A.L.PLANT CERAINTY 41 To do ths tewelwa skuld bels so tttehornaiz taon saef P(u) P(jw) IW2(jw)l,,w,T, tkatis Wa(jw)l.,w. A littetimewithBodemanitde skws thtasuitaienstolTwis W,(= 0218 04s+i≤ FgulC4is teBodemanitideptor t wa ad RTs)1for=04,ewoRtvan(4 101 100 10 么 10-3 0 100 101 102 103 Figul4 Bodepts of W (dah ad r)1 (slid)4 To getareing forby conseRativeths is compaectar fIQucie teatauncr ta飞st withecovling disk fs:sff1.lW2(0wlg≤ Example 3 Suppsetrattepattasf(rfunction is =点 PLANT UNCERTAINTY  To do this the weight W￾ should be chosen so that the normalized perturbation satises P j P j  jW￾jj   that is ej  jW￾jj   A little time with Bode magnitude plots shows that a suitable rstorder weight is W￾s   s s   Figure  is the Bode magnitude plot of this W￾ and exp s  for    the worst value 10-3 10-2 10-1 100 101 10-1 100 101 102 103 Figure  Bode plots of W￾ dash and exps  solid To get a feeling for how conservative this is compare at a few frequencies  the actual uncer tainty set  P j P j       ej     with the covering disk fs  js jjW￾jjg Example  Suppose that the plant transfer function is P s  k s