Problems:

Problem $1(10$ pts$)$:

Recall that when using SI units the torque constant and back$-$EMF constants for a motor are the same value $K.$ Given this, a simple DC motor's transfer function between input voltage $V_{in}(s)$ and output velocity $(s)$ is given as

$G(s)=\frac{s}{V_{in}}(s)=\frac{K}{(Js+b)(Ls+R)+K^2}$

A$.$ For an input $5$ V impulse function $(5$ Volt impulse input at time $t=0)$ what will the final $($angular$)$ position be$?$ Note, the transfer function given, $G(s),$ is written for $($angular$)$ velocity $(4$ pts$)$

B$.$ If you were given values for $K,J,b,L$ and $R,$ how would you decide if the output velocity will have any overshoot in it$?(4$ pts$)$

C$.$ We wish to apply a feedback controller, with controller transfer function $C(s).$ Draw a block diagram of a feedback system, as discussed in the course, using this controller to control the plant $G(s)(2$ pts$).$