INC  541  Modern  Control  Theory  Using  State  Space  MethodsLecture#9:  Digital  control  system  with  

state  feedback  Assoc.  Prof.  Benjamas  PanomruKanarug  

benjamas.pan@kmuK.ac.th

State  regulator  design  for  digital  control  system  

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Example:  pole  placement  design  

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Design  of  state  observers  1.  predicPon  observer  

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Design  of  predicPon  observers  

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Transposed  auxiliary  system:  

Design  of  state  observers  (cont.)  

2.  Current  observer:  use  when  computaPon  Pme  is  quite  short  compared  to  the  sampling  Pme  

EsPmate  an  approximaPon  of  x(k+1)  based  on  x_hat(k)          m  is  obtained  as  before,  except  c  is  replaced  by  cF  BP INC541 6

Design  of  state  observers  (cont.)  

3.  reduced-­‐order  observer  

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Reduced  order  observer  

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Error  equaPon:  

CharacterisPc  equaPon:  

Servo  design  

•  Feedforward  control  •  Feedback  with  integral  control  

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Feedforward  control  

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Control  law:  

Feedforward  gain:  

State  feedback  with  integral  control  

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Integral  state:  

System:  

Control  law:  

State  feedback  with  integral  control  (cont.)  

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Example  

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