Designing a lead compensation for a 3rd order system
To verify the solution, you should obtain the closed-loop transfer function using a feedback of \$H(s) = 1\$, then check if the new system matches a maximum overshoot of 25% of less and that the settling time was reduced to at least 5 seconds.

Here is the code used in verification (works for both Matlab &amp; octave):


num1 = [1]
den1 = [1 4 0 0]
num2 = [60.944 24.3776];
den2 = [1 12.041 32.164 0 0]

g1 = tf(num1, den1)
g2 = tf(num2, den2)
sys1 = 1 / (1 + g1)
sys2 = 1 / (1 + g2)

t = 0:0.05:20
c1 = step(sys2, t)
c2 = step(sys1, t)

plot(t,c1,'-',t,c2)
title('Exam 3. Question 1.')
xlabel('t Sec')
ylabel('Outputs c1, c2')
text(10, -0.25,'Compensated System')
text(6,1.2,'Uncompensated System')