pid control, linear systems

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PID control, linear systems CS 4758

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Page 1: PID control, linear systems

PID  control,  linear  systems  

CS  4758  

Page 2: PID control, linear systems

•  Review  of  Poten<al  Fields  and  RRTs.  

•  Discrete  <me  Linear  systems:    –  reachability,  controllability.  

•  Bang-­‐bang  controller.  •  PID  controller.  – Stability  of  system  with  P  controller.  

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where,  e(t)  =  x(t)  –  xdesired(t)  

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Stability  of  P  controller.    

For  discrete  <me  linear  system:    The  magnitude  of  the  real  part  of  the  eigenvalues  of  the  state  transi<on  matrix  should  be  less  than  1.    E.g.,  For  A  =  1,  and  B  =  1,    X(t+1)  =  (1-­‐kp)  x(t)  |1-­‐kp|  <  1  =>  For  0  <  kp  <  2,  the  system  will  be  stable.