ME$0344$ Final Project

Q$1.$ An armature$-$controlled dc motor whose torque$-$speed characteristics are

shown below drives the load also shown.

e$\_($a$)^(+)+[$

i$.$ Find the transfer function of the system thetam$//$Ea$.$

ii$.$ Use MATLAB$/$Simulink to simulate the step response of the system.

Mark on the plot the steady$-$state value, percent overshoot, and the rise

time, peak time, and settling time.

iii. Use MATLAB$/$Simulink to simulate the step response of the closed$-$loop

system assuming unity feedback. Mark on the plot the steady$-$state

value, percent overshoot, and the rise time, peak time, and settling

time. Compare the results in ii and iii.

iv$.$ Design a PID controller to obtain zero$-$steady state error with $20\%$

improvement on the settling time.

Q$2.$ The open$-$loop transfer function of the plant for a specific application is

Gp$($s$)=(6)/($s$(2$s$+2)(3$s$+24))$

Plot the root locus of the system using MATLAB.

Is it possible with proportional control to achieve settling time less than $2\mathrm{.}07$ sec for this

plant. Explain why based on the root locus plot.

Use PD control to improve the response, so that the dominant time constant is $0\mathrm{.}5$ sec

or less and the damping ratio is $0\mathrm{.}707$ or greater.

Project Requirements:

i$.$ The deadline for this $20$ grades project is Sunday $12$ January $2025.$

ii$.$ You can work in a group $($max $3$ students$)$ or individually.

iii. You must submit a report with the results and simulation files

$($MATLAB$/$Simulink$).$

this is a control systems I project