4CCE1CM2
Part 2 Coursework
Coursework II
The coursework is released on 28th February 2024 and is due at 4pm on 19th March.
Extensions can only be approved by applying via student records. Only students with an approved MCF should use the late submission portal. Work submitted up to 24 hours late without an approved MCF will be subject to a 10-mark deduction.
The coursework is designed to help you demonstrate that you can:
- Derive and manipulate the Laplace transforms of function, equations and systems
- Generate the step, impulse and frequency response of 1st and 2nd order systems
You should generate a PDF report containing your worked solutions, extracts of code and images of any plots you generate. The PDF should be maximum 10 pages including figures.
All plots should have a title, labelled axis and units. All plots and results must be produced using Matlab (include your code). To achieve the highest marks you should plot in such a way that each answer (analytical, lsim, Simulink) can be directly compared (i.e overlaid).
You may choose to use matlab livescript. to produce your work and to save this as a PDF. You can input screenshots from your Simulink model into this and can generate equations. For more information about live-scripts see the guidance here.
This coursework is worth 15% of your total mark and should take around 9 hours to complete. To pass the module you need to achieve a mark of at least 40% overall and a mark of at least 30% on the examination, and a mark of at least 30% average across the first and second coursework.
The values of m, F, k and c are given by F = 50, m = 10, c = 2 and k = 5.
Figure 1 mass-spring-damper system with mass m, spring-stiffness k and damping coefficient C. x(t) represents the displacement of the mass due to the input f(t).
The mathematical model of this system is given by :
mx，，(t) = F(t) − kx(t) − cx′ (t)
This coursework utilises the lsim command in Matlab which you can find by looking through lecture livescripts.
1. Derive the transfer function between the input force F(t) and the position of the mass
x(t) assuming zero initial conditions [10 marks]
2. Use the Laplace Method to solve this equation analytically for a constant input force
F(t) assuming zero initial conditions. Plot x(t) over time and compare with the results
found using the lsim command in Matlab. [20 marks]
3. Derive and plot the response of the system to an impulse input using analytical
methods and use the ‘impulse’ function in Matlab to verify your answer. [10 marks]
4. Use the initial and final value theorems to predict the steady state unit step response
and use the ‘step’ function in Matlab to verify your answer [10 marks]
5. Find and plot the response of the system to a sinusoidal input F(t) = 50sin3t using the
Matlab command lsim and compare this with the steady state frequency response found by calculating the gain and phase. [25 marks]
6. Generate a Simulink model to represent this system in time (i.e. NOT using a transfer
function block) and simulate with a unit step input, a constant input of F(t) = 50 and a sinusoidal input of F(t) = 50 sin3t. Include a description of how you generated each input and any block parameters used. Insert the scopes generated. You can use screenshots to insert these into a livescript. . [25 marks]