For the entire report:
1. Present results and diagrams clearly with explanations for complicated features. Include the legend, title, x-axis and y-axis labels
2. Have all of the simulations and experiments been completed correctly?
3. Do your answers have enough context/background information included? Overall production quality of the report?
4. Please answer the questions in the order suggested below.
Task 1A
1. Include your Simulink diagrams, MATLAB scripts and plots
2. Why is the saturation block for the control signal unnecessary now?
3. For this task, the suggested solution does not have the +/- block to subtract the output from the reference signal as shown below in the red square. Why is this not required for the discrete PI controller? Show evidence.
Task 1B
1. Include your Simulink diagrams, MATLAB scripts and plots
2. Compare the simulation with the experimental results. Identify key similarities. If there were significant differences with the simulation, identify and explain possible sources for the differences.
3. Discuss possible reasons for why the closed-loop performance for Lab 4, Task 2A/2B is different to Lab 5, Task 1A/1B despite using the same controller parameters. Hint: There is a subtle difference between using the saturation block vs. the proper anti-windup implementation.
Task 2B
1. Include your Simulink diagrams, MATLAB scripts and plots
2. Show the derivation for how your controller parameters c2, c1 and c0 were designed.
3. Discuss the effects of changing λ on the reference-tracking ability of the system and also, the control signal.
4. What was your choice for λ? What were the calculated controller parameters?
5. Show evidence that the design criteria have been achieved in simulation.
6. What are some factors that could limit the maximum gradient of the ramp that the closed- loop system could track?
7. How is the suggested controller (C(s) = (c2s2 + c1s + c0)/s2) able to track both, a ramp as well as a constant value (essentially, a step signal)? Support your answer using the final value theorem on the:
a. Feedback error assuming a ramp reference R(s) = 1/s2, and also:
b. Feedback error assuming a step reference R(s) = 1/s
8. Would a standard PID controller (C(s) = c2s2 + c1s + c0) be able to track a ramp reference signal? Use the final value theorem to support your answer.
9. In simulation, verify that the suggested controller (C(s) = c2s2 + c1s + c0) is able to track a step reference signal. Use a reference signal of 50?, overshoot ≤ 20%, settling within 1000 seconds. You may need to adjust λ. Confirm that the controller is able to reject an OUTPUT disturbance of -5? and is robust under limited amounts of measurement noise (Sources: Random Number: Mean = 0, Variance = 0.2)
Task 2C
1. Include your Simulink diagrams, MATLAB scripts and plots
2. Identify if/when the control signal was limited by the saturation block in simulation and in the experiment.
3. Compare the simulation with the experimental results. Identify key similarities. If there were significant differences with the simulation, identify and explain possible sources for the differences.
4. Assume that somebody performed these operations: Run Simulink on the Arduino, the program is running on the Arduino for some time - say 10 seconds, then, the power switch is switched on. Normally, this would result in higher overshoot and oscillations which were not consistent with the simulations. Why might this happen?
5. What should have been observed, was that after a peak overshoot, the control input should suddenly drop to near-zero. Qualitatively, explain why this is the expected outcome referring to your understanding of the plant, environment, and control theory.
6. Assuming that the board temperature is hot (e.g. 70?), would it be possible to design a control system that tracks a negative ramp reference signal i.e. controlled cooling? What factors would limit the negative gradient of the reference signal that could be tracked?