Electrical Engineering Question

Assignment Execution Instructions Control Coursework (DC Motor & PID Controller Design)

You are required to complete a full control system design and analysis for a DC motor using both theoretical derivations and simulation tools. The work must be carried out accurately, professionally, and in accordance with the provided specifications.

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### 1. System Modelling

Begin by deriving the mathematical model of the DC motor system.

– Use the given physical parameters:

– Moment of inertia (J = 0.01 kgm)

– Viscous friction (b = 0.1 Nms)

– Back EMF constant (Ke = 0.01 V/rad/s)

– Torque constant (Kt = 0.01 Nm/A)

– Resistance (R = 1 )

– Assume inductance L 0

– Derive the transfer function:

1. Between angular velocity and input voltage:

[

frac{omega(s)}{V(s)}

]

2. Then derive the transfer function for angular position:

[

frac{theta(s)}{V(s)} = frac{omega(s)}{V(s)} cdot frac{1}{s}

]

– Clearly show all steps, assumptions, and simplifications.

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### 2. Closed-Loop System Representation

– Based on the provided block diagram, determine the overall closed-loop transfer function.

– Simplify the block diagram step-by-step and present the final equivalent form.

– Clearly explain each step in the simplification process.

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### 3. Controller Design (I-PD / PID)

Design a controller that satisfies the following performance requirements:

– Rise time ( t_r < 0.15 ) seconds

– Overshoot ( M_p < 5% )

– Settling time ( T_s < 0.25 ) seconds (1% criterion)

– Steady-state error = 0 (for step input)

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### 4. Gain Calculation

– Calculate controller gains:

– Proportional gain ( K_p )

– Integral gain ( K_i )

– Derivative gain ( K_d )

– Use appropriate methods such as:

– Pole placement

– Standard second-order system approximations

– Show all calculations clearly.

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### 5. Simulation (MATLAB & Simulink)

– Implement the system in Simulink, including:

– The plant (DC motor model)

– The designed controller (PID or I-PD)

– Verify that the system meets all required performance criteria.

– Extract and present response graphs (step response).

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### 6. Performance Analysis

– Analyze system behavior and discuss trade-offs:

– Effect of increasing/decreasing overshoot

– Effect on rise time and settling time

– Stability considerations

– Provide clear engineering justification.

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### 7. PID Tuning (Ziegler-Nichols Method)

– Research and explain the Ziegler-Nichols tuning method.

– Convert the controller to a standard PID structure if needed.

– Apply the tuning method and obtain new gain values.

– Compare results with the previous design.

– Validate performance using Simulink.

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### 8. Report Writing

Prepare a professional report (maximum 10 A4 pages) including:

– Introduction

– System modelling

– Controller design

– Simulation results

– Discussion

– Conclusion

– References

Requirements:

– Include all calculations

– No appendices allowed

– Use proper academic formatting and referencing

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### 9. Submission Requirements

Submit the following files:

1. PDF report

2. MATLAB script file (.m)

3. Simulink file (.slx)

– Compress all files into a single ZIP folder

– Name format: [Your Name]_[UWE ID].zip

– Submit via Moodle

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### Important Notes

– All work must be original

– Any plagiarism will result in a zero grade

– Ensure all requirements are strictly followed

– Do not leave submission until the last minute