125 – CONTROL- MEC .

You are required to complete the Control Systems case study assignment fully and accurately using MATLAB and Simulink. Follow the instructions below carefully and ensure all results are correct, well-presented, and supported by simulation.

1. System Modeling

– Use the given open-loop transfer function G(s) and assume a unity feedback configuration.

– Build the system model in MATLAB.

2. Initial System Analysis (Uncompensated System)

– Plot the Step Response of the system.

– Determine the following parameters:

– Percentage Overshoot (%OS)

– Settling Time (Ts)

– Steady-State Error (ess)

– Plot the Ramp Response and calculate the steady-state error for the ramp input.

3. Lead Compensator Design

– Design a Lead Compensator to improve the transient response.

– Ensure that:

– Percentage Overshoot is reduced

– Settling Time is reduced

– Improvement should be at least 50% compared to the original system

– Use Root Locus or Bode Plot methods for design.

– Show clearly how the compensator parameters were selected (zero, pole, gain).

– Plot the new Step Response after applying the Lead Compensator.

4. Lag Compensator Design

– Design a Lag Compensator to improve steady-state accuracy for a ramp input.

– Reduce the steady-state error to meet the required specification.

– Clearly show calculations for error constants (Kv).

– Plot the Ramp Response after compensation.

5. Combined Lead-Lag Compensator

– Combine both Lead and Lag compensators.

– Apply them to the system and simulate the final compensated system.

– Plot both Step and Ramp responses.

6. Performance Comparison

– Compare uncompensated and compensated systems.

– Present results in a clear table including:

– Overshoot

– Settling Time

– Steady-State Error

– Calculate percentage improvement for each parameter.

7. Graphical Analysis

– Include the following plots:

– Step Response (before and after)

– Ramp Response (before and after)

– Root Locus

– Bode Plot

– All graphs must be properly labeled.

8. MATLAB Implementation

– Write clean and organized MATLAB code.

– Use comments to explain each step.

– Ensure the code runs without errors.

9. Simulink Model

– Build the system in Simulink showing:

– Original system

– Lead compensator

– Lag compensator

– Clearly label all blocks.

10. Final Report

– Prepare a complete report including:

– Title Page

– Table of Contents

– Introduction

– Methodology

– Results and Discussion

– Conclusion

– References (APA 7th edition)

– Include all graphs and explanations.

– Write a clear analysis of how the compensators improved system performance.

11. AI-Based Summary

– Provide a final summary explaining the findings and improvements based on system behavior and graphs.

12. Required Files Submission

You must provide all of the following files:

– MATLAB script file (.m)

– Simulink model file (.slx)

– All generated graphs (as images)

– Final report (Word document)

Ensure that all files are complete, correctly named, and ready for submission. The work must be original, well-structured, and ready for viva discussion.

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