Find the transfer function between output X and input R for

Find the transfer function between output X and input R for the block diagram shown below. For the system ABOVE, plot the Bode diagram. If the absolute value of the phase angle must be less than approximately 45degree and the magnitude must be less than approximately -30 dB. what frequency range is acceptable?

Solution

X/R=[(20S+100)/(10S^2+70S+600)]*[(S-1)/(10S+1)]

X/R=[(20S^2-20S+100S-100)/(100S^3+700S^2+6000S+10S^2+70S+600)]

X/R=[(20S^2+80S-100)/(100S^3+710S^2+6070S+600)]