead to falling for large enough perturbations. The subcriticality becomes stronger as the acceleration feedback gain increases or the saturation torque limit decreases. These explain some features of human balancing failure related to the increased reaction delay of inactive elderly people.

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Quantization improves stabilization of dynamical systems with delayed feedback

Cited by 16 publications

References 35 publications

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

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

The Hybrid Micro-chaos Map: Digitally Controlled Inverted Pendulum with Dry Friction

Saturation limits the contribution of acceleration feedback to balancing against reaction delay

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