Question $5-$ Modelling $(10$ marks$)$

Fig. Q$5$ shows the diagrams of a mechanical system and an electrical system. By comparing the system force$/$voltage equations of these two systems, explain how these two systems are analogous to each other.

Fig. Q$5$

Question $6-$ Transient and Steady State Analysis $(10$ marks$)$

A second$-$order system is subject to a unit step input. Regarding the output of this response, explain the following terms:

i$.$ Delay time

ii$.$ Rise time

iii. Peak time

iv$.$ Maximum overshoot

v$.$ Settling time

Use a graph to support your explanation.

Question $7-$ PID Control $(10$ marks$)$

List out the step$-$to$-$step procedure of obtaining the tuning values of the PID controller, by using the Ziegler$-$Nichols Transient Response Method.