The schematic of an elevator system is shown in the Figure I. It comprises an elevator car and platform of mass $\backslash ($ M $\backslash ),$ pulled up or lowered down using an inextensible cable wound on a pulley. The elevator pulley is driven by a permanen moment of inertia $($P$/$P$)$ DC motor$)$ connected directly to it$.$ motor$-$pulley combination about its an which the inextensible by $\backslash ($ J$\_\{0\}\backslash )$ The diameter of the pulley drum, is wound, is $\backslash ($ D$=2$ r $\backslash ).$ The torque pres the elevator car can be mor at time $\backslash ($ t $\backslash )$ is $\backslash (\backslash$tau$($t$)\backslash ),$ clockwise posito the seventh floor level whicised from the ground floor level to all floors are of equal height is distance of $\backslash ($ H $\backslash )$ units of length. All floors are of equal height

Questions Q$.1$ to Q$.3$ pertain to the Elevator system of Figure $1,$

Q$.1.($a$)$ Explain with neat sketches, the electromechanical effects in the PM DC motor used to actuate the elevator system of Figure $1.[10]$

$($b$)$ Design drive circuits separately for the current control mode and the voltage control mode, for its actuation and analyze the role of each component used in it$.$ How is the effect of the 'fly$-$back kick' prevented by the drive? Explain.

Q$.2.($a$)$ Construct a bond graph model for the dynamics of the clevalor system. What is the minimum number of state variables required to model the system completely? Identify them.

$($b$)$ Derive the equations for dynamics of the system in terms of state variables and parameters, and provide your interpretation $[10]$

$($c$)$ What is the power drawn by the actuator system at any instuth of time? Express it in terms of states and parameters of the system? What are the factors affecting the power drawn?

Q$.3.($a$)$ Devise a scheme of sensors for measuring and acquiring to information related to the height of the elevator at any level $(10)$ information is to be acquired by an $8-$bit microcontrollet sy syem