EEE116代做、MATLAB语言代写、MATLAB编程设计调试、代写Computer Skills

日期：2019-04-29 09:27

EEE116 Experimental, Computer Skills and

Sustainability: MATLAB Group Assignment

Due on Monday, 13th May, 2019, 18:00

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Assignment Regulations

This is a group assignment. Each group MUST submit one soft copy of the group

report via the ICE before the due date.

A coversheet can be created in your own way, but the following information MUST

be included: your group number, student ID number, full name and email address

of each group member.

All the formula, derivations, completed MATLAB scripts and functions with

original highlighted text format in MATLAB editor, computational results in the

command window, and plotted figures, should be part of the answers.

There is no hard requirement on how the report must be organized. You can

organize your report question by question (i.e. give one section for each question).

Then, for each section, you can organize it in your own way. However, the contents

and information required by each individual question MUST be provided.

You may refer to textbooks and lecture notes to discover approaches to problems,

however, the assignment should be your own group work.

Where you do make use of other reference, please cite them in your work. Students

are reminded to refer and adhere to plagiarism policy and regulations set by XJTLU.

References, in IEEE style can be attached as an appendix.

A contribution form MUST be provided which can be given as the final page of

your report. You can follow the example contribution form provided in the final

page of this document.

Assignments may be accepted up to 5 working days after the deadline has passed;

a late penalty of 5% will be applied for each working day late without an extension

being granted. Submissions over 5 working days late will not be marked. Emailed

submissions will NOT be accepted without exceptional circumstances.

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MATLAB Group Assignment for EEE116

Part I: developing basic programming skills by solving

simple engineering problems

Question I-A, Numerical method for solution of ordinary differential equations.

(25 Marks)

The classical method of solving ordinary differential equations (ODE) is the 4th order

Rugge-Kutta method. The algorithm is given below:

Assume we have a 1st order ODE:

(I-A.1)

For the given time period, we need to find out the time variation of y, given

the initial condition. This kind of problem is referred to as initial value

problems.

For solution, let us have divide the time period into N intervals (i.e. N+1 time instants),

then the value of y at (n+1)th time instant is given by the following relations with n

from 0 to N with h as the time interval size:

(I-A.3)

Question (a) (15 Marks): Now, solve an RC circuit problem: the equation for the

voltage y across the capacitor is

(I-A.4)

where is the applied voltage to the circuit. Suppose that RC = 0.2 s and that the

capacitor voltage, y, is initially 2 V (i.e.). Suppose also that the applied

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voltage is 

sin V. Plot the voltage y(t) for 0 ≤ 5 s.

Requirements:

(1) (7 Marks) Write a function file to give a general ODE solver using Runge-Kutta

method, e.g.

function [ t,y ] = marunge4s( dyfun,tspan,y0,h )

where “marunge4s” is the function name; “dyfun” is the name of the ODE to be solved

which is defined by using a function; “tspan” is the time period to be simulated; y0 is

the initial condition of the solved-for variable, “h” is the time interval size.

(2) (5 Marks) Do the above question. i.e. solve Equation I-A.1, by calling the function

created. Then, plot the voltage y(t) for 0 ≤ 5 s.

Hints: For this question, you need to create your own function file using Runge-Kutta

method (This is done for Question (1)), which is similar to ode45 (a MATLAB standard

function of solving ODEs), to solve the ODE defined by another function (refer to hints

of Question (3) for how to do this). Then, the calling pattern of your function (to solve

ODEs) should be, e.g.

[t,y1]=marunge4s('RC_circuit',[0 0.5],2,0.001);

where “RC_circuit” is the name of the ODE you have defined using a function

file; 0.001 is h, the time interval size. You need to use the function ‘feval’ in your

function “marunge4s” if the pattern is shown above. If you do not wish to use ‘feval’,

then the calling pattern should be:

[t,y1]=marunge4s(@RC_circuit,[0 0.5],2,0.001);

(3) (3 Marks) Check your solution by using a MATLAB standard function for solving

ODEs, i.e. ode45: you need to plot results of voltage y(t) for 0 ≤ ?? ≤ 5 s, obtained by

using both your user defined function and ode 45, then, compare the results and

comment on the features (e.g. whether they are the same or not?)

Hints: An example of using ode45: we need to first define the ODE to be solved which

can be done by using a function, e.g.

