16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde Lecture 18 Last time: Semi-free configuration design This is equivalent to H6cr○e D(s) perhaps B). We must stabilize F if it is given as unstabe e desig e (and lote n, s enter the system at the same place. F is fixed C(s) 1+C(S)F(SB(s) so that having the optimum H, we determine C from (s) 1-H(SF(S)B(S) We do not collect H and F together because if F is non-minimum phase, we would not wish to define h by H_(HFopt This leads to an unstable mode which is not observable at the output-thus cannot be controlled by feeding back Associate weighting functions with the given transfer functions F(s)→wF(1) D(s)→>D(1)16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 1 of 5 Lecture 18 Last time: Semi-free configuration design This is equivalent to: Note n s, enter the system at the same place. F is fixed. We design C (and perhaps B). We must stabilize F if it is given as unstable. ( ) ( ) 1 () () () C s H s CsFsBs = + so that having the optimum H , we determine C from ( ) ( ) 1 () () () H s C s H sFsBs = − We do not collect H and F together because if F is non-minimum phase, we would not wish to define H by ( )opt HF H F = This leads to an unstable mode which is not observable at the output – thus cannot be controlled by feeding back. Associate weighting functions with the given transfer functions. () () () () () () H F D Hs w t Fs w t Ds w t → → →