17 Problem A.5.13 Ogata 4edition (response unit-step, damping ratio, undamped natural frecuency)

Laplace.T	Root-locus	Transient response	Frecuency response

17 Problem A.5.13 Ogata 4edition (response unit-step, damping ratio, undamped natural frecuency)
Let's plot the response to unit-step input for several values of damping ratio $\zeta=[0.3,0.5,0.7,0.8]$ and undamped natural frecuency $\omega_{n}=[1,2,4,6]$ by Scilab

$\begin{displaymath}\frac{C(s)}{R(s)}=\frac{(\omega _{n}^{2})}{(s^{2}+2\cdot \zeta \cdot \omega \cdot s+\omega _{n}^{2})}\end{displaymath}$

Program in Scilab:
s=%s

a=[1 2 4 6];

b=[0.3 0.5 0.7 0.8];

t=0:0.01:16;

for i=1:4,

num(i)=a(i)^2;

den(i)=s^2+2*b(i)*a(i)*s+a(i)^2;

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

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

plot2d(t,c,i);
end;

xgrid;

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

legends(['case1','case2','case3','case4'],[1,2,3,4],opt=4);