Question

For the systems below, do what you ask, solve the calculations in a handwritten and step-by-step manner:

A) The system with unit feedback is operating with 15% of overdrive. Using frequency response techniques, design a compensator to result in Kv = 50 with margin frequency and the phase margin remaining approximately the same as the system without compensation:
G (s) = k / s * (s + 7)

B) The unit feedback system shown is operating with a 15% overrun. Using frequency response methods, design a compensator to result in a 5-fold improvement in steady-state error without significantly changing the transient response:
G (s) = K / (s + 1) * (s + 5) * (s + 10)

Answer 1

MATLAB code:

num=[45.83];

den=[1 7 0];

sys=tf(num,den)

bode(sys)

[Gm,Pm,Wgm,Wpm] = margin(sys)

Output:

MATLAB code:

num=[350];

den=[1 7 0];

sys=tf(num,den)

bode(sys)

[Gm,Pm,Wgm,Wpm] = margin(sys)

Output:

MATLAB code:

num=[1];
den=[1 7 0];
sys=tf(num,den)
bode(sys)
[Gm,Pm,Wgm,Wpm] = margin(sys)

Output: