題組內容

Problem 3 (10%) Consider an unstable plant with PI controller depicted in Fig. 4, where Kp , KI , a and input signal r are all constants.
  61a5b40a5f0a1.jpgOne wants to design the PI controller and feedback gain c to stabilize the overall controlled system and to meet the following requirements:
 (i) The controlled system has to be asymptotically stable.
 (ii) Settling time 61a5b44d57815.jpg are dampin ratio and natural frequency of a second order system respectively.
(iii) Damping ratio 61a5b4f507f72.jpg

(a) (7%) Find the relationship among a, KPand KI in order to satisfy the above three requirements.