STABILISASI SISTEM KONTROL LINIER DENGAN PENEMPATAN NILAI EIGEN

Authors

  • Fauri .

DOI:

https://doi.org/10.25077/jmu.2.3.126-133.2013

Abstract

Salah satu kajian dalam sistem kontrol linier adalah mengenai kestabilan
sistem tersebut. Sistem xË™ = Ax + Bu adalah stabil jika bagian riil dari semua nilai
eigen matriks A adalah negatif. Sebaliknya, jika ada bagian riil matriks A yang non
negatif maka sistem xË™ = Ax + Bu adalah tidak stabil. Dalam penelitian ini dikaji
tentang proses stabilisasi sistem kontrol linier dengan penempatan nilai eigen. Sistem
xË™ = Ax + Bu yang tidak stabil dikatakan dapat distabilkan jika terdapat kontrol u =
− Fx sedemikian sehinggga sistem loop tertutup x˙ = ( A − B F)x adalah stabil, artinya
matriks F dipilih sedemikian sehingga bagian riil dari semua nilai eigen matriks A −
B F adalah negatif. Dengan teorema yang diberikan, diperoleh syarat yang menjamin
eksistensi matriks feedback F sedemikian sehingga sistem x˙ = ( A − B F)x adalah stabil,
tetapi nilai eigen dari matriks A − B F dapat diatur sesuai keinginan. Suatu contoh
diberikan untuk mengilustrasikan proses stabilisasi ini.

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Published

10-09-2013

Issue

Vol. 2 No. 3 (2013)

Section

Articles

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