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+//caption:determine_transfer_function,Wn,zeta

+//example 6.10.10

+//page 179

+//J=moment of inertia,f=C,Ke=error detector gain,Wn=natural frequency, zeta=damping ratio,Km=torque constant

+syms J f s

+Ke=5.73;

+Km=0.045;

+n=sym('N1/N2')

+n=subs(n,'N1/N2',1/10);

+J=0.25*float(n^2);//referred to motor side

+f=1*float(n^2);//referred to motor side

+//from the block diagram given in fig 6.10.6 on page 179,

+a=(Ke*Km)

+b=1/(J*s^2+f*s)

+c=(b*float(a))

+G=(n*c);

+G=simple(G)

+H=1;

+d=(1+G*H);

+d=simple(d);

+CL=G/d;

+CL=simple(CL)

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

+e=poly([328800 127516 31879],'s','coeff')

+printf("the characterstics eq. is:\n");

+disp(e);

+f=coeff(e)

+Wn=sqrt((f(1,1)/f(1,3)))//natural_frequency

+zeta=((f(1,2)/f(1,3))/(2*Wn))//damping ratio

+//part(b)

+syms Td

+g=1+s*Td

+h=(g*G)

+i=1+h*H

+i=simple(i);

+CL2=(h/i)

+CL2=simple(CL2);

+disp(CL2,"C(s)/R(s)=");

+poly(0,'s');

+l=s^2+(10.32*Td+4)*s+10.32;

+printf("on simplyfying the characterstics eq. is:");

+disp(float(l));

+Wn1=sqrt(10.32)//natural_frequency

+//2*zeta1*Wn1=10.32*Td+4

+zeta1=1;//as damping is critical

+Td=(2*zeta1*Wn1-4)/10.32;

+disp(Td,"time const. of advanced phase circuit,Td=");

+