Quantization-induced control error in a digitally controlled system

Csernák, Gábor

doi:10.1007/s11071-016-2859-1

Cited by 2 publications

(6 citation statements)

References 12 publications

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“…As it was shown in [9], there is only one fixed point in the phase space -at the origin -if large control gain P > 2 α 2 is chosen from the domain of stability. The corresponding large attractor immediately disappears if friction is present.…”

Section: Topological Patterns Sticking Zonesmentioning

confidence: 99%

“…where S i and C i are the coefficients of sinh( ) , α Γ T i 0 and cosh( ) , α Γ T i 0 , respectively in Eq. (9). Both S i and C i depend on the state of the system (i.e., x i , v i or μ i ) at the beginning of the sampling interval.…”

Section: The Hybrid Micro-chaos Mapmentioning

confidence: 99%

“…Thus, one can expect to have several attractors when the difference between the control gain P and α 2 is relatively small. At certain parameter combinations (see [9]), the neighboring attractors merge and form a larger attractor.…”

Section: Topological Patterns Sticking Zonesmentioning

confidence: 99%

“…An upper estimate for the control error -the distance of the outermost attractor from the origin -can be given for that frictionless case, when the eigenvalues of U are positive and real [9]:…”

Section: Topological Patterns Sticking Zonesmentioning

confidence: 99%

“…As it was proved, sampling and quantization leads to chaotic behavior and the appearance of coexisting chaotic attractors and repellors in the phase-space of the considered system. The finer structure of these strange objects was discussed in [9], where an estimate was given for the maximal quantization-related control error.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Topological Patterns Sticking Zonesmentioning

confidence: 99%

Section: The Hybrid Micro-chaos Mapmentioning

confidence: 99%

Section: Topological Patterns Sticking Zonesmentioning

confidence: 99%

Section: Topological Patterns Sticking Zonesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Gyebrószki

Csernák²

2019

Period. Polytech. Mech. Eng.

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Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Shi

Deng

2021

Entropy

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Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.

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Quantization-induced control error in a digitally controlled system

Cited by 2 publications

References 12 publications

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

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

Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

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