ELEC0021 - Programming and Control Systems 2022
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ELEC0021 - Programming and Control Systems
2022
Answer ALL questions
Section A - Control
1. Consider the system described by the following block diagram in Figure 1.1.
Figure 1.1
(a) Write the transfer function between the input u1 and the output y as a function of P(s), Q(s), R(s).
[5 marks]
(b) Write the transfer function between the input u2 and the output y as a function of P(s), Q(s), R(s).
[5 marks]
Consider now a dynamical system described by the transfer function
T(s) = 
(c) Compute, if possible (please justify this), the steady-state value of the output y(t) when the system described by T(s) is driven by a unitary step input (u(t) = 1(t)) starting from null initial conditions.
[5 marks]
(d) Compute the analytic expression of the system response y(t) in time domain, starting from
null initial conditions, when the system described by T(s) is driven by the input u(t) = −2 ∙ 1(t).
[5 marks] (e) Compute the analytic expression of the system response y(t) in time domain, starting from
null initial conditions, when the system described by T(s) is driven by the input u(t) = −26(t),
where 6(t − t0 ) is the unitary impulse function at timet0 . Hint: consider exploiting the formulation of the system response to the unitary step.
[5 marks]
2. Consider the system described by the following block diagram in Figure 2.1, where the transfer function is
(1 − S)(1 + 10S)
L(S) = u (1 + S)2 , u > 0.
Figure 2.1
(a) Sketch the asymptotic Bode diagrams for the system with u = 0.5 (using the provided logarithmic charts).
[5 marks] (b)
(i) Sketch the Nyquist plot for the frequency response of the system with u = 0.5.
[3 marks] (ii) Consider the Nyquist plots for values of u > 0. By using the Nyquist criterion, determine
the values of u for which the system is asymptotically stable, marginally stable and unstable, respectively. Mathematically justify your answer.
[5 marks]
(c) Using a different approach than the one used in Point (b), determine the values of u for which the system is asymptotically stable, marginally stable and unstable, respectively.
[5 marks]
(d) Consider the system described by the block diagram in Figure 2.1, where the transfer function now is
L(S) = u
|
|
|
(1 + S)2 |
Compute the phase margin for the system when u = 10 and T = 0.5. Discuss the system’s stability.
[7 marks]
Section B - Programming
3. The Python class Land shown below represents a piece of land modelled as a grid. Every element in the grid represents the height above the sea level (in meters) of the piece of land in that square. The method numberOfPeaks must return the number of peaks, where a peak is an element in the array representing the grid surrounded by 8 elements with lower values.
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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.
38. |
import numpy as np class Land: #initialisation of the grid size and content
def __init__(self, size): self.size=3 self.setSize(size) self.grid=np.random.random([self.size,self.size])*10 self.grid=self.grid.round(2) # “pretty” print def __str__(self): return "Grid of "+ str(self.size)+"x"+str(self.size)+"\n"+str(self.grid) #size of grid is setup def setSize(self,size): if(size>=3): self.size=size #returns True if element [i,j] is a peak, False otherwise def isPeak(self,i,j): for k in range(i-1,i+2): for m in range(j-1,j+2): if(self.grid[i,j]<self.grid[k,m]): return False return True
#returns number of peaks in the grid def numberOfPeaks(self): #code of method def main(): grid_size=int(input("Please, enter the size of the grid: ")) land1=Land(grid_size) print(land1) print("This land has", land1.numberOfPeaks(), "peaks") if __name__=="__main__": main() |
(a) Write the code of the method numberOfPeaks, that returns the number of peaks in the land. Document your code.
[5 marks]
(b) Write an example of the information printed on screen when the user enters number 2. Please, explain your answer referring to specific lines in the code to support your explanation.
[5 marks]
(c) Modify the function main to be robust against any abnormal input from the user.
[5 marks]
(d) The algorithm KNN is trained with the following data:
|
Volume |
Weight |
Price |
|
4 |
3 |
1000 |
|
4 |
4 |
1000 |
|
0 |
1 |
25 |
|
1 |
1 |
25 |
|
5 |
3 |
1000 |
|
1 |
2 |
25 |
What is the prediction for K=3 for an object with a volume of 2 and a weight of 2? Please explain.
[5 marks]
4.
(a) Write a Python function randomList(list) which takes as parameter a list and returns a randomly chosen element from that list. Document your code. Note: you should NOT use the random package Random choice(list) method which does exactly this.
[5 marks]
(b) Let’s assume there is no built-in operator ** or function pow in Python. Implement a
power(m,
n) function which calculates mn for a floating-point base m and an integer exponent n, where base and exponent can have any value, positive, zero or negative. If the exponent is a floating-point number with a non-zero decimal part, the function should print an error message and return 0. Document your code.
If we were to make power(m, n) a method of a class Math, present it as method of that class but without its implementation, simply add a comment in the method body.
[10 marks]
5.
(a) What is meant by public instance variables and why making instance variables public is not considered good practice in object-oriented programming? What is a better approach for class design? Comment on the approach used in Python for such design and compare it to that of other object-oriented programming languages.
Give an example of a class that demonstrates the benefits of a design with no public instance variables.
[6 marks]
(b) A Fibonacci series starts with 0 and 1 and every subsequent number is the sum of the previous two. As such, it lends itself naturally to a recursive implementation.
Implement a class that provides a method that allows its user to calculate the Fibonacci value of a number n recursively but also allows its user to find out how many times this method has been called; focus on good object-oriented design. Write also an excerpt of code that uses this class to calculate the Fibonacci value of integer n and print out the value and the times the relevant method was called. Document your code.
[9 marks]
2022-08-16