62 CHAPTER 10.DESIGN FOR PERFORMANCE Hence our design should produce actual step response 4 delayed ideal step response4 One furt her adjustment is required in the problem setup:W must be stable and strictly proper, so the function above is modi<ed to 83+-28+- Ws)- 8+000-）8+-2)0400-8+可1 The procedure can now be applied. Step<Since P∈S we take N-PM--X=0、Y-- Step.The model-matching problem is to minimize kW M.NQim)k:=kW PQim)k14 Since P has only one right half-plane zero,at s=545-08,we have from Section 9.- minkW×.PQimk=|W545-08川=-402-04 Thus the spec kW Ski o -is not achievable for this P and W.Let us scale W as w) 049 -W4 -402- Then W 545-08)=049 and the optimal Qim is W:09 Qim- W P that is Qim0)-s00008s+002-s+04-768s3+0s707s3+-89-0s+00026） s+64-08-33+6488978+980- Step 3 Set 8):= 28+4 Compute kW PQim)k for decreasing values of 2 until the norm is o 2 2-Norm 0.- 一-2 0.05 =0- 0.0≈ 0.988 Take2=040≈ Step 4 Q=Qim/ Step5C=Q=×.PQ) CHAPTER  DESIGN FOR PERFORMANCE Hence our design should produce actual step response  delayed ideal step response One further adjustment is required in the problem setup W￾ must be stable and strictly proper so the function above is modied to W￾s  s  s  s   s    s    The procedure can now be applied Step Since P  S we take N  P M  X  Y   Step  The model matching problem is to minimize kW￾MY NQimk￾  kW￾ P Qimk￾ Since P has only one right half plane zero at s    we have from Section  min kW￾ P Qimk￾  jW￾ j     Thus the spec kW￾Sk￾ is not achievable for this P and W￾ Let us scale W￾ as W￾     W￾ Then jW￾ j   and the optimal Qim is Qim  W￾  W￾P that is Qims  s  s    s   s    s   s    s   s  s    Step  Set J s   s    Compute kW￾ P QimJ k￾ for decreasing values of until the norm is  Norm         Take    Step  Q  QimJ Step  C  Q P Q