Robus t (b This note has been written for a b asic course in robust and optimal control at 9th term of the ystem Construction Line, nstitute of Electronic Sy stems, Aalborg University. Originally the note was intended for a course consisting of six modules of four hours each. Currently, the courses at Aalborg University has been reduced to five modules, and hence, the note cont ains material, that can not be included in the course. The note has been adapted to a level, whid can be expected of 9th term students at the System Construction Line. The students are expected to be acquainted with classical feedback control theory The purposes of the note is to provide an introduction to mo dern robust and optimal control especially in Hoo and i theory. n Chapter 1, a short introduction to the concept of robust control is given; m Chapter 2 nominal and robust stability for single variable(SoSO)systems is described. n Chapter 3 nominal and robust performance for sso sy stems is analyzed, and the concepts Hoo and H2 optimal control are introduced. Chapter 4 gives an introduction to the analysis of multi variable systems, and in Chapter 5, st ability and performance of multi variable systems are studied. n Chapter 6, a solution to the Hoo control problem presented. Finally, in Chapter 7, an introduction to the structured singular value I is given, and controller design with i is treated. Robust optimal control; robust st ability; robust performance; Hoo optimal control; I ana I synthes afigution of thb authors The authors are with Grundfos A/S, and with the Department of Control Engineering, an tute of Electronic Systems, Aalborg University, DK-9220 Aalborg o, Denmark. The depart lenthasthefollowinghomepagehttp://www.conTroL.auc.dk.Theemailsofthelasttwo authors are: ipa, js]@control. auc.dk￾
   ￾
 $#  $   4#  (  #* * #    #' *    $ ' ( $
+ '  * # 5#  ￾ #  ( % * #*
+ ' ) #, # +6 7#)#+ $  4 #   (  * *# #) ( #8 '  ( ( $ *$6   + $ *   ) #, # + $    *   9, '   $ *  $  * # ' # $ *   #*  # $ * 6 $  $        ,  4$#*$ *  8 *  (  $ '      $
+ '  * # 5# 6 $      8 *    *:#  4# $ *#* ( * *  $ +6 $   ( $  #  ,#  # * #  '     #' *   *#+ #
￾  ￾ $ +6 ￾ $    $ # * #  $ **  (  *  # )#, ; ￾ $   '#    ## + ( #) ,# <
￾
7= + ' #  *# 6 ￾ $  " '#    ('* (
￾
7 + ' # +>   $ **  
￾ 
￾  #' *   # * 6 $  )#,   # * #  $ +# ( ' # ,# + '  # $  !  ## +   ('* ( ' # ,# + '   # 6 ￾ $     #  $
￾ *   ' #    6 -#+ # $  1  # * #  $  *   #) , ￾ # )#,   *    #) 4# $ ￾ #   6 
 ?  #' * ;   ## +;   ('* ;
￾  #' * ; ￾ +#; ￾ + $ #;     
 $  $  4# $ @( A
  4# $ $ &  '  (   %)# #) ￾ #  ( % * #*
+ ' ) #, # + &2 ) 3 & '6 $    '  $ $ (4#) $' ) B ￾


 6 $ '# ( $  4  $  B 
  ￾