The function file defining the ODE to be solved:

function [ ydot ] = RC_circuit( t,y )

%define the ODE by using a function to be called by

%MATLAB function ode45 or

%your own function solver using Runge-Kutta method

Vsource=100*sin(2*pi*50*t);

ydot=-5*y+5*Vsource;

end

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Then, use ode45 function to solve the equation you just defined using a function, as

shown below:

The main programme written in a script file:

clear all

close all

clc

%

%'RC_circuit' is the ODE name defined by a function

%[0 0.5] is the time period for the simulation

%2 is the initial conditions, v_c(t=0)=2 V

[t,y]=ode45('RC_circuit',[0 0.5],2);

plot(t,y(:,1))

xlabel('time (s)')

ylabel('capacitor voltage (V)')

Question (b) (10 Marks): Now, we consider the RLC circuit with R, L and C connected

in series, in which the capacitor voltage vc is governed by a 2nd order ODE:

(I-A.5)

where v(t) is the applied power supply voltage. Suppose we have R = 100 ohms, L =

0.5 Henries and C = 2e-6 Farads. Solve the equations with the following conditions:

(1) (5 Marks) Model input: Initial conditions:

0, then plot the results, i.e. the voltage

(2) (5 Marks) Model input:, with f = 50 Hz; Initial

(0) = 0 , then plot the results for both two

initial conditions, i.e. the voltage 

Hints: The 2nd order ODE can be written into a set of 2 1st oder ODEs (see below), and

then the question becomes to solve 2 1st order ODEs using Kugge-Kutta method.

Assume two vector spaces, X and Y, with the size of 2 × 1 each, then we let:

] . For using MATLAB supplied function,

ode45, an example is given below:

The function file defining the ODE to be solved:

function [ xdot ] = CircuitRLC( t,x )

%define the ODE by using a function to be called by

%MATLAB function ode45 or

%your own function solver using Runge-Kutta method

Vsource=100*sin(2*pi*50*t);

C=2e-6;

R=100;

L=0.5;

xdot=zeros(2,1);

xdot(1)=x(2);

xdot(2)=Vsource/(L*C)-(R/L)*x(2)-(1/(L*C))*x(1);

end

The main programme written in a script file:

clear all

close all

clc

%

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%[0 0.5] is the time period for the simulation

%[100 0] is the initial conditions, v_c(t=0)=100 V,

dv_c/dt(t=0)=0

[t,x]=ode45('CircuitRLC',[0 0.3],[100 0]);

plot(t,x(:,1))

xlabel('time (s)')

ylabel('capacitor voltage (V)')

The user defined function file required in Question (a), “marunge4”, should also be able

to solve this kind of 2nd order ODEs, not just one 1st order ODE. Think about how to do

this.

Requirements: for Question I-A, in your report, the following information needs to

be included:

a) Circuit diagram, the relevant equation derivations and all the known conditions

stated in the question;

b) Flow chart of the programme design;

c) Coding with detailed notes on the key steps;

d) Results.

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Question I-B, Kinematics analysis for a slider-crank linkage.

(25 Marks)

Consider a slider-crank linkage which is the fundamental mechanism used in car

engines, a schematic diagram is shown in Figure I-B.1. Knowing the geometrical

parameters of the mechanism and the rotational speed of the driver linkage, try to do

the kinematics analysis for the mechanism to calculate the displacements, velocity and

acceleration.

Figure I-B.1. Schematic of a slider-crank linkage mechanism.

The general procedure of kinematic analysis is given below:

(a) Displacement analysis

The position vector equation is

(I-B.1)

Write it in the form of complex numbers, it becomes

Separate the real and imaginary parts, we have

(I-B.3)

Then we have

(I-B.4)

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(b) Velocity analysis

Find the first derivative of equation (B.2), we have

(I-B.5)

Separate the real and imaginary parts, we have

(I-B.6)

Write the above equation in the matrix form

[

(I-B.7)

(c) Acceleration analysis

Get the second derivative for equation (B.2) then separate real and imaginary parts

(equivalent to directly differentiate equation (B.6)), we have

(I-B.9)

For the mechanism of Figure I-B.1, suppose L1 = 100 mm, L2 = 300 mm,

10, the dimensions of the slider block is [x,y]=[80 mm,20 mm], try to do the

following:

(1) (10 Marks) Calculate the displacement, velocity and acceleration for Slider C (sc,

vc, ac) and the angular counterparts for Linkage 2 (??2, ??2, ??2). You can create a function

file (e.g. [outputs] = slider_crank(inputs)) for this by using Equations (I-B.4), (I-B,7)

and (I-B.9).

(2) (5 Marks) Plot the results as a function of the driver rotational angle (??1) which

ranges from 0 to 720 deg. Call the function created in Question (1) to get the results

then plot them out.

(3) (10 Marks) Create the movie showing the movement of this mechanism, when the

driver rotational angle (??1) varies from 1 to 360 deg. You may need to use the MATLAB

functions “getframe” and “movie()”.

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Requirements: for Question I-B, in your report, the following information needs to

be included:

a) The schematic diagram of the mechanism, the relevant equation derivations and all

the known conditions stated in the question;

b) Flow chart of the programme design;

c) Coding with detailed notes on the key steps;

d) Results.

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Problem I-C, Solve nonlinear equations using Newton-Raphson method.

(10 Marks)

Write a programme to solve the circuit with a diode as shown in Figure I-C.1.

Figure I-C.1. A simple diode circuit, where VPS = 5 V and R = 2 kohms.

