lead_c
Enter the vectors of the numerator (numo) and denominator (denum) pol.
Start with the highest order term. Ex: [1 2 3] corr. (s^2 + 2 s + 3)
Both vectors should have the same length
Enter numo: [0 0 4]

numo =

     0     0     4

Enter deno: [1 2 0]

deno =

     1     2     0

 OPEN-LOOP SYSTEM (without Compensator): 
 
num/den = 
 
       4
   ---------
   s^2 + 2 s
Enter desired Kv: 20

Kv =

    20

 Phase margin "Pm" at the Gain crossover frq. "Wcp" 

Pm =

   17.9642


Wcp =

    6.1685

 Gain margin "Gm" in dB at the  Phase crossover frq " Wcg" 

Gm =

   Inf


Wcg =

   Inf

Zeros and poles of closed-loop system without compensator:

zeros =

   Empty matrix: 0-by-1


poles =

  -1.0000 + 6.2450i
  -1.0000 - 6.2450i

 Settling time "sett" and zeta "zeta" of same closed-loop system:

sett =

    4.0000


zeta =

    0.1581

 Press CR to continue
 Press CR to continue
Phase lead in degrees: 38

a =

    0.2379


Kc =

   42.0375

At "Wcp" the gain of the transfer function is equal to sqrt(a).
Use this frequency as the new gain crossover frequency wc

Wcp =

    8.9461

Enter wc, the new gain crossover frequency : 9

wc =

     9


Tt =

    4.3896


aTt =

   18.4527

 Compensator: 
 
num/den = 
 
    s + 4.3896
   -----------
   s + 18.4527
 Compensator gain Kc: 

Kc =

   42.0375

 Compensated Open-Loop trsf. function;
 
num/den = 
 
       168.1498 s + 738.1094
   -----------------------------
   s^3 + 20.4527 s^2 + 36.9055 s
 Phase margin "Pm" at the Gain crossover frq. "Wcp" 

Pm =

   50.6342


Wcp =

    8.9217

 Gain margin "Gm" in dB at the  Phase crossover frq " Wcg" 

Gm =

   Inf


Wcg =

   Inf

 Zeros and poles of Closed-loop system with compensator:

zeros =

   -4.3896


poles =

  -7.0161 + 8.1077i
  -7.0161 - 8.1077i
  -6.4205          

 Settling time "sett" and zeta "zeta" of compens. closed-loop system:

sett =

    0.5701


zeta =

    0.6544

 Press CR to continue
 Press CR to continue
 Enter decision ( >0 to continue) :0

decision =

     0

diary