z domain root locus

z = tf('z');
sys = (0.0173*z)/((z - 0.9048)*(z - 0.8187));
rlocus(sys)
axis([-1 1 -1 1])
zeta = 0.5;
Wn = 0.2;
zgrid(zeta,Wn)

 http://ctms.engin.umich.edu/CTMS/index.php?aux=Extras_Dsserror

Design a compensator

HW #6

s = tf('s');
k=19.678
sys = (100*k)/(s*(s + 16.8)^2);
sys_cl = feedback(sys,1)
step(sys_cl)

Root Locus for Lightly Damped Systems

 HW # 7
s = tf('s');
sys = (100)/((s + j*2)*(s - j*2));
rlocus(sys)
axis([-10 4 -6 10])
Zeta = 0.456;
Wn = 1.8;
sgrid(Zeta,Wn)

 

G(s)K(s)/(1+G(s)K(s)

r = roots(p)
p = [1 20 114.5 190.5]



    1.0000   20.0000  114.5000  190.5000


r =

  -11.4580
   -5.5420
   -3.0000

 

 s = tf('s');
k=3.02
sys = (110.5*k*(s + 1))/(s*(s + 1.53)*(s + 3)*(s + 5.542)*(s +11.45));
sys_cl = feedback(sys,1)
step(sys_cl)

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root locus -lead compensation

s = tf('s');
sys = (20*16.8)/(s*(s + 5)*(s + 20));
rlocus(sys)
axis([-11 0 -1 4])
Zeta = 0.5;
Wn = 4.8;
sgrid(Zeta,Wn)