Derive theoretical models for the study of engineering control systems
Digital, Technology, Innovation and Business
MECH50497 Second Order Response and Velocity Feedback of a DC Motor Module
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Module Name: |
Applications of Control (Distance Learning) |
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Module Number: |
MECH50497 |
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Title of Assignment: |
Second Order Response and Velocity Feedback of a DC Motor Module |
The assignment is a written laboratory report of guide length 2500 words handed in via Turnitin on the Module MECH50497 on Blackboard VLE.
The report to be laid out with Title, Contents, Introduction, Description of work, Collation of Results, Analysis of Results to answer the questions set out below, any additional results and deductions, Summary and Conclusion.
The marks will be weighted 20% for structure and layout (incorporating Title, Contents and Conclusion) and 80% for the analysis and answers to the questions posed (incorporating Description of Work, Collation of Results, Analysis of Results to answer the questions set out in the assignment, any additional results and deductions, and Summary), broken down into sections as follows:
Positional Step Response – 22% (11% description, collation and summary, 11% analysis and discussion based on answers to questions) Closed Loop Magnitude Response – 26% (13% description, collation and summary, 13% analysis and discussion based on answers to questions)
Velocity Feedback – 20% (10% description, collation and summary, 10% analysis and discussion based on answers to questions)
Potentiometer and Simple Servo Circuit – 12% (6% description, collation and summary, 6% analysis and discussion based on answers to questions)
The results obtained from the laboratory in this assignment are enclosed in an accompanying document; you will need to make use of these results to answer the questions provided within the assignment and interpret the results in relation to control theory. However, the assignment should be written up as a report, hence use the questions as a guide to what needs to be included in the report, rather than answering them explicitly.
The deadline for the assignment is 23:59 on Friday 19th December 2025.
Hand in is via Turnitin on Blackboard only on, or before, the deadline shown.
Marking criteria:
Written reports produced using IT skills.
In order to achieve a minimum pass grade (40%) students are expected to produce reports that show a basic understanding of the subject area using standard available material. The reports are to be produced electronically using relevant illustrations, where applicable.
In order to achieve a First for the assignment (70% and above) students must produce reports that demonstrates extensive, well researched knowledge of the subject area, expressing competent personal opinions and arguments. The reports must be electronically produced, well-illustrated and adequately referenced.
Learning Outcomes assessed by the assignment:
- Derive theoretical models for the study of engineering control systems: Knowledge & Understanding.
- Improve on an undamped control system in order for it to exhibit a stable response: Enquiry; Problem Solving.
- Investigate and report upon the use of control in improving a system’s response: Communication.
Assessment marking criteria
Second Order Response and Velocity Feedback of a DC Motor Module
Positional Step Response
The responses proposed are SMALL SIGNAL RESPONSES. They assume no saturation. To ensure this is the case in our experiments the value
Command voltage x Proportional Gain
must be less than approximately ±4.5V or the drive amplifier will saturate. Also ensure that the brake should be OFF (in position 0).
Construct the system in Fig 52 below
Set the following:
Proportional IN, kp = 0.3 Integral OUT
Derivative OUT Filter OUT
Adjust the oscilloscope so that both traces overlap when held at ground and use settings of 1V/cm and 0.5s/cm.
Use the signal generator to apply a square wave input of ±2V at 0.2Hz
Observe that the output response is very overdamped and does not rotate to the commanded position due to the combination of low gain and significant friction. This is demonstrated in Fig 53 below.
Increase kp in stages and study the response.
- What is happening to the rise time and the steady state response as kp increases?
- What happens to the system at kp = 0.5?
At this point it may be advisable to switch the time base of the oscilloscope to 0.25s/cm.
3. Record the time taken for the output to reach its final steady value when critically damped.
Continue to increase kp to the point where, although there is overshoot, the response stops just short of oscillating, as shown in Fig 54.
4. At what value of kp does this typically occur?
5. Record the time to peak, T, and the peak overshoot (%) using (A/B)x100. (Note that A and B can be cm, volts, degrees or whatever because it is a ratio, though it would be advisable to use cm.)
