$1.$ If the system is represented in cascade form with the states measurable shown as $\backslash ($ z$\_\{1\}=\backslash )\backslash ($ y$,$ z$\_\{2\}$ z$\_\{3\}\backslash ),$ as shown in Figure design a controller to yield a closed loop response of $\backslash (10\backslash \%\backslash )$ overshoot with a settling time of $1$ second.

a$)$ Design the controller in the plant to phase variables state space form after making sure that it is controllable and implement it in Simulink using the $\backslash ($ z $\backslash )$ state vector.

b$)$ Check the steady state reference tracking error to unit step input and fix it if it is not zero.

c$)$ Verify the performance.

d$)$ Now assume that states are not measurable all you have is the output. Design an observer to drive the state feedback controller. Observer will be $10$ times as fast as the plant and the third pole will be $10$ times as far from the imaginary axis as the observer's dominant poles.

e$)$ Show the control system performance when the state feedback is provided from the state estimation