Assume Gps 1s 3s 4s 5 for a unity feedback system shown

Assume G_p(s) = 1/(s + 3)(s + 4)(s + 5) for a unity feedback system shown below. Using Bode Diagrams to design a controller that simultaneously satisfies the following three conditions (A) Steady state error to unit step into is 5% (B) Phase margin: 45 degrees (C) Gain crossover frequency: 5.5 rad/s

Solution

let controller = kp + ki/s

ess = .05 =1/s (kp + ki/s)/(s+3)(s+4)(s+5)

ki =3

kp =1.2 using phase cross ovdr frequency