Karin Routh Hurwitz na Tatsuniya ta Gaskiya
Ba a gano littattafan network synthesis, zan iya cewa idan koyar daɗi na gwamnati yana zaɓe a hagu mai zurfi na s plane, zai yi gwamnati baya ba. Saboda wannan addinin A. Hurwitz da E.J.Routh suka fara tattaunawa abubuwa da muhimmancin samun gwamnati. Zan yi tafiƙar waɗannan abubuwa biyu don samun gwamnati. Abubuwan da ya bayyana shi ne da A. Hurwitz, wanda ake kira Hurwitz Criterion for stability ko Routh Hurwitz (R-H) Stability Criterion.
Hurwitz Criterion
Na amfani da tushen tushen musamman don gina sabon tsari ta Hurwitz don tabbatar da samun gwamnati. Muna kiran tushen musamman na gwamnati a haka
Yana da n determinants don tushen musamman na nth order.
Tara da hakan tara da neman determinants daga haskukun tushen musamman. Tashar da daɗi na tushen musamman na kth order an rubuta a haka:
Determinant one : Kyakkyawan wannan determinant shine |a1| inda a1 shine haska na sn-1 a tushen musamman.
Determinant two : Kyakkyawan wannan determinant shine
Idan adadin abubuwa a cikin har row shine mafi kyau a determinant, a nan determinant number shine biyu. Row na farko tana da hasken biyu na odd, row na biyu tana da hasken biyu na even.
Determinant three : Kyakkyawan wannan determinant shine
Idan adadin abubuwa a cikin har row shine mafi kyau a determinant, a nan determinant number shine uku. Row na farko tana da hasken uku na odd, row na biyu tana da hasken uku na even, row na uku tana da zero a farko da hasken biyu na odd.
Determinant four: Kyakkyawan wannan determinant shine,
Idan adadin abubuwa a cikin har row shine mafi kyau a determinant, a nan determinant number shine hudu. Row na farko tana da hasken hudu, row na biyu tana da hasken hudu na even, row na uku tana da zero a farko da hasken uku na odd, row na hudu tana da zero a farko da hasken uku na even.
Daga binciken tsafta tara da neman determinant. Tsarin na biyu na determinant shine a haka:
Don tabbatar da samun gwamnati, lura da maɗaƙiwar determinant. Idan maɗaƙiwar determinant duka suna fi karshen kadan, yana nufin cewa gwamnati ya samu. Amma idan maɗaƙiwar determinant babu da shi, gwamnati baya ba.
Routh Stability Criterion
Wannan criterion tana da sunan modified Hurwitz Criterion of stability of the system. Zan yi tafiƙar wannan criterion a biyu. Part na farko zai kasance abubuwan da ke da muhimmancin samun gwamnati, part na biyu zai kasance abubuwan da ke da muhimmancin samun gwamnati. Zan ruwaito tushen musamman na gwamnati a haka
1) Part one (necessary condition for stability of the system): A nan ana da biyar addini da suka rubuta a haka:
Duka hasken tushen musamman suna da shi da real.
Duka hasken tushen musamman suna da shi.
2) Part two (sufficient condition for stability of the system): Za a gina Routh array. Don gina Routh array, za a yi tashar da daɗi a haka:
Row na farko tana da hasken biyu. An sautoci daga hasken biyu na farko zuwa hasken biyu na azumi. Row na farko shine a haka: a0 a2 a4 a6…………
Row na biyu tana da hasken odd. An sautoci daga hasken odd na farko zuwa hasken odd na azumi. Row na biyu shine a haka: a1 a3 a5 a7………..
Abubuwan row na uku za a gina a haka:
(1) First element : Faɗa a0 da abubuwan diagonally opposite a column na biyu (i.e. a3) then subtract this from the product of a1 and a2 (where a2 is diagonally opposite element of next column) and then finally divide the result so obtain with a1. Mathematically we write as first element
(2) Second element : Multiply a0 with the diagonally opposite element of next to next column (i.e. a5) then subtract this from the product of a1 and a4 (where, a4 is diagonally opposite element of next to next column) and then finally divide the result so obtain with a1. Mathematically we write as second element
Similarly, we can calculate all the elements of the third row.
(d) The elements of fourth row can be calculated by using the following procedure:
(1) First element : Multiply b1 with the diagonally opposite element of next column (i.e. a3) then subtract this from the product of a1 and b2 (where, b2 is diagonally opposite element of next column) and then finally divide the result so obtain with b1. Mathematically we write as first element
(2) Second element : Multiply b
