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Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay.

作者信息

Oziablo Piotr, Mozyrska Dorota, Wyrwas Małgorzata

机构信息

Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland.

出版信息

Entropy (Basel). 2020 Jul 14;22(7):771. doi: 10.3390/e22070771.

DOI:10.3390/e22070771
PMID:33286543
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7517321/
Abstract

In this paper, we discuss the implementation and tuning algorithms of a variable-, fractional-order Proportional-Integral-Derivative (PID) controller based on Grünwald-Letnikov difference definition. All simulations are executed for the third-order plant with a delay. The results of a unit step response for all described implementations are presented in a graphical and tabular form. As the qualitative criteria, we use three different error values, which are the following: a summation of squared error (SSE), a summation of squared time weighted error (SSTE) and a summation of squared time-squared weighted error (SST2E). Besides three types of error values, obtained results are additionally evaluated on the basis of an overshoot and a rise time of the output signals achieved by systems with the designed controllers.

摘要
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/55737a9f901b/entropy-22-00771-g018.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/ed361add8af4/entropy-22-00771-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/8650e2680077/entropy-22-00771-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/294d87fccd61/entropy-22-00771-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/d9d9a42650ea/entropy-22-00771-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/a30f7da5ec26/entropy-22-00771-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/6704f6bd60cb/entropy-22-00771-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/efa1be05933d/entropy-22-00771-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/28a74c188d21/entropy-22-00771-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/ebbf6805a876/entropy-22-00771-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/5366d8449a4f/entropy-22-00771-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/cb1139699ef8/entropy-22-00771-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/5b7b9be00eaa/entropy-22-00771-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/a7d9bf8e5b7e/entropy-22-00771-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/06a3bfdb6580/entropy-22-00771-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/6bb5c54a2816/entropy-22-00771-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/d2c4868d1ad6/entropy-22-00771-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/5e26c3f49c7b/entropy-22-00771-g017.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/55737a9f901b/entropy-22-00771-g018.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/ed361add8af4/entropy-22-00771-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/8650e2680077/entropy-22-00771-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/294d87fccd61/entropy-22-00771-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/d9d9a42650ea/entropy-22-00771-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/a30f7da5ec26/entropy-22-00771-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/6704f6bd60cb/entropy-22-00771-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/efa1be05933d/entropy-22-00771-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/28a74c188d21/entropy-22-00771-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/ebbf6805a876/entropy-22-00771-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/5366d8449a4f/entropy-22-00771-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/cb1139699ef8/entropy-22-00771-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/5b7b9be00eaa/entropy-22-00771-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/a7d9bf8e5b7e/entropy-22-00771-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/06a3bfdb6580/entropy-22-00771-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/6bb5c54a2816/entropy-22-00771-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/d2c4868d1ad6/entropy-22-00771-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/5e26c3f49c7b/entropy-22-00771-g017.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b460/7517321/55737a9f901b/entropy-22-00771-g018.jpg

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本文引用的文献

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Applications of variable-order fractional operators: a review.变阶分数阶算子的应用：综述
Proc Math Phys Eng Sci. 2020 Feb;476(2234):20190498. doi: 10.1098/rspa.2019.0498. Epub 2020 Feb 12.