(Solved): Consider a cascaded dual-loop control system as shown in Figure 3, where the outer-loop controller ...

Consider a cascaded dual-loop control system as shown in Figure $3$, where the outer-loop controller $C_p(s)=1$ is a proportional controller, the inner-loop controller $C_v(s)=1+\frac{1}{s}$ is a Proportional Integral (PI) controller. The plant to be controlled is a concatenation of $G_v(s)=$ $\frac{10}{s+2}$ and $G_p(s)=\frac{1}{s}$, which are controlled by $C_v(s)$ and $C_p(s)$, respectively. $D(s)$ is the disturbance to the plant. (1) Obtain the transfer function from the reference input $R(s)$ to the tracking error $E(s)$ and identify the type number; (10 marks) (2) Obtain the transfer function from the disturbance input $D(s)$ to the tracking error $E(s)$ and identify the type number. (10 marks)