6. Use PI controller for the system model in (2). In a new Simulink model, redraw the block diagram of the new model with the PI controller. a. Plot the root locus of the system with PI controller using MATLAB. Discuss the stability of the system. b. For all possible combinations of PI controller of the previously selected values of P and I controllers, plot the time response of the angular displacement (6) due to a unit-step reference input with and without unit-step disturbance D(s). Discuss the stability, maximum overshoot, settling time, and steady-state error in all cases. Briefly describe how your controller will respond to the disturbance D(s). 7. Give a brief conclusion and provide optimum values of the PI controller for the undisturbed system. The design requirements for the system are: a. Both Kp and Ki should not exceed 10. b. Maximum overshoot is less than 20%. c. Settling time is less than 60 sec. Project Instructions: ➤ This project is teamwork of 2-3 members. All group members' names must be submitted to their lab instructor before the end of week 13. A half-mark deduction will be given to those who fail to provide the names by the specified time. A technical report, Word processed, must be submitted in week 15 (before the presentation) and a PowerPoint presentation is required for all groups. ➤ The presentation should be presented in front of the lab instructor only. Other students should wait outside for their turn to come. Failure to attend the presentation will result in zero marks for the presentation. You should expect questions related to the whole project (MATLAB code, theory, etc.) The grade distribution for the Lab project is Report 3% + Presentation 3% = Total 6%./nLab Project: PI Controller for an Electromechanical System (Teamwork: 2-3 members, Report and Presentation: due in week 15)* The project is to design a PI controller to control the position of a shaft of an electromechanical system that has the following transfer function: Fixed field R L TF= e(s) V(s) Km s(Tms+1)' or TF= n(s) V (s) Km = Tms+1 "' Armature circuit i where is the angular velocity (6) in s-domain. Assume the provided Excel file shows the response of (ė) for a step input of (v) with a magnitude of 10 V. Requirements: V(s) bė Rotor Km (s) TS +1 1. Obtain the system parameter from the Excel file (Km and 7). Plot on the same graph the experimental data and the simulation results. Compare between them. 2. Use Simulink to draw the block diagram of the system. Plot the time response of the angular displacement (e) due to a unit step input of the voltage (v). Discuss the stability. 3. For the same model in (1), add a unit-step disturbance D(s) to the system, and plot the time-response of the angular displacement (6). The unit-step input of the voltage (v) is unchanged. Discuss the stability. 4. Add P controller to the system model in (2). In a new Simulink model, redraw the block diagram of the new model with the P controller. a. Plot the root locus of the system with P controller using MATLAB. Discuss the stability. b. Use low, mid, and high values for Kp and plot the time-response of the angular displacement (6) due to a unit-step reference input with and without unit-step disturbance D(s). Discuss the stability, maximum overshoot, settling time, and steady-state error in all cases. Briefly describe how your controller will respond to the disturbance D(s). 5. Add I controller only to the system model in (2). In a new Simulink model, redraw the block diagram of the new model with the I controller. a. Plot the root locus of the system with the I controller using MATLAB. Discuss the stability of the system. b. Use low, mid, and high values for Ki and plot the time-response of the angular displacement (6) due to a unit-step reference input with and without unit-step disturbance D(s). Discuss the stability, maximum overshoot, settling time, and steady-state error in all cases. Briefly describe how your controller will respond to the disturbance D(s).

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