For the following unity feedback closed$-$loop system,

A$.$ Transfer Function Selection:

Each student is required to choose a transfer function based on their student number as outlined below:

Bubrace$(16$ubrace${)}_{a}05\mathrm{.}0200$ubrace$(3$ubrace${)}_b$ubrace$(2$ubrace${)}_c$

If your student's number is as above, then your transfer function will be:

$G(s)=\frac{9\mathrm{.}5}{s(s+8)(s+2)}$

B$.$ PID Controller Design:

Design a PID controller that achieves an overshoot of less than $5\%$ and a settling time of less than $2$ sec$.$

a$)$ By using either the root locus method or the algebraic approach.

b$)$ By Matlab auto$-$tuning. $[$using the command: $>>$ pidtool $($sys$)]$

C$.$ Matlab Simulation:

You are required to simulate the results obtained in Part B using Matlab through various methods:

a$)$ M$-$file: By implementing the corresponding code and plotting the step response of both the uncontrolled and controlled closed$-$loop systems on a single figure.

b$)$ Matlab Simulink: By constructing the corresponding block diagrams, observe the step response of both the uncontrolled and controlled closed$-$loop systems on a single figure.

D$.$ Controller Implementation:

It is required to implement your controller:

a$)$ Multisim: by building the corresponding Op$-$Amps circuit in Multisim.

Important Remarks:

$$ This project accounts for $15\%$ of the total course grade.

$$ All assignments must be submitted in both hardcopy $($printed report$)$ and softcopy $($via the UBIS system$).$ The hard$-$copy should be handed in during the lecture, while the soft$-$copy must be uploaded to the UBIS system. The softcopy should include the report, MATLAB files, and Multisim files.

$$ The report must include all calculations, design details, figures, and codes.

$$ Plagiarism is strictly prohibited; any copied work will receive a grade of ZERO.