Question

Solve the following problems:

P.1 Design a PID (or a Pl only) for the following unity feedback system as shown in the figure, where G(s) = к (s+1)(s+3)(s+10) R(8) G(s) The PID (or Pl only), needs to meet the following requirements: a) Mp < 25% b) Ts<2sec for a step input and zero steady-state error Hint: If designing a PID start by adding a pole at the origin before starting the steps seen in class. P.2 Design a PID (or a PI only) for the following unity feedback system as shown in the figure, where G(s) = K (s+1)(s+4) R(S) E(S) Cs) G(S) The PID (or Pl only), needs to meet the following requirements: a) Tp < 1.047 b) Mp < 1.5% Hint: If designing a PID start now by designing the Pl with the pole and zero close to the origin and then the PD using the all the system's poles and zeros including the PI.

Answer 1

ginen GS) = K (S+1) (5+3) (stid) required specifications MP < 251 Is < 2 sec for step Pipe for step ile zero steady state error Consider type 1 system, general form of OLTF of type 1 system 's(S+2&wn) k MP <254 е - TE UI-9h K&/UTA X100 = 25 - = 0.25 0.25 10 =1.778 on both sides . -TC/U squaring 는 Inch * 3.162 (1-5?) ( +3162)¢* = 3162. = 3.162 3.162 = 0.243 & =0.492 Scanned with 2 CS T + 3.162

ste ts <alec Settiling time for † 2.1. tolerence band. ts 4 kali &wn 4 0.492Xwn 42 wn> 0.492X & Wn >4.065 I take W, =4.07 steady state error for unit step ess A Amplitude of step funn. Itke zaposition Eonor constant. s(s+2(mn) It sto G(S) sto kp= ess=ite > any way PQ OLTA for type 1 System steady state step ilp. zero for is error OLT FE PID X GCS 2 K S( Stę wn) к PID X (5+1+3)+10) (s+1(8+3)6+10) SCS+4) a & wn 2X0.492x 4.07 = 4 PID CS Scanned CamScanner