Question

Implement a PID controller to control the transfer function shown below. The PID controller and plant transfer function should be in a closed feedback loop. Assume the feedback loop has a Gain of 5 associated with it i.e. . The Transfer function of a PID controller is also given below. Start by:

6. Implement a PID controller to control the transfer function shown below. The PID feedback loop has a Gain of 5 associated with it i.e. (HS) = 5). The Transfer function of a PID controller is also given below. Start by: i) Briefly explaining what the different transfer functions in the PID controller are and how they influence the output signal [3] ii) For gain values of Kp = 10 and Ki = 5, calculate the new transfer function of the overall system [6] 10 Transfer function of system, G,(s) = 10 $+5 PID controller transfer function Controller (s)= K + 7+K S Where G,(s)the forward path transfer function of the plant, Kp is the Proportional Controller Gain, Ki is the Integral Controller Gain and Kp is the Derivative Controller Gain.

Answer 1

Solution Given PID Controller and feedback H(S) = 5 Ø The general Transfer function of PLD Controller is given by Gcontroller (s) = (Kp + kg + kps) there are 3 transfer funchin proportional, Integral and derivative - proportional part limit the overshoot (up) r. Integral part reduces steady state emos to zero ( kl/s) - derivatives part is used for faster and stable output Ĉ kps) % Giren Kp=10 1 Ki E5 Given Gp(s) = 1845) Gesl . . - - -- - 10(kps?+ 108 +5) Ges) = - s(5+5) - Ges) - Transfer function you = it Goh CHCS)] lo (kps² Hos+5) S(5+5) so (kps²+ losts) . . It S(5+5) TOS) - lockos²+105+5) 52155+ 50 (kps² + los 75) lokys²+ loost 50 (1+50 kg) 52 +5055 +250 Note: Value of Kp is nesto TCS) = not given