(Solved): The forward path transfer function \( G(s) \) of a unity ratio feedback system is given by \( G(s) ...

The forward path transfer function \( G(s) \) of a unity ratio feedback system is given by \( G(s)=\frac{K}{s(s+1)(s+2)} \). Figure Q3 shows a sketch of its Nyquist plot. Figure Q3 (a) Copy Figure Q3 on to your answer script and clearly mark the points associated with calculating phase margin and gain margin. Also explain what are "Gain cross over frequency" and Phase cross over frequency". 4 Marks (b) Draw a rough sketch (you are ONLY required to show calculations related to finding sections of loci on real axis, angles of asymptotes and the centre of asymptotes) of the root locus of this unity ratio system. (c) Construct Routh's table using the denominator polynomial of the closed loop system transfer function. 6 Marks (d) Find the value of \( K \) for which the system is marginally stable (output will show sustained oscillations). 4 Marks (e) Clearly indicate (on rough sketches) the points corresponding to \( K \) value calculated in (d) in the root locus and Nyquist diagram. 2 Marks