(Solved): a) A block diagram of a magnetic tape drive system is shown in Figure 1.1 where, G1=mG2=(s+1) ...

a) A block diagram of a magnetic tape drive system is shown in Figure $$1.1$$ where, $$\begin{array}{l}{G}_1=m\\ G_2=\frac{1}{(s+1)(4s+1)}\\ G_3=\frac{0.5}{0.5s+1}\end{array}$$ i. Derive a unity feedback transfer function for the system. ii. Determine the gain $$m$$ needed to maintain the position error at $$5\%$$ of the input signal. b) Figure 1.2 shows a modified magnetic tape drive with a single sensor system. Figure $$1.2$$ i. By using similar transfer functions (i.e.. $$G_1,G_2$$ and $$G_3$$ ) as in question Q1 a), determine the steady-state error due to a unit step disturbance, $$D(s)$$ to the system.