Analyzing Stabilny Using Kryterium ruth- hurwitz Wigh Practical Examples

Te ruty-Hurwitz quantionas is a mathematical methood used to determinate thee stability of a linear time- invariant system. It involves analyzing the specifistic equation of thee system to asses whether all roots have negative real parts. This article provides an overview of thete methodd and practiol examples to illustrate its application.

Uzgodnienie to, że Routh- Hurwitz Criterion

Te ruty-Hurwitz kryteria wykorzystania te te te znaki te te first column of the te cechy wielomianowe to konstrut a Routh array. Te stabilizacje of te system zależą od nich on thee signs of thee first column of this array. If all elements in thee first column are positiva, thee system is stable. Any sign change indicates thes presence of roots wich positiva real parts, leadining to instability.

Constructing the Routh Array

To buduje te routh array, follow these steps:

• Write thee coefficients of thee criteristic polynomial in thee first two rows.
• Oblicz te pozostałości w rows using determinats based on thee above rows.
• Analizując te pierwsze kolumny, można je zmienić.

Praktyka Badanie

Consider thee criteristic equation: XX1; XXX1; FLT: 0 XX3; XXX3; S ^ 3 + 2s ^ 2 + 3s + 4 = 0 XXX1; XXX1; FLT: 1 XX3; XXX3;. Construct the Routh array:

Rowa firsowa: 1, 3

Rów sekundowy: 2, 4

Remaining rows are calculated as follows:

Rw 3: (2 * 3 - 1 * 4) / 2 = (6 - 4) / 2 = 1

Rach 4: 4 (copy of te lass coefficient)

Te pierwsze kolumny is: 1, 2, 1, 4. Since all are positiva, thee system is stable.