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+//caption:determine_characterstics_eq_and_steady_state_error

+//example 6.10.11

+//page 181

+//J=moment of inertia,f=C,K=controller gain,Wn=natural frequency, zeta=damping ratio

+syms f J K Kt

+s=%s;

+A=sym((1/(J*s^2+f*s)));

+J=250;

+K=8*10^4;

+B=eval(A)

+a=(K*B);

+H1=s*Kt;

+b=(1+a*H1);

+b=simple(b);

+CL1=a/b;

+CL1=simple(CL1);

+H=1;

+c=1+CL1*H;

+c=simple(c);

+CL=CL1/c

+CL=simple(CL);

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

+Wn=sqrt(80000/250)//natural frequency

+//2*zeta*Wn=(80000*Kt+f)/250

+zeta=1;//for critical damping

+d=2*zeta*Wn;

+v=[320 d 1];

+CH=poly(v,'s','coeff');

+r=float(5*2*%pi/60);

+//steady state error for unit ramp input is:Ess= (2*zeta/Wn)

+Ess=(2*zeta/Wn)*r;

+disp(Ess,"steady_state_error=");