(Solved): (a) For the transfer function given below, plot the unit step response, unit ramp response, unit im ...

(a) For the transfer function given below, plot the unit step response, unit ramp response, unit impulse response and determine the rise time, peak time, overshoot, settling time and steady state errors according to different system inputs. $H(s)=\frac{C(s)}{R(s)}=\frac{10}{s^2+2s+10}$ (b) Repeat part a for the system given below in state space form $\begin{array}{l}\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{cc}?1& ?0.5\\ 1& 0\end{array}\right]\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0.5\\ 0\end{array}\right]u\\ y=\left[\begin{array}{ll}1& 0\end{array}\right]\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]\end{array}$