The current-voltage characteristic of the diode is

(I-C.2)

Equation (I-C.2) is nonlinear which is difficult to be solved analytically. Therefore, try

to write a program using Newton-Raphson algorithm to solve it, then print the result of

the solved value VD in the command window. Details of the Newton-Raphson method

and the example has ben given in MATLAB lecture notes “Matlab Tutorial 2-2018-19”,

Slides 50-55.

Requirements: for Question I-C, in your report, the following information needs to

be included:

a) Circuit diagram, the relevant equation derivations and all the known conditions

stated in the question;

b) Flow chart of the programme design;

c) Coding with detailed notes on the key steps;

d) Results.

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Part II: Use Simulink to solve simple engineering problems

Question II-A, The motion of a two-mass suspension model.

(20 Marks)

Consider the two-mass suspension model shown in Figure II-A.1. The equations of

motion are:

(II-A.1)

(1) (15 Marks) Develop a Simulink model of this system. In your report, you need to

give information on:

a) Answer a question: whether to use a state-variable representation or a transferfunction

representation of the model, and why?

(3 Marks)

b) How is the Simulink model derived? In your report, you need to present (i) all

the relevant equation derivations based on which you get the Simulink model,

and (ii) the complete Simulink model.

(6 Marks)

c) For each block you have in your Simulink model, give details on all the settings,

and the reasons for your settings.

(6 Marks)

(2) (5 Marks) Use the Simulink model to plot the response for the following input, f(t).

The initial conditions are zero,

(II-A.2)

Figure II-A.1. Two-mass suspension model.

Hints:

a) The input to your model, can be implemented by using “Signal Builder” block.

b) To complete this question, you can also read and understand contents in my lecture

notes: Matlab Tutorial 3-2018-19, specially from pp. 21.

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Question II-B, The motion of a single-mass suspension model of the vehicle

suspension system.

(20 Marks)

Consider the single-mass suspension model shown in Figure II-B.1, which is typical

representation of the vehicle suspension system. The spring and damper forces ???? and have the nonlinear models. When the vehicle strikes a bump, the road surface profile

can be represented by the trapezoidal function y(t) shown in Figure II-B.2. Now, the

system model (derived from Newton’s law) becomes:

is the is the nonlinear spring function shown in Figure

II-B.3, and is the nonlinear damper function given by:

(1) (15 Marks) Develop a Simulink model of this system. In you report, you need to

state clearly:

a) Answer a question: whether to use a state-variable representation, or a transferfunction

representation, or nonlinear treatment, to create the corresponding

model in Simulink, and why?

(3 Marks)

b) How is the Simulink model derived? In your report, you need to present (i) all

the relevant equation derivations based on which you get the Simulink model,

and (ii) the complete Simulink model.

(6 Marks)

c) For each block you have in your Simulink model, give details on all the settings,

and the reasons for your settings.

(6 Marks)

(2) (5 Marks) Use the Simulink model to plot the response of this system, i.e. x and

(y-x) versus t. The initial conditions are zero, i.e. ?? = 0 and ??? = 0.

a) Plot the responses in Simulink using Scope. In your report, present the screen

shots.

(2 Marks)

b) Export the data into MATLAB workspace which enable you to use “plot”

command to plot the responses. In your report, state (i) how do you export

Simulink results to workspace, and, (ii) present the plots you have done using

“plot” command, and show clearly the axis labels (i.e. for x and y axis, what

quantities do you plot and units) and legends if applicable.

(3 Marks)

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Hints:

a) The road surface profile, y(t) as shown in Figure II-B.2, which is the input to your

model, can be implemented by using “Signal Builder” block.

b) The spring function, as shown in Figure II-B.3, can be implemented by using

“Look-Up Table” block.

c) The damper function, given by Equation (II-B.2), can be implemented by using

“MATLAB function” block.

d) To complete this question, you can also read and understand contents in:

My lecture notes: Matlab Tutorial 3-2018-19, specially from pp. 47.

Textbook: Palm William, Introduction to MATLAB for Engineers (3

rd Edn.),

McGraw Hill Professional, Section 10.9, Chapter 10.

Figure II-B.1. Single-mass model of a vehicle suspension.

Figure II-B.2. Road surface profile.

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Figure II-B.3. Nonlinear spring function.

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Contribution Form – MATLAB Group Assignment

Group____:

Name and

Student ID

number

Overall

contribution

(%)

Problem analysis

and equation

derivations, etc.

(%)

MATLAB

programming

(%)

Report writing

(%)

Comments

A

12345678

37 40 60 10 For example: Lead in the

completion of the

assignment and contribute

the most in MATLAB

programming

B

12345678

30 20 15 55 For example: Work closely

with other group members,

contributes particularly in

Component 3.

C

12345678

28 35 20 30 For example: Work closely

with other group members,

contributes almost evenly

in Component 1 and 3.

D

12345678

5 5 5 5 For example: He/she

contributes very little.

Total 100% 100% 100% 100%

The parts highlighted in red are which you need to fill in.

The contribution form will be used to monitor the workload distribution within the

group, and will also provide a basis for differentiate your marks (if there are

substantial workload differences between team members).