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+//caption:determine_factor_by_which_K_should_be_reduced
+//example 6.10.7
+//page 175
+syms T K //K=forward_path_gain,T=time_constant
+s=%s;
+G=K/(s*(s*T+1));
+G=simple(G);
+printf("the_forward_path_transfer_function: \n" );
+disp(G,"G(s)=");
+H=1;//backward path transfer function
+CL=G/.H;
+CL=simple(CL);
+printf("the_overlall_transfer_function: \n" );
+disp(CL,"C(s)/R(s)=");
+printf("the_characterstic_equation_is:\n ");
+disp("s^2+s/T+K/T=0");
+//from char. eq. we get Wn^2=K/T and 2*zeta*Wn=1/T, so
+Wn=sqrt(K/T);//natural frequency
+zeta=(1/2)*sqrt(1/K*T)
+//let K1 be forward path gain when Mp1=60% and zeta1 be corresponding damping factor
+syms K1 K2 zeta1 zeta2
+Mp1=(exp(-(zeta1*%pi)/sqrt(1-zeta1^2)))*100//max. overshoot
+//on solving we get :
+zeta1=0.158
+//similarly let K2 be forward path gain when Mp2=20% and zeta2 be corresponding damping factor, which gives
+zeta2=0.447
+//assuming time const. T to be const. we get
+k=(K1/K2);
+k=(zeta1/zeta2)^2;
+disp(k,"K1/K2=");
+
+
+