16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde dodd. 2d.d A 2(a+K) For the disturbance: Steady state response 0 to constant input d O 0(s)= K O=lim(sO(s) lim l 3-0(s+Ks) K O F(s)=F(s)-Fdesired(s) K s+K +K K F(S= K+sK-s Using Cauchy,s Theorem: e?=Res( pole at s=-k) KN 1 Page 6 of716.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 6 of 7 22 2 2 10 02 1 2 012 12 2 2 2( ) s cd cd c e I ddd dd A a K + == → = + For the disturbance: Steady state response O to constant input d ( ) 0 0 2 2 2 2 1 1 1 1 ( ) lim ( ) 1 lim ss s s ss O s d sK K s d O s s Ks O sO s d d s s Ks K d D O K K → → = = + + = + = ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ + = = () () () 1 ( ) ( ) e s desired n ee n Fs Fs F s K s sK sK K F s s K K K Ss N K sK s = − − = −= + + − = + − − = + − Using Cauchy’s Theorem: ( ) 2 2 Res pole at 1 ( )2 n e sK K N KN K K = =− = = +