Inaccuracies Revealed During the Analysis of Propagation of Measurement Uncertainty Through a Closed-Loop Fractional-Order Control System

Wiora, Alicja

doi:10.1007/978-3-030-17344-9_16

Cited by 1 publication

(4 citation statements)

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“…The fundamental conclusion led from the observation is that the shape of the response is dependent on the chosen model. The previous work [22] proves that also parameters used in the approximation influence the shape. It means that the parameters of the FO model obtained by best-fitting to experimental results are biased by choosing the approximation model and its parameters.…”

Section: Closed-loop Control Systemmentioning

confidence: 92%

“…The presented data show the influence of the approximation model on the placement of the points. The influence of the order of the approximation filter on errors was investigated in our previous work [22]. Here, we gather selected data for FO inertia in Table 3.…”

Section: Nyquist Plotmentioning

confidence: 99%

“…To validate the influence of the selected model on the answer of FO control system, we take the same example as in our previous works [22,68]. It is a real case described elsewhere [24].…”

Section: Closed-loop Control Systemmentioning

confidence: 99%

“…In our previous work [22], we noticed that the determined time response trajectory of FO system is influenced by parameters used during the approximation of FO differentiation. This is due to the fact that it is necessary to approximate the FO differential equations with integer-order (IO) equations.…”

Section: Introductionmentioning

confidence: 99%

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Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter

Wiora

2020

Symmetry

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Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system.

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Section: Closed-loop Control Systemmentioning

confidence: 92%

Section: Nyquist Plotmentioning

confidence: 99%

“…To validate the influence of the selected model on the answer of FO control system, we take the same example as in our previous works [22,68]. It is a real case described elsewhere [24].…”

Section: Closed-loop Control Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations