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.