申論題

Problem 3 (10%) Consider an unstable plant with PI controller depicted in Fig. 4, where K_p , K_I , a and input signal r are all constants.
  One 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  are dampin ratio and natural frequency of a second order system respectively.
(iii) Damping ratio

(b) (3%) In addition to the specifications (i) to (iil), another requirement is that the steady-state error due to a unit-step input function is less than 0.01. According to this requirement, write down the mathmethical constraint(s) of a., K_Pand K_I .