Transcription of 第10 単元 Hurwitz の安定性 ... - lab.kochi-tech.ac.jp
1 10 Hurwitz .. Hurwitz .. Gc (s ) G (s ).. H (s ).. Gc( s ) G ( s). W (s) =. 1 + Gc( s ) G ( s ) H ( s ). 1 + Gc( s) G ( s) H ( s) = 0 . a 0 s n + a1 s n 1 + L + a n 1 s + a n = 0 . a 0 ( s P1 )( s P2 )( s Pn ) = 0 .. Hurwitz .. Hurwitz . 10-1. Hurwitz . a 0 , a1 , L , a n Hurwitz . a1 a3 a5 L. a1 a3 a0 a 2 a 4 L. H 1 = a1 H2 = , Hn =. a0 a2 LL L. L L a n 2 a n . a 0 , a1 , L , a n . H i > 0(i = 1,2, L , n) . H 1 > 0, H 2 > 0, L , H n > 0.. K . R(s ) K 1 Y (s). 0 .5 s + 1 . s ( s + 1). G1 ( s ) .. R(s ) K Y (s).
2 S ( + 1)( s + ).. K. W (s) =. + 2 + + K. 3. D(s ) . D( s ) = 3 + 2 + + K. 10-2. Hurwitz D(s ) 10 . D( s ) = s 3 + 2 + 11s + 10 K. Hurwitz . 10 K 0. H3 = 1 11 0. 0 10 K. D (s ) . H 1 = 7 .5. 10 K. H2 = = 11 10 K > 0. 1 11. 10 K 0. H3 = 1 11 0 = 10 10 K (10 K ) 2 > 0. 0 10 K.. 0 < K < 10-3.. ( s 10). (1) G1 ( s ) =. s + 4 + s + 103. 5. ( s 12). (2) G2 ( s ) = 2. s + 6s ( s 1). (3) G3 ( s ) =. ( s 1)( s + 2)( s + 3). ( s 7). (4) G4 ( s ) =. ( s + 1)( 2 + + ). ( s 25). (5) G5 ( s ) =. ( s )( s 2 + 19 s + 90). Hurwitz .
3 ( s 2 ). (1) G1 ( s ) = 3. s + 3s 2 + 4s + 5. ( s 2 ). (2) G2 ( s ) =. s 4 + 3s 3 + 4s 2 + 5s + 6. ( s 2 ). (3) G3 ( s ) =. s 5 + 3s 4 + 4s 3 + 5s 2 + 6s + 7. 10-4.