6. Determine the damping ratio, ξ, by referring to Fig 51 below.
7. Calculate the natural frequency, wn, from
Closed Loop Magnitude Response
Retaining the circuit as set up in Fig 52, use the signal generator to apply a sinusoidal input of ±0.5V at 0.4Hz.
Set kp to 4.
Ensure the command trace and output potentiometer trace overlay each other with the oscilloscope inputs at ground.
8. What is observed about the output sinusoid in relation to the input sinusoid?
Slowly increase the input frequency. The output amplitude should begin to increase.
9. For each frequency, note the ratio of the output amplitude to the input amplitude (the Magnitude Ratio) and the phase difference between the input and output sinusoids.
To calculate the phase difference, use the following expression: Phase (degrees) = 0.36 x Time difference (ms) x Frequency (Hz)
10. Plot a graph of Magnitude Ratio against input frequency.
11. At what frequency is the output amplitude at a maximum?
12. At the frequency of maximum output amplitude, what is the phase shift between the input and the output sinusoids?
13. As the frequency increases further, what happens to the output amplitude and the phase difference between the input and output sinusoids?
For kp = 4, the system is very underdamped (ξ approximately = 0.2).
If the expression for maximum magnitude ratio, M, is:
And the frequency at which the maximum magnitude ratio occurs is:
14. Calculate M and w using ξ = 0.2 and wn = 2p x 0.4Hz.
15. How do these calculated values compare with the values measured from the plotted graph?
The phenomena of amplitude magnification is termed RESONANCE. The system is easily excited by certain frequencies because it is underdamped. Fig 58 shows the general trend for varying damping ratio.
The critical case is ξ = 0.707. Below this M is > 1 at some frequency. The frequency gets nearer to wn as ξ tends towards 0.
Velocity feedback
Construct the system in Fig 60. The amplifier in the inner feedback loop allows the amount of velocity feedback to be adjusted.
Set the following:
Proportional IN, kp = 1 Integral OUT Derivative OUT
Filter OUT
Auxiliary Amplifier Gain = 0.1
Use the signal generator to apply a square wave input of ±0.5V at 0.4Hz.
The output response is close to critical damping as before since the velocity feedback has little effect at the moment.
Increase the proportional gain kp to 4.
16. What happens to the system response in terms of overshoot?
Gradually increase the auxiliary amplifier gain from 0.1 up to 3, taking note of the overshoot and settling time in the process.
17. What happens in respect of overshoot and settling time
Set kp = 4 and auxiliary amplifier gain = 0.1. Switch to a triangle input of ±2.5V at 0.4Hz.
Ensure that the input and output traces line up when grounded.
18. What can be observed on the oscilloscope? Is there any time delay between the input signal and the output signal?
Gradually increase the proportional gain.
19. What happens to the response on the oscilloscope?
Set kp to 10, the input to 0.4Hz and obtain a good trace.
Increase the velocity feedback by increasing the auxiliary amplifier gain from 0.1 up to 8.
20. What happens to the response on the oscilloscope?
21. What can be deduced about the effect of velocity feedback.
The potentiometer as a feedback device
Connect the power supply to the +12V, 0V and -12V terminals as shown in figure
1. The output (VO) should vary between ±12V as the potentiometer rotates. This can be measured using a voltmeter connected between the VO terminals and the 0V terminals.
Completeatableofpotentiometeranglesandoutputvoltagesforanglesfrom 90˚ to270˚in stepsof10˚(positive rotation isclockwise).
Asimpleservocircuit
Set up the system up as shown in the following diagram, ensuring that the signal generator is replaced by the command potentiometer.
Setthecommandto180˚andtheproportionalgainto1.2.
Theoutputdiscshouldalsobeat180˚-ifnotcheckthecalibrationofthe command unit. Measurethecommandpotentiometeroutputwhichshouldbezerovolts. Now rotate it until there is a 1 volt change.
22. Notehowthevoltageoftheinputpotentiometervarieswhenyou move it.
23. Whatistheservomotordoingtotheoutput potentiometer?
Reducethegainto1andrepeat.
Repeat at kp= 0.5.
24. Whatcanyouobserveabouttheoutputmovement?
