(Solved): Consider a type-1 unity feedback system with an open-loop transfer function as shown in Figure Q3. ...

Consider a type-1 unity feedback system with an open-loop transfer function as shown in Figure $$\mathrm{Q}3$$. It is desired to have a velocity error constant $${\mathrm{K}}_{\mathrm{v}}=10$$ and phase margin of the system is at least $$45^{?}$$. a) Plot the Bode plot of the luncompensated system. $$[10$$ marks $$]$$ b) By using lead compensation scheme, design a suitable compensator function $${\mathrm{G}}_{\mathrm{c}}(\mathrm{s})$$ and compensator open-loop transfer function, $$G_c(s)G_p(s)$$. [8 marks] c) Plot the Root Locus of $$G_c(s)G_p(s)$$. [7 marks]