Design and Build a DC Motor Control System Using Simulink Blocks $-$ ExamQuestion:A DC motor drives a factory conveyor belt system, and its speed needs to be controlled toensure consistent product delivery. The motor is part of a feedback control system wherethe speed is controlled using a PID controller. However, the system currently only usesproportional control and experiences slow response and steady$-$state error when loadconditions change.You are tasked with analyzing the current system, improving its performance, and buildingthe circuit to control the conveyor belts speed using appropriate Simulink blocks.Tasks:$1.$ System Analysis :$-$ You are provided with the following parameters for the DC motor system:$-$ Motor Inertia J $=0\mathrm{.}02$ kg$$m$^2-$ Motor Resistance R $=1-$ Motor Inductance L $=0\mathrm{.}5$ H$-$ Back EMF constant K$\_$b $=0\mathrm{.}01$ V$$s$/$rad$-$ Damping coefficient B $=0\mathrm{.}05$ N$$m$$s$-$ Desired speed $\_$desired $=100$ rad$/$s$-$ Predict how the current proportional$-$only control system will behave when there is achange in load.$-$ Discuss the role of inertia and damping in the motors performance and how they impactthe systems response time and stability$\mathrm{.}2.$ Build the Control Circuit:You are now tasked with building a control circuit to improve the conveyor belt systemsperformance. The system should regulate the speed of the DC motor using a PID controllerwith feedback from the motors velocity sensor$.-$ Build the DC motor control system using appropriate Simulink blocks to:$-$ Use a PID controller to control the motors speed.$-$ Provide an error signal based on the difference between the desired and actual speed ofthe conveyor.$-$ Visualize the systems performance using appropriate blocks to monitor the motorsspeed over time$\mathrm{.}3.$ Tuning the Controller:After building the control system, tune the PID controller to improve system performance.Specifically:a$.$ Explain how increasing the proportional gain K$\_$p affects the systems response.b$.$ What role does the integral gain K$\_$i play in reducing steady$-$state error?c$.$ How would increasing the derivative gain K$\_$d affect the systems stability andovershoot?$4.$ System Behavior Prediction:Once youve tuned the PID controller, predict how the system will behave if the load on theconveyor suddenly increases:$-$ How will the control system react to maintain the desired speed?$-$ Will the system return to the desired speed, and how long will it recover?Governing Equations:$1.$ DC Motor Electrical Equation:V $=$ L di$/$dt $+$ R i $+$ K$\_$b Where V $=$ input voltage $($V$),$ L $=$ motor inductance $($H$),$ R $=$ motor resistance $(),$ i $=$ motorcurrent $($A$),$ Kb $=$ back EMF constant $($V$$s$/$rad$),=$ angular velocity $($rad$/$s$)\mathrm{.}2.$ Torque Equation for Motor:T$\_$m $=$ J d$/$dt $+$ B $+$ T$\_$lWhere Tm $=$ motor torque $($N$$m$),$ J $=$ rotational inertia $($kg$$m$^2),$ B $=$ damping coefficient$($N$$m$$s$),$ Tl $=$ load torque $($N$$m$)\mathrm{.}3.$ Rotational Dynamics: $=$ dtWhere, $=$ angular position $($rad$),=$ angular velocity $($rad$/$s$)\mathrm{.}4.$ Control System Equation:V$\_$control $=$ K$\_$p e$($t$)+$ K$\_$i e$($t$)$ dt $+$ K$\_$d de$($t$)/$dtWhere: e$($t$)=$ error signal $($difference between desired and actual position$),$ K$\_$p$,$ K$\_$i$,$ K$\_$d $=$