Fall 2001 16.311726 Hard to see how this helps, but consider the scalar case SI-A BK -BN new det-LC sI-Ac-BN →C(-BKBN+(s-A)BN)=0 CBN(BK-SI-A-BK-LCD)=0 CBNSI-A-LCD=0 So that the zero of the y /r path is the root of sI -[A-LC which is the pole of the estimator With this selection of G- Bn the estimator dynamics are can celed out of the response of the system to a reference command No such cancelation occurs with the previous implementation Fifth: select N to ensure that the steady-state error is zero As before, this can be done by selecting N so that the dC gain of the closed-loop y/r transfer function is 1 A-BK B C O r lDC LC A B e The new implementation of the controller is Cc= AcIc+ Ly+ BNr K a+Nr Which has two separate inputs y and r Selection of N ensure that the steady-state performance is good The new implementation gives better transient performanceFall 2001 16.31 17–26 • Hard to see how this helps, but consider the scalar case: new det   sI − A BK −BN¯ −LC sI − Ac −BN¯ C 0 0   = 0 ⇒ C(−BKBN¯ + (sI − Ac)BN¯ )=0 −CBN¯ (BK − (sI − [A − BK − LC])) = 0 CBN¯ (sI − [A − LC]) = 0 – So that the zero of the y/r path is the root of sI −[A−LC]=0 which is the pole of the estimator. – With this selection of G = BN¯ the estimator dynamics are can￾celed out of the response of the system to a reference command. – No such cancelation occurs with the previous implementation. • Fifth: select N¯ to ensure that the steady-state error is zero. – As before, this can be done by selecting N¯ so that the DC gain of the closed-loop y/r transfer function is 1. y r DC
C 0  −
A −BK LC Ac −1 
B B N¯ = 1 • The new implementation of the controller is x˙ c = Acxc + Ly + BNr ¯ u = −Kxc + Nr ¯ – Which has two separate inputs y and r – Selection of N¯ ensure that the steady-state performance is good – The new implementation gives better transient performance.