//denominator polynomial// //Defines s as polynomial variable s=poly(0,'s'); //Creates transfer function in forward path F=syslin('c',[81/((s+18)*s)]); //Creates transfer function in backward path B=syslin('c',(1+0*s)/(1+0*s)); //Calculates closed-loop transfer function CL=F/.B // compare CL with Wn^2/(s^2+2*zeta*Wn+Wn^2) y=denom(CL)//extracting the denominator of CL //Extracting the coefficients of the denominator polynomial z=coeff(y) //Wn^2=z(1,1) ,comparing the coefficients Wn=sqrt(z(1,1)) //2*zeta*Wn=z(1,2) zeta=z(1,2)/(2*Wn) // zeta=damping factor //NOTE= here sqrt(1-2zeta^2) becomes complex so the other solution is Wr=0 & Mr=1 Mr=1 Wr=0 Wc=Wn*((1-2*zeta^2)+sqrt(4*zeta^4-4*zeta^2+2)) BW=Wc //BANDWIDTH