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+//caption:determine_Wn,zeta_and_Mp

+//example 6.10.16

+//page 187

+s=%s;

+num=1;

+den=sym('s*(1+0.5*s)*(1+0.2*s)');

+c=num/den;

+c=simple(c);

+disp(c,"C(s)/E(s)=");

+G=c;

+H=1;

+CL=G/(1+G*H);

+CL=simple(CL);

+disp(CL,"C(s)/R(s)=");

+A=pfss((10/(s^3+7*s^2+10*s+10)));

+d=denom(A(1));

+b=coeff(denom(A(1)))

+printf("for oscillatory roots:")

+Wn=sqrt(b(1,1));//natural_frequency

+//2*zeta*Wn=1.5;

+zeta=1.5/(2*Wn);//damping ratio

+Mp=exp((-zeta*%pi)/sqrt(1-zeta^2))*100;//%_peak_overshoot

+disp(Wn,"natural_frequency=");

+disp(zeta,"damping ratio=");

+disp(Mp,"%_peak_overshoot=");
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