535 – 2 – CONTROL

You are required to complete the Control Systems coursework accurately and professionally. Follow the instructions below step by step to ensure a complete and correct submission.

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### 1. System Modelling

Begin by modelling the DC motor system based on the given parameters in the assignment.

– Use the electrical and mechanical equations of the DC motor.

– Assume armature inductance (L = 0).

– Ignore load torque as stated.

Your tasks:

1. Derive the transfer function:

– From input voltage (V(s)) to angular velocity (omega(s))

2. Then derive:

– From input voltage (V(s)) to angular position (theta(s))

All steps must be clearly shown, including:

– KVL equation

– Torque equation

– Laplace transform

– Final simplified transfer function

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### 2. Closed-Loop System

– Construct the full block diagram including the controller.

– Simplify the closed-loop system into a single transfer function.

– Show all block diagram reduction steps clearly.

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### 3. Controller Design (IPD / PID)

Design a controller that satisfies the required performance specifications.

Performance requirements:

– Rise time (t_r < 0.15s)

– Overshoot (M_p < 5%)

– Settling time (T_s < 0.25s)

– Steady-state error = 0

Tasks:

– Calculate controller gains:

– (K_p)

– (K_i)

– (K_d)

– Use appropriate methods such as:

– Pole placement

– Standard second-order system relations

– Clearly justify your design choices.

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### 4. Simulation (MATLAB & Simulink)

– Implement the full system in Simulink.

– Include:

– Plant (DC motor transfer function)

– PID controller

– Feedback loop

– Verify that the system meets all performance requirements.

– Provide:

– Step response graph

– Measured values (rise time, overshoot, settling time)

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### 5. Ziegler-Nichols Tuning

– Research the Ziegler-Nichols tuning method.

– Convert the system to a standard PID structure (if required).

– Apply the tuning method.

– Compare results with your designed controller.

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### 6. Discussion

Provide a detailed discussion including:

– Effect of increasing/decreasing:

– Overshoot

– Rise time

– Settling time

– Trade-offs between performance parameters

– Comparison between manual design and Ziegler-Nichols results

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### 7. Report Writing

Prepare a professional report including:

1. Introduction

2. System Modelling

3. Controller Design

4. Simulation Results

5. Ziegler-Nichols Method

6. Discussion

7. Conclusion

8. References

Important notes:

– Maximum 10 pages (A4)

– No appendices allowed

– All calculations must be included

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### 8. Submission Requirements

Submit the following:

– Word and PDF report

– MATLAB file (.m)

– Simulink file (.slx)

Compress all files into a single ZIP folder named as:

[Your Name]_[Your UWE ID].zip

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Ensure the work is original, well-structured, and clearly explained. Any missing steps, unclear calculations, or failure to meet performance criteria will result in mark deductions.

Complete the task with full accuracy and engineering-level quality.