Introduction

This coursework is to be carried out individually. It includes some questions and is designed to meet the Learning Outcomes of this module, as presented in the module proforma, i.e.

Learning Outcomes:

1. Code programs using MATLAB

2. Apply MATLAB and Simulink to aid the analysis of engineering problems

An LRC circuit is shown in Fig.1.

Fig.1 the LRC circuit

The variables and physical parameters are given as follows:

The variables and physical parameters are given as follows:

u(t)        ---           input voltage signal (V)

y(t)        ---           output voltage signal (V)

i(t)         ---           current signal (A)

R₁          ---           resistor 1,            R₁  = 10 + N/100 (W)

R₂          ---           resistor 2,            R₂  = 100 - N/100 (W)

L            ---           inductor,              L = 0.2 (H)

C            ---           capacitor,            C = 0.001 (F)

where N is the last two digits of your student number. For example, if your student number is 234567, then N = 67.

1. With u(t) as the input, i(t) and y(t) as outputs, derive a system mathematical model with two first-order differential equations.

2. Simulate the circuit in Fig.1 using the following input,

with the zero initial values of the current going through the inductor and the voltage on the capacitor. Simulate the system using the fourth order Runge-Kutta method for 0.6 seconds and obtain the outputs, choosing the time step h = 0.001 sec. The task includes

(a). Code an M-file to simulate the system. The physical parameters should be included in the M-file and are given the numerical values at the beginning.

(i) Incorrectness in using the Runge-Kutta method,

(ii) Incorrectness in using input u(t),

(iii) Other mistakes,

(b). Draw three figures in one screen with u(t) at the top, i(t) in the middle and y(t) at the bottom, to show the correct simulation results.

3. Report Presentation

• Necessary explanations should be given in the M-file.
• All text should be typed and Microsoft Equation should be used for math expressions.
• All figures should include title, labels and legends as appropriate.
• All M-files and any functions that coded by you should be displayed.
• An introduction, discussions and conclusions should be included in the assignment.
• The assignment should be written logically, clearly and completely.