(Solved): 3. (a) The block diagram of a closed system is shown below in Figure 3 (i) Using block reduction t ...

3. (a) The block diagram of a closed system is shown below in Figure 3 (i) Using block reduction techniques, determine the transfer function \( \frac{Y}{R} \) | in terms of the transfer function of the individual blocks. (9. Marks) (ii) Verify the solution for the transfer function from part (i) using Mason's rule. (9) Marks) (b) In the case of a second order system with two real negative poles, the addition of a zero may introduce some overshoot depending on the location of the zero. (i) Determine the values for \( \mathrm{c} \) for which the step response of the transfer function \[ G(s)=\frac{2(1+c s)}{(s+1)(s+2)} \] will have an overshoot. (4 Marks) (ii) Determine the maximum overshoot for \( c=2 \) (2 Marks) (iii) Sketch a plot of the response. (2 Marks)