Fall 2001 16.311725 AT+ B(Nr)(A-LC] c+ LCI+Gr (A-LC). C+ BNr-(A-LC c+Gr (A-LC).I+BNr-Gr (A-LC)C+(BN-G Thus we can eliminate the effect of r on a by setting g= Bn Fourth: if this generalization does not change the closed-loop poles of the system, then what does it change? The zeros of the y/r transfer function, which are given b I-A BK-BN general detI-LC SI-AcI-G 0 SI-A BK 0 previous det I-LC SI-AcL 0 sⅠ-ABK BN new det LC SI-A-BNFall 2001 16.31 17–25 ˙ x˜ = Ax + B(Nr ¯ ) − ({A − LC}xc + LCx + Gr) = (A − LC)x + BNr ¯ − ({A − LC}xc + Gr) = (A − LC)˜x + BNr ¯ − Gr = (A − LC)˜x + (BN¯ − G)r • Thus we can eliminate the effect of r on ˜x by setting G ≡ BN¯ • Fourth: if this generalization does not change the closed-loop poles of the system, then what does it change? – The zeros of the y/r transfer function, which are given by: general det   sI − A BK −BN¯ −LC sI − Ac −G C 0 0   = 0 previous det   sI − A BK 0 −LC sI − Ac L C 0 0   = 0 new det   sI − A BK −BN¯ −LC sI − Ac −BN¯ C 0 0   = 0