5. Find the transfer function, \( T(s)=C(s) / R(s) \), for the system shown in Figure P5.5. Use the following methods: a. Block diagram reduction [Section: 5.2] b. MATLAB. Use the following MATLAB transfer functions: ML \[ \begin{array}{l} G_{1}(s)=1 /(s+7), G_{2}(s)=1 /\left(s^{2}+2 s+3\right), \\ G_{3}(s)=1 /(s+4), G_{4}(s)=1 / s, \\ G_{5}(s)=5 /(s+7), G_{6}(s)=1 /\left(s^{2}+5 s+10\right), \\ G_{7}(s)=3 /(s+2), G_{8}(s)=1 /(s+6) . \end{array} \] Hint: Use the append and connect commands in MATLAB's Control System Toolbox . FIGURE P5.5
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