16 Problem A.5.12 Ogata 4edition (response to unit-step,rise time, peak time, maximum overshoot and settling time)

Laplace.T	Root-locus	Transient response	Frecuency response

16 Problem A.5.12 Ogata 4edition (response to unit-step,rise time, peak time, maximum overshoot and settling time)

Let's plot the system's response to unit-step and calculate rise time, peak time, maximum overshoot and settling time by Scilab

$\begin{displaymath}\frac{C(s)}{R(s)}=\frac{(6.3223\cdot s^{2}+18\cdot s+12.811)}{(s^{4}+6\cdot s^{3}+11.3223\cdot s^{2}+18\cdot s+12.811)}\end{displaymath}$

Program in Scilab:

s=%s

num=6.3223*s^2+18*s+12.811;

den=s^4+6*s^3+11.3223*s^2+18*s+12.811;

cr=syslin('c',num/den);

t=0:0.01:20;

c=csim('step',t,cr);

xgrid;

plot2d(t,c);

xtitle(System's response to unit-step'
,'t(seg)','Amplitude')

k=1;

while(c(k)<1),k=k+1;end;

riset=0.01*(k-1);

[cpico,kpico]=max(c);

peakt=0.01*(kpico-1);

movershoot=cpico-1;

kr=20/0.01+1;

while(c(kr)>0.98&c(kr)<1.02),kr=kr-1;end;

settlingt=0.01*(kr-1);

riset

peakt

movershoot

settlingt

Results:

-->riset
 riset  =
 
    0.85  
 
-->peakt
 peakt  =
 
    1.67  
 
-->movershoot
 movershoot  =
 
    0.6182275  
 
-->settlingt
 settlingt  =
 
    10